Neural Network Control-Based Adaptive Learning Design for Nonlinear Systems With Full-State Constraints

Trajectory tracking control for ships with fixed-time prescribed performance considering input saturation and dead zone

To enable underactuated ships to achieve trajectory tracking under unknown external disturbances, model uncertainties, and actuator saturation and dead zone, a fixed-time prescribed performance trajectory tracking control method is designed. Firstly, the position tracking errors are constrained by designing the barrier Lyapunov function, and the prescribed performance function is set as the constraint boundary to address the issue of fixed constraint boundaries in traditional methods. Secondly, RBF neural networks are employed to estimate the model uncertainties, and adaptive laws are used to estimate the upper bound of the composite disturbances. Finally, the controller is designed by incorporating fixed-time convergence theory and further using fixed-time sliding mode surface in order to overcome the shortcomings of traditional control algorithms in terms of slow response and the use of finite-time convergence with respect to the initial state. Through Lyapunov stability analysis, it is proven that all signals in the closed-loop system are bounded, and the velocity tracking errors can achieve global fixed-time convergence. Simulation results demonstrate that the proposed control scheme enables underactuated ship to achieve trajectory tracking even in the presence of input saturation and dead zone. Statistical results show that the performance indicators of the proposed controller are significantly smaller than those of the first group in the comparative experiments, with a shorter settling time. Moreover, compared to traditional saturation handling methods, the input curves of the proposed controller are smoother and more aligned with practical engineering requirements.

Prescribed time control of position and force tracking for dualarm robots with output error constraints

This paper studies the practical prescribed-time control problem for dual-arm robots handling an object with output constraints. Firstly, by utilizing the property that the sum of internal forces in the grasping space is zero, the system model is obtained and decomposed into the contact force model and free motion model, which are orthogonal to each other. Furthermore, by combining the performance function and constraint function, the original system tracking error is transformed to a new one, whose boundedness can ensure that the original system variable converges to the predetermined range within the specified time. Then, a comprehensive neuroadaptive controller including position control term and contact control force control term is designed. Finally, the simulation results of two planar three link robots working together on a common object verify the effectiveness and superiority.

Preassigned Time Adaptive Neural Tracking Control for Stochastic Nonlinear Multiagent Systems With Deferred Constraints

This article studies a preassigned time adaptive tracking control problem for stochastic multiagent systems (MASs) with deferred full state constraints and deferred prescribed performance. A modified nonlinear mapping is designed, which incorporates a class of shift functions, to eliminate the constraints on the initial value conditions. By virtue of this nonlinear mapping, the feasibility conditions of the full state constraints for stochastic MASs can also be circumvented. In addition, the Lyapunov function codesigned by the shift function and the fixed-time prescribed performance function is constructed. The unknown nonlinear terms of the converted systems are handled based on the approximation property of the neural networks. Furthermore, a preassigned time adaptive tracking controller is established, which can achieve deferred prescribed performance for stochastic MASs that provide only local information. Finally, a numerical example is given to demonstrate the effectiveness of the proposed scheme.

Adaptive Finite-Time-Based Neural Optimal Control of Time-Delayed Wheeled Mobile Robotics Systems

For nonlinear systems with uncertain state time delays, an adaptive neural optimal tracking control method based on finite time is designed. With the help of the appropriate LKFs, the time-delay problem is handled. A novel nonquadratic Hamilton-Jacobi-Bellman (HJB) function is defined, where finite time is selected as the upper limit of integration. This function contains information on the state time delay, while also maintaining the basic information. To meet specific requirements, the integral reinforcement learning method is employed to solve the ideal HJB function. Then, a tracking controller is designed to ensure finite-time convergence and optimization of the controlled system. This involves the evaluation and execution of gradient descent updates of neural network weights based on a reinforcement learning architecture. The semi-global practical finite-time stability of the controlled system and the finite-time convergence of the tracking error are guaranteed.

Fast Finite-Time Observer-Based Event-Triggered Consensus Control for Uncertain Nonlinear Multiagent Systems with Full-State Constraints

This article studies a class of uncertain nonlinear multiagent systems (MASs) with state restrictions. RBFNNs, or radial basis function neural networks, are utilized to estimate the uncertainty of the system. To approximate the unknown states and disturbances, the state observer and disturbance observer are proposed to resolve those issues. Moreover, a fast finite-time consensus control technique is suggested in order to accomplish fast finite-time stability without going against the full-state requirements. It is demonstrated that every signal could be stable and boundless, and an event-triggered controller is considered for the saving of resources. Ultimately, the simulated example demonstrates the validity of the developed approach.

Adaptive neural identification and non-singular control of pure-feedback nonlinear systems

This paper proposes a new constructive identification and adaptive control method for nonlinear pure-feedback systems, which remedies the 'explosion of complexity' and potential control singularity encountered in the traditional adaptive backstepping controllers. First, to avoid using the backstepping recursive design, alternative state variables and the corresponding coordinate transformation are introduced to reformulate the pure-feedback system into an equivalent canonical model. Then, a high-order sliding mode (HOSM) observer is used to reconstruct the unknown states for this canonical model. To remedy the potential singularity in the control, the unknown system dynamics are lumped to derive an alternative identification structure and one-step control synthesis, where two radial basis function neural networks (RBFNN) are adopted to online estimate these lumped dynamics. In this framework, the online estimation of control gain is not in the denominator of controller, and thus the division by zero in the controllers is avoided. Finally, a new online learning algorithm is constructed to obtain the RBFNNs' weights, ensuring the convergence to the neighborhood of true values and allowing accurate identification of unknown dynamics. Theoretical analysis elaborates that the convergence of both the tracking error and the estimation error is obtained simultaneously. Simulations and practical experiments on a hydraulic servo test-rig verify the effectiveness and utility of the suggested methods.

Finite-Time Adaptive Neural Control for a Class of Nonlinear Systems With Asymmetric Time-Varying Full-State Constraints

In this article, an adaptive finite-time tracking control scheme is developed for a category of uncertain nonlinear systems with asymmetric time-varying full-state constraints and actuator failures. First, in the control design process, the original constrained nonlinear system is transformed into an equivalent "unconstrained" one by using the uniform barrier function (UBF). Then, by introducing a new coordinate transformation and incorporating it into each recursive step of adaptive finite-time control design based on the backstepping technique, more general state constraints can be handled. In addition, since the nonlinear function in the system is unknown, neural network is employed to approximate it. Considering singularity, the virtual control signal is designed as a piecewise function to guarantee the performance of the system within a finite time. The developed finite-time control method ensures that all signals in the closed-loop system are bounded, and the output tracking error converges to a small neighborhood of the origin. At last, the simulation example illustrates the feasibility and superiority of the presented control method.

Adaptive Learning Control Algorithms for Infinite-Duration Tracking

Learning control is applicable to systems that operate periodically or over finite time intervals. Currently, there is a lack of research results about learning control approaches to infinite-duration tracking, without requiring periodicity or repeatability. This article addresses the problem of adaptive learning control (ALC) for systems performing infinite-duration tasks. Instead of using integral adaptation, incremental adaptive mechanisms are exploited, by which the numerical integration for implementation can be avoided. The comparison with the conventional integral adaptive mechanisms indicates that the suggested methodology can be an alternative to the adaptive system designs. Using an error-tracking approach, the approximation-based backstepping design is carried out for systems in the strict-feedback form, where a novel integral Lyapunov function is shown to be efficient in the treatment of state-dependent control gain. Theoretical results for the performance analysis are presented in detail. In particular, the robust convergence of the tracking error is established, while the boundedness of the variables of the closed-loop system is characterized, with the aid of a key technical lemma. It is shown that the proposed control method can provide satisfactory tracking performance and simplify the controller designs. Numerical results are presented to demonstrate effectiveness of the learning control schemes.

Performance Improvement of Active Suspension Constrained System via Neural Network Identification

A robust adaptive control method for a certain type of quarter active suspension system (ASS) is proposed in this work. The constraint issue of ASS is put into consideration primarily. Due to the limitation of the traditional barrier Lyapunov functions (BLFs), the integral barrier Lyapunov function (iBLF) is introduced to exert direct constraints on state variables in each stage under the backstepping frame, and neural networks (NNs) are applied to identify those unknown functions. Then, an adaptive law based on the projection operator is defined to eliminate the influence caused by the actuator failure. It is widely known that only the vertical displacement and velocity constraints are not violated, can the ASSs become stable and secure. It can be ultimately confirmed that all signals in the closed-loop system are bounded, and the control goals are satisfied. Last but not least, the feasibility of the approach is illustrated directly through a contrast simulation example.

Adaptive Learning Control of Switched Strict-Feedback Nonlinear Systems With Dead Zone Using NN and DOB

This article investigates the adaptive learning control for a class of switched strict-feedback nonlinear systems with external disturbances and input dead zone. To handle unknown nonlinearity and compound disturbances, a collaborative estimation learning strategy based on neural approximation and disturbance observation is proposed, and the adaptive neural switched control scheme is studied in a dynamic surface control framework. In the adaptive learning control design, to obtain the evaluation information of uncertain learning, the prediction error is constructed based on the composite learning scheme. Then, the prediction error and the compensated tracking error are applied to construct the adaptive laws of switched neural weights and switched disturbance observers. The system stability analysis is carried out through the Lyapunov approach, where the switching signal with average dwell time is considered. Through the simulation test, the effectiveness of the proposed adaptive learning controller is verified.

Adaptive composite dynamic surface neural control for nonlinear fractional-order systems subject to delayed input

In the article, the adaptive composite dynamic surface neural controller design problem for nonlinear fractional-order systems (NFOSs) subject to delayed input is discussed. A fractional-order auxiliary system is first designed to solve the input-delay problem. By using the developed novel estimation models, the defined prediction errors and the states of error system can decide the weights of radial basis function neural networks (RBFNNs). During the dynamic surface controller design process, the developed fractional-order filters are designed to handle the complexity explosion problem when the classical backstepping control technique is utilized. It is shown that the designed adaptive composite neural controller ensures that all the system state variables are bounded and the tracking error of the considered system finally tends to a small neighborhood of zero. Finally, the results of the simulation explain the feasibility of the developed controller. In addition, the developed controller can also be applied to single input and single output(SISO) nonlinear systems subject to a unitary input function.

Reinforcement learning based adaptive optimal control for constrained nonlinear system via a novel state-dependent transformation

Existing schemes for state-constrained systems either impose feasibility conditions or ignore the optimality. In this article, an adaptive optimal control scheme for the strict-feedback nonlinear system is proposed, which benefits from two design steps. Firstly, a novel nonlinear state-dependent function (NSDF) is formulated to equivalently transform the system into a non-constrained one to deal with state constraints without the requirements on feasibility conditions. Secondly, an adaptive optimal control scheme is designed for the non-constrained system, in which reinforcement learning (RL) is utilized to yield the optimal controller in each designing procedure. Updating rules of the actor and critic neural network are driven by the modified adaptive laws, used to approximate the optimal virtual and actual controllers. It is proved that all the signals in the closed-loop system are bounded and the output tracking error converges to an adjustable neighborhood of the origin not affected by the proposed NSDF. Two simulation examples are presented illustrating the effectiveness of the proposed scheme.

Neural-Network-Based Adaptive Tracking Control for Nonlinear Multiagent Systems: The Observer Case

This article focuses on the neural-network (NN)-based adaptive tracking control issue for a class of high-order nonlinear multiagent systems both subjected to the immeasurable state variables and unknown external disturbance. Combining with the radial basis function NNs (RBF NNs), the composite disturbance observer and state observer for each follower are established, respectively. The purpose of this work is to develop NN-based adaptive tracking control schemes such that the output of each follower ultimately tracks that of the leader and all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded by utilizing the backstepping technique. Furthermore, so as to cope with the sparsity of the control resources, the proposed method is extended to the event-triggered case and the adaptive event-triggered tracking control protocol is formulated for nonlinear multiagent systems. Finally, the numerical example is performed to verify the efficacy of the proposed approach.

Event-Triggered Approximate Optimal Path-Following Control for Unmanned Surface Vehicles With State Constraints

This article investigates the problem of path following for the underactuated unmanned surface vehicles (USVs) subject to state constraints. A useful control algorithm is proposed by combining the backstepping technique, adaptive dynamic programming (ADP), and the event-triggered mechanism. The presented approach consists of three modules: guidance law, dynamic controller, and event triggering. First, to deal with the "singularity" problem, the guidance-based path-following (GBPF) principle is introduced in the guidance law loop. In contrast to the traditional barrier Lyapunov function (BLF) method, this article converts the USV's constraint model to a class of nonlinear systems without state constraints by introducing a nonlinear mapping. The control signal generated by the dynamic controller module consists of a backstepping-based feedforward control signal and an ADP-based approximate optimal feedback control signal. Therefore, the presented scheme can guarantee the approximate optimal performance. To approximate the cost function and its partial derivative, a critic neural network (NN) is constructed. By considering the event-triggered condition, the dynamic controller is further improved. Compared with traditional time-triggered control methods, the proposed approach can greatly reduce communication and computational burdens. This article proves that the closed-loop system is stable, and the simulation results and experimental validation are given to illustrate the effectiveness of the proposed approach.

Practical Prescribed Time Control of Euler-Lagrange Systems With Partial/Full State Constraints: A Settling Time Regulator-Based Approach

Many important engineering applications involve control design for Euler-Lagrange (EL) systems. In this article, the practical prescribed time tracking control problem of EL systems is investigated under partial or full state constraints. A settling time regulator is introduced to construct a novel performance function, with which a new neural adaptive control scheme is developed to achieve pregiven tracking precision within the prescribed time. With the specific system transformation techniques, the problem of state constraints is transformed into the boundedness of new variables. The salient feature of the proposed control methods lies in the fact that not only the settling time and tracking precision are at the user's disposal but also both partial state and full state constraints can be accommodated concurrently without the need for changing the control structure. The effectiveness of this approach is further verified by the simulation results.

Prescribed Finite-Time Adaptive Neural Tracking Control for Nonlinear State-Constrained Systems: Barrier Function Approach

The purpose of this article is to present a novel backstepping-based adaptive neural tracking control design procedure for nonlinear systems with time-varying state constraints. The designed adaptive neural tracking controller is expected to have the following characters: under its action: 1) the designed virtual control signals meet the constraints on the corresponding virtual control states in order to realize the backstepping design ideal and 2) the output tracking error tends to a sufficiently small neighborhood of the origin with the prescribed finite time and accuracy level. By combining the barrier Lyapunov function approach with the adaptive neural backstepping technique, a novel adaptive neural tracking controller is proposed. It is shown that the constructed controller makes sure that the output tracking error converges to a small neighborhood of the origin with the prespecified tracking accuracy and settling time. Finally, the proposed control scheme is further tested by simulation examples.

Time-/Event-Triggered Adaptive Neural Asymptotic Tracking Control for Nonlinear Systems With Full-State Constraints and Application to a Single-Link Robot

This study proposes the time-/event-triggered adaptive neural control strategies for the asymptotic tracking problem of a class of uncertain nonlinear systems with full-state constraints. First, we design a time-triggered strategy. The effect caused by the residuals of the estimation via radial basis function (RBF) neural networks (NNs), and the reasonable upper bounds on the first derivative of the reference signal and the derivative of each virtual control, can be eliminated by designing appropriate adaptive laws and utilizing the basic properties of RBF NNs. Moreover, the construction of the barrier Lyapunov functions (BLFs) in this work ensures the compliance of the full-state constraints and also holds the asymptotic output tracking performance. Then, based on the time-triggered strategy, we further design a relative threshold event-triggered strategy. The proposed event-triggered adaptive neural controller can solve the main control objective of this work, that is: 1) the full-state constraint requirements of the system are not violated and 2) the output signal asymptotically tracks the reference signal. Compared with the traditional method, the event-triggered strategy can improve the utilization of communication channels and resources and has greater practical significance. Finally, an example of single-link robot under the proposed two strategies illustrates the validity of the constructed controllers.

Adaptive Fuzzy Decentralized Dynamic Surface Control for Switched Large-Scale Nonlinear Systems With Full-State Constraints

In this study, an adaptive fuzzy decentralized dynamic surface control (DSC) problem is investigated for switched large-scale nonlinear systems with deferred asymmetric and time-varying full-state constraints. Due to the existence of additional general nonlinearities, complicated output interconnections, and full-state constraints, it is difficult to address the above control problem using existing methods. Fuzzy-logic systems are, therefore, utilized to approximate the unknown nonlinear functions, and the DSC technique is adopted to overcome the "curse of dimensionality" problem. A novel fuzzy adaptive decentralized controller design is presented using the proposed convex combination technique. Furthermore, it is proven that under the proposed controller and state-dependent switching law, all states of the closed-loop system are bounded and deferred asymmetric, and the time-varying full-state constraints are strictly obeyed. The simulation results are presented to demonstrate the effectiveness of the proposed method.

DSC-based RBF neural network control for nonlinear time-delay systems with time-varying full state constraints

The presented control scheme in this paper aims at stabilizing uncertain time-delayed systems requiring all states to change within the preset time-varying constraints. The controller design framework is based on the backstepping method, drastically simplified by the dynamic surface control technique. Meanwhile, the radius basis function neural networks are utilized to deal with the unknown items. To prevent all state variables from violating time-varying predefined regions, we employ the time-varying barrier Lyapunov functions during the backstepping procedure. Moreover, appropriate Lyapunov-Krasovskii functionals are used to cancel the influence of the time-delay terms on the system's stability. Under the presented control laws and Lyapunov analysis, it is proven that constraints on all state variables are not breached, good tracking performance of desired output is achieved, and all signals in the closed-loop systems are bounded. The effectiveness of our control scheme is confirmed by a simulation example.

Adaptive Finite-Time Tracking Control of Nonholonomic Multirobot Formation Systems With Limited Field-of-View Sensors

This article studies the vision-based tracking control problem for a nonholonomic multirobot formation system with uncertain dynamic models and visibility constraints. A fixed onboard vision sensor that provides the relative distance and bearing angle is subject to limited range and angle of view due to limited sensing capability. The constraint resulting from collision avoidance is also taken into account for safe operations of the formation system. Furthermore, the preselected specifications on transient and steady-state performance are provided by considering the time-varying and asymmetric constraint requirements on formation tracking errors for each robot. To address the constraint problems, we incorporate a novel barrier Lyapunov function into controller design and analysis. Based on the recursive adaptive backstepping procedure and neural-network approximation, we develop a vision-based formation tracking control protocol such that formation tracking errors can converge into a small neighborhood of the origin in finite time while meeting the requirements of visibility and performance constraints. The proposed protocol is decentralized in the sense that the control action on each robot only depends on the local relative information, without the need for explicit network communication. Moreover, the control protocol could extend to an unconstrained multirobot system. Both simulation and experimental results show the effectiveness of the control protocol.

General Bitwidth Assignment for Efficient Deep Convolutional Neural Network Quantization

Model quantization is essential to deploy deep convolutional neural networks (DCNNs) on resource-constrained devices. In this article, we propose a general bitwidth assignment algorithm based on theoretical analysis for efficient layerwise weight and activation quantization of DCNNs. The proposed algorithm develops a prediction model to explicitly estimate the loss of classification accuracy led by weight quantization with a geometrical approach. Consequently, dynamic programming is adopted to achieve optimal bitwidth assignment on weights based on the estimated error. Furthermore, we optimize bitwidth assignment for activations by considering the signal-to-quantization-noise ratio (SQNR) between weight and activation quantization. The proposed algorithm is general to reveal the tradeoff between classification accuracy and model size for various network architectures. Extensive experiments demonstrate the efficacy of the proposed bitwidth assignment algorithm and the error rate prediction model. Furthermore, the proposed algorithm is shown to be well extended to object detection.

Observer-Based NN Control for Nonlinear Systems With Full-State Constraints and External Disturbances

For full-state constrained nonlinear systems with input saturation, this article studies the output-feedback tracking control under the condition that the states and external disturbances are both unmeasurable. A novel composite observer consisting of state observer and disturbance observer is designed to deal with the unmeasurable states and disturbances simultaneously. Distinct from the related literature, an auxiliary system with approximate coordinate transformation is used to attenuate the effects generated by input saturation. Then, using radial basis function neural networks (RBF NNs) and the barrier Lyapunov function (BLF), an opportune backstepping design procedure is given with employing the dynamic surface control (DSC) to avoid the problem of "explosion of complexity." Based on the given design procedure, an output-feedback controller is constructed and guarantees all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. It is shown that the tracking error is regulated by the saturated input error and design parameters without the violation of the state constraints. Finally, a simulation example of a robot arm is given to demonstrate the effectiveness of the proposed controller.

Research Review for Broad Learning System: Algorithms, Theory, and Applications

In recent years, the appearance of the broad learning system (BLS) is poised to revolutionize conventional artificial intelligence methods. It represents a step toward building more efficient and effective machine-learning methods that can be extended to a broader range of necessary research fields. In this survey, we provide a comprehensive overview of the BLS in data mining and neural networks for the first time, focusing on summarizing various BLS methods from the aspects of its algorithms, theories, applications, and future open research questions. First, we introduce the basic pattern of BLS manifestation, the universal approximation capability, and essence from the theoretical perspective. Furthermore, we focus on BLS's various improvements based on the current state of the theoretical research, which further improves its flexibility, stability, and accuracy under general or specific conditions, including classification, regression, semisupervised, and unsupervised tasks. Due to its remarkable efficiency, impressive generalization performance, and easy extendibility, BLS has been applied in different domains. Next, we illustrate BLS's practical advances, such as computer vision, biomedical engineering, control, and natural language processing. Finally, the future open research problems and promising directions for BLSs are pointed out.

Adaptive Fuzzy Control for a Class of MIMO Underactuated Systems With Plant Uncertainties and Actuator Deadzones: Design and Experiments

In the field of modern industrial engineering, many mechanical systems are underactuated, exhibiting strong nonlinear characteristics and high flexibility. However, the lack of control inputs brings about many difficulties for controller design and stability/convergence analysis., some unavoidable practical issues, e.g., plant uncertainties and actuator deadzones, make the control of underactuated systems even more challenging. Hence, with the aid of elaborately constructed finite-time convergent surfaces, this article provides the first solution to address the control problem for a class of multi-input-multi-output (MIMO) underactuated systems subject to plant uncertainties and actuator deadzones. Specifically, this article overcomes the main obstacle in sliding-mode surface analysis for MIMO underactuated systems, that is, by the presented analysis method, the asymptotic stability of the system equilibrium point is strictly proven based on the composite surfaces. In addition, the unknown parts of the actuated/unactuated dynamic equations and actuator deadzones can be simultaneously handled, which is important for real applications. Furthermore, we apply the proposed method to two kinds of typical underactuated systems, that is: 1) tower cranes and 2) double-pendulum cranes, and implement a series of hardware experiments to verify its effectiveness and robustness.

Periodic event-triggered adaptive tracking control design for nonlinear discrete-time systems via reinforcement learning

In this paper, an event-triggered control scheme with periodic characteristic is developed for nonlinear discrete-time systems under an actor-critic architecture of reinforcement learning (RL). The periodic event-triggered mechanism (ETM) is constructed to decide whether the sampling data are delivered to controllers or not. Meanwhile, the controller is updated only when the event-triggered condition deviates from a prescribed threshold. Compared with traditional continuous ETMs, the proposed periodic ETM can guarantee a minimal lower bound of the inter-event intervals and avoid sampling calculation point-to-point, which means that the partial communication resources can be efficiently economized. The critic and actor neural networks (NNs), consisting of radial basis function neural networks (RBFNNs), aim to approximate the unknown long-term performance index function and the ideal event-triggered controller, respectively. A rigorous stability analysis based on the Lyapunov difference method is provided to substantiate that the closed-loop system can be stabilized. All error signals of the closed-loop system are uniformly ultimately bounded (UUB) under the guidance of the proposed control scheme. Finally, two simulation examples are given to validate the effectiveness of the control design.

Full-state constrained neural control and learning for the nonholonomic wheeled mobile robot with unknown dynamics

The adaptive learning and control are proposed for the full-state(FS) constrained NWMR system with external destabilization. First, the constrained state is reformulated as the unconstrained state. Then, approximating the unknown dynamics in the closed-loop (CL) system is conducted via radial basis function (RBF) NN. Also, a sliding term is designed to deal with the external destabilization and the neural network training error. The derived adaptive neural controller can realize the asymptotic stability of a robot system without violating FS constraints. Moreover, the neural weights are converged so that the unknown dynamics are expressed by the constant weights in the CL system. It is also applicable to other similar control tasks. Lastly, the proposed algorithm is simulated and validated.

Adaptive NN Control of Electro-Hydraulic System with Full State Constraints

This paper presents an adaptive neural network (NN) control approach for an electro-hydraulic system. The friction and internal leakage are nonlinear uncertainties, and the states in the considered electro-hydraulic system are fully constrained. In the control design, the NNs are utilized to approximate the nonlinear uncertainties. Then, by constructing barrier Lyapunov functions and based on the adaptive backstepping control design technique, a novel adaptive NN control scheme is formulated. It has been proven that the developed adaptive NN control scheme can sustain the controlled electro-hydraulic system to be stable and make the system output track the desired reference signal. Furthermore, the system states do not surpass the given bounds. The computer simulation results verify the effectiveness of the proposed controller.

Asymptotic Tracking Control for Uncertain MIMO Systems: A Biologically Inspired ESN Approach

In this study, a biologically inspired echo state network (ESN)-based method is established for the asymptotic tracking control of a class of uncertain multi-input multi-output (MIMO) systems. By mimicking the characters of real biological systems, a diversified multiclustered echo state network (DMCESN) is proposed in this work and then it is applied to deal with the modeling uncertainties and coupling nonlinearities in the control systems. Different from the most existing neural network (NN)-based control methods that only ensure the uniform ultimate boundedness result, the proposed method can allow the tracking error to achieve asymptotic convergence through rigorous theoretical analysis. The effectiveness of the proposed method is also confirmed by numerical simulation by comparing with multilayer feedforward network-based control scheme and traditional ESN-based control, admitting better tracking performance of the proposed control.

Neural network-based adaptive synchronization for second-order nonlinear multiagent systems with unknown disturbance

This paper handles the distributed adaptive synchronization problem for a class of unknown second-order nonlinear multiagent systems subject to external disturbance. It is supposed to be an unknown one for the underlying external disorder. First, the neural network-based disturbance observer is developed to deal with the impact induced by the strange disturbance. Then, a new distributed adaptive synchronization criterion is put forward based on the approximation capability of the neural networks. Next, we propose the necessary and sufficient condition on the directed graph to ensure the synchronization error of all followers can be reduced small enough. Then, the distributed adaptive synchronization criterion is further explored because it is difficult to obtain the relative velocity measurements of the agents. The distributed adaptive synchronization criterion without the velocity measurement feedback is also designed to fulfill the current investigation. Finally, the simulation example is performed to verify the correctness and effectiveness of the proposed theoretical results.

Command-filter-based adaptive neural tracking control for a class of nonlinear MIMO state-constrained systems with input delay and saturation

This paper investigates the problem of adaptive tracking control for a class of nonlinear multi-input and multi-output (MIMO) state-constrained systems with input delay and saturation. During the process of the control scheme, neural network is employed to approximate the unknown nonlinear uncertainties and the appropriate barrier Lyapunov function is introduced to prevent violation of the constraint. In addition, for the issue of input saturation with time delay, a smooth non-affine approximate function and a novel auxiliary system are utilized, respectively. Moreover, adaptive neural tracking control is developed by combining the command filtering backstepping approach, which effectively avoids the explosion of differentiation and reduces the computation burden. The introduced filtering error compensating system brings a significant improvement for the system tracking performance. Finally, the simulation result is presented to verify the feasibility of the proposed strategy.

An Implicit Function-Based Adaptive Control Scheme for Noncanonical-Form Discrete-Time Neural-Network Systems

This article proposes a new implicit function-based adaptive control scheme for the discrete-time neural-network systems in a general noncanonical form. Feedback linearization for such systems leads to the output dynamics nonlinear dependence on the system states, the control input, and uncertain parameters, which leads to the nonlinear parametrization problem, the implicit relative degree problem, and the difficulty to specify an analytical adaptive controller. To address these problems, we first develop a new adaptive parameter estimation strategy to deal with all uncertain parameters, especially, those of nonlinearly parameterized forms, in the output dynamics. Then, we construct a key implicit function equation using available signals and parameter estimates. By solving the equation, a unique adaptive control law is derived to ensure asymptotic output tracking and closed-loop stability. Alternatively, we design an iterative solution-based adaptive control law which is easy to implement and ensure output tracking and closed-loop stability. The simulation study is given to demonstrate the design procedure and verify the effectiveness of the proposed adaptive control scheme.

Tracking Control of Unknown and Constrained Nonlinear Systems via Neural Networks With Implicit Weight and Activation Learning

For systems with irregular (asymmetric and positively-negatively alternating) constraints being imposed/removed during system operation, there is no uniformly applicable control method. In this work, a control design framework is established for uncertain pure-feedback systems subject to the aforementioned constraints. By introducing a novel transformation function and with the help of auxiliary constraining boundaries, the original output-constrained system is augmented to unconstrained one. Unknown nonlinearity is approximated by neural networks (NNs) with not only neural weight updating but also activation online adjustment. The resultant control scheme is able to deal with constraints imposed or removed at some time moments during system operation without the need for altering control structure. When applied to high-speed trains, the developed control scheme ensures position tracking under speed constraints, simulation demands, and confirms the effectiveness of the proposed method.

Robust Tracking Control of the Euler-Lagrange System Based on Barrier Lyapunov Function and Self-Structuring Neural Networks

This article studies the robust tracking control problems of Euler–Lagrange (EL) systems with uncertainties. To enhance the robustness of the control systems, an asymmetric tan-type barrier Lyapunov function (ATBLF) is used to dynamic constraint position tracking errors. To deal with the problems of the system uncertainties, the self-structuring neural network (SSNN) is developed to estimate the unknown dynamics model and avoid the calculation burden. The robust compensator is designed to estimate and compensate neural network (NN) approximation errors and unknown disturbances. In addition, a relative threshold event-triggered strategy is introduced, which greatly saves communication resources. Under the proposed robust control scheme, tracking behavior can be implemented with disturbance and unknown dynamics of the EL systems. All signals in the closed-loop system are proved to be bounded by stability analysis, and the tracking error can converge to the neighborhood near the origin. The numerical simulation results show the effectiveness and the validity of the proposed robust control scheme.

Nonlinear Model Predictive Control of Single-Link Flexible-Joint Robot Using Recurrent Neural Network and Differential Evolution Optimization

A recurrent neural network (RNN) and differential evolution optimization (DEO) based nonlinear model predictive control (NMPC) technique is proposed for position control of a single-link flexible-joint (FJ) robot. First, a simple three-layer recurrent neural network with rectified linear units as an activation function (ReLU-RNN) is employed for approximating the system dynamic model. Then, using the RNN predictive model and model predictive control (MPC) scheme, an RNN and DEO based NMPC controller is designed, and the DEO algorithm is used to solve the controller. Finally, comparing numerical simulation findings demonstrates the efficiency and performance of the proposed approach. The merit of this method is that not only is the control precision satisfied, but also the overshoots and the residual vibration are well suppressed.

Globally Exponentially Stable Tracking Control of Self-Restructuring Nonlinear Systems

This article proposes a neural networks (NNs)-based tracking control approach for a class of uncertain high-order self-restructuring nonaffine dynamic systems. Unlike most existing NN-based works that normally ignore the precondition on the functionality and reliability of NN unit and thus can only ensure semiglobal stability, the proposed method explicitly addresses the issue of reliable in-loop operation of NN approximation-based control unit, resulting in a safeguarded NN-based control solution capable of ensuring globally stable tracking. Furthermore, the control method proposed guarantees exponentially globally stable tracking for systems with self-restructuring nonlinearities and uncertainties, distinguishing itself from those that only yield uniformly ultimately bounded (UUB) regulation/tracking results for nonlinear systems with fixed structures. All of these features are achieved by the proposed strategy consisting of two cooperative control units: 1) safeguard control and 2) NN-based control. The role of the safeguard control is to force the states (starting from any initial condition) to enter a stable region, so that the NN-based control can be activated trustworthily and safely. It is such cooperation of the two units that not only ensures the tracking error entering the stable region first within a prespecified finite time but also guarantees the tracking error converging to zero exponentially thereafter, resulting in global zero-error tracking. Both the theoretical analysis and numerical simulation authenticate the effectiveness of the proposed method.

Optimal Robot-Environment Interaction Under Broad Fuzzy Neural Adaptive Control

This article proposes a novel control strategy based on a broad fuzzy neural network (BFNN) which is subjected to contact with the unknown environment. Compared with the conventional fuzzy neural network (NN), a prominent feature can be achieved by taking the advantage of the broad learning system (BLS) to explicitly tackle the problem of how to choose a sufficient number of NN units to approximate the unknown dynamic model. Aiming at providing a soft compliant contact scheme without the requirement of the environment model, an adaptive impedance learning is developed to establish the optimal interaction between the robot and the environment. Meanwhile, the problems related to the state constraints are addressed by incorporating a barrier Lyapunov function (BLF) into the design of a trajectory tracking controller. The proposed method can achieve desired tracking and interaction performance while guaranteeing the stability of the closed-loop system. In addition, simulation and experimental studies are performed to verify the effectiveness of BFNN under optimal impedance control with a two degree-of-freedom (DOF) manipulator and a Baxter robot, respectively.

Intrinsic Plasticity-Based Neuroadptive Control With Both Weights and Excitability Tuning

This brief presents an intrinsic plasticity (IP)-driven neural-network-based tracking control approach for a class of nonlinear uncertain systems. Inspired by the neural plasticity mechanism of individual neuron in nervous systems, a learning rule referred to as IP is employed for adjusting the radial basis functions (RBFs), resulting in a neural network (NN) with both weights and excitability tuning, based on which neuroadaptive tracking control algorithms for multiple-input-multiple-output (MIMO) uncertain systems are derived. Both theoretical analysis and numerical simulation confirm the effectiveness of the proposed method.

Neuro-learning-based adaptive control for state-constrained strict-feedback systems with unknown control direction

A neural networks (NNs)-based learning policy is proposed for strict-feedback nonlinear systems with asymmetric full-state constraints and unknown gain directions. A state-constrained function is introduced such that the proposed adaptive control policy works for systems with constraints or without constraints in a unified structure. Furthermore, the unified state-constrained function can also deal with symmetric and asymmetric constraints without changing adaptive structures, which also avoids discontinuous actions. With Nussbaum gain technique and NNs-based approximation technique, the proposed control method can also effectively deal with the unknown signs of control gains, and matched and mismatched uncertainties are also solved by NN approximation technique. According to the Lyapunov theory, the tracking errors can be proved to be semi-globally uniformly ultimately bounded (SGUUB). Finally the effectiveness of the proposed scheme is validated by numerical simulations.

Hybrid Neural Adaptive Control for Practical Tracking of Markovian Switching Networks

While neural adaptive control is widely used for dealing with continuous- or discrete-time dynamical systems, less is known about its mechanism and performance in hybrid dynamical systems. This article develops analytical tools to investigate the neural adaptive tracking control of the hybrid Markovian switching networks with heterogeneous nonlinear dynamics and randomly switched topologies. A gradient-descent adaptation law built on neural networks (NNs) is presented for efficient distributed adaptive control. It is shown that the proposed control scheme can guarantee a stable closed-loop error system for any positive control gain and tuning gain. The tracking error is demonstrated to be practically uniformly exponentially stable with a threshold in the mean-square sense. This study further reveals how the topological structure affects the NN function, by measuring the influence of the switched topologies on the learning performance.