Adaptive Decentralized Neural Network Tracking Control for Uncertain Interconnected Nonlinear Systems With Input Quantization and Time Delay

Quantized-output-feedback practical prescribed-time design strategy for decentralized tracking of a class of interconnected nonlinear systems with unknown interaction delays

This paper proposes a decentralized practical prescribed-time (PT) tracking design using quantized output feedback (QOF) for uncertain interconnected lower-triangular systems with unknown time-delay interconnections. The local output signals are assumed to be only measured and quantized for the PT tracker design under a band-limited network. By employing a PT-dependent scaling function, a decentralized memoryless PT observer based on quantized local outputs is developed to estimate local unmeasurable state variables. Owing to output quantization, the available output feedback signals become discontinuous. As a result, the tracking error between the actual (i.e., unquantized) local output and the local desired signal cannot be utilized in the local virtual controller. To address this issue, a novel adaptive compensation mechanism is derived to design the local PT neural network tracking laws using only quantized local outputs and estimated states. The proposed PT tracking controller does not require information on the interconnected nonlinear functions and interaction delays. During the Lyapunov stability analysis, the boundary layer error decomposition approach is employed to address the issue of non-differentiability in the local virtual control laws. The proposed QOF control system achieves practical PT stability. It is shown that the settling time of local tracking errors can be predetermined, regardless of the design parameters and initial conditions. Finally, the proposed QOF decentralization strategy is supported with illustrative examples and a comparison to demonstrate its benefits.

Event-Triggered-Based Distributed Consensus Tracking for Nonlinear Multiagent Systems With Quantization

In this article, an observer-based adaptive neural network (NN) event-triggered distributed consensus tracking problem is investigated for nonlinear multiagent systems with quantization. In the first place, the limited capacity of the communication channel between agents is considered. The event-trigger mechanism and dynamic uniform quantizers are set up to reduce information transmission. The next NN is utilized to handle the unknown nonlinear functions. Finally, in order to estimate the unmeasurable states, an NN-based state observer is designed for each agent by using a dynamic gain function. To settle the difficulty caused by the coupling effects of event-triggered conditions and the scaling function in dynamic uniform quantizers and observers, a distributed control protocol with estimated information of its neighbors is designed, which ensures distributed consensus tracking of the nonlinear multiagent systems without incurring the Zeno behavior. The effectiveness of the control protocol is illustrated by a simulation example.

Observer-Based Decentralized Control for Non-Strict-Feedback Fractional-Order Nonlinear Large-Scale Systems With Unknown Dead Zones

This article addresses the output-feedback decentralized control issue for the fractional-order nonlinear large-scale nonstrict-feedback systems with states immeasurable and unknown dead zones. The unknown nonlinear functions are identified by neural networks (NNs), and immeasurable states are estimated by establishing an NNs' decentralized state observer. The algebraic loop issue is solved by using the property of NN basis functions and designing the fractional-order adaptation laws. In addition, the fractional-order dynamic surface control (FODSC) design technique is introduced in the adaptive backstepping control algorithm to avoid the issue of "explosion of complexity." Then, by treating the nonsymmetric dead zones as the time-varying uncertain systems, an adaptive NNs' output-feedback decentralized control scheme is developed via the fractional-order Lyapunov stability criterion. It is proven that the controlled fractional-order systems are stable, and the tracking and observer errors can converge to a small neighborhood of zero. Two simulation examples are given to confirm the validity of the put forward control scheme.

Neural Network-Based Cooperative Trajectory Tracking Control for a Mobile Dual Flexible Manipulator

For a mobile dual flexible manipulator (MDFM) system, this article focuses on the problem of cooperative trajectory tracking under unknown dynamics and time-varying trajectories. The dynamic model of the wheeled mobile manipulator system in 2-D space is established. Taking into account the unmodeled dynamics of the system, unknown terms of the system are approximated by integrating the radial basis function neural network (RBFNN) structure. By introducing the servo system, the cooperative trajectory tracking control (CTTC) strategy is designed, which realizes the system's cooperative operation, time-varying trajectory tracking, and vibration suppression. The performance of the proposed control scheme is verified through theoretical analysis and numerical simulations.

Time-/Event-Triggered Adaptive Neural Asymptotic Tracking Control of Nonlinear Interconnected Systems With Unmodeled Dynamics and Prescribed Performance

This article proposes two adaptive asymptotic tracking control schemes for a class of interconnected systems with unmodeled dynamics and prescribed performance. By applying an inherent property of radial basis function (RBF) neural networks (NNs), the design difficulties aroused from the unknown interactions among subsystems and unmodeled dynamics are overcome. Then, in order to ensure that the tracking errors can be suppressed in the specified range, the constrained control problem is transformed into the stabilization problem by using an auxiliary function. Based on the adaptive backstepping method, a time-triggered controller is constructed. It is proven that under the framework of Barbalat's lemma, all the variables in the closed-loop system are bounded and the tracking errors are further ensured to converge to zero asymptotically. Furthermore, the event-triggered strategy with a variable threshold is adopted to make more precise control such that the better system performance can be obtained, which reduces the system communication burden under the condition of limited communication resources. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control scheme.

Finite-Time Command-Filtered Composite Adaptive Neural Control of Uncertain Nonlinear Systems

This article presents a new command-filtered composite adaptive neural control scheme for uncertain nonlinear systems. Compared with existing works, this approach focuses on achieving finite-time convergent composite adaptive control for the higher-order nonlinear system with unknown nonlinearities, parameter uncertainties, and external disturbances. First, radial basis function neural networks (NNs) are utilized to approximate the unknown functions of the considered uncertain nonlinear system. By constructing the prediction errors from the serial-parallel nonsmooth estimation models, the prediction errors and the tracking errors are fused to update the weights of the NNs. Afterward, the composite adaptive neural backstepping control scheme is proposed via nonsmooth command filter and adaptive disturbance estimation techniques. The proposed control scheme ensures that high-precision tracking performances and NN approximation performances can be achieved simultaneously. Meanwhile, it can avoid the singularity problem in the finite-time backstepping framework. Moreover, it is proved that all signals in the closed-loop control system can be convergent in finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.

Decentralized Dynamic Event-Triggered Output Feedback Adaptive Fixed-Time Funnel Control for Interconnection Nonlinear systems

A decentralized dynamic event-triggered output feedback adaptive fixed-time (DDETOFAFxT) funnel controller is described for a class of interconnected nonlinear systems (INSs). A novel dynamic event-triggered mechanism is designed, which includes a triggering control input, fixed threshold, decreasing function of tracking error, and a dynamic variable. To obtain the unknown states, a decentralized linear filter is designed. By introducing a prescribed funnel and using an adding a power integrator technique and a neural network method, a DDETOFAFxT funnel controller is designed to obtain better tracking performance and effectively alleviate the computational burden. Furthermore, it is ensured that the tracking error falls into a preset performance funnel. A simulation example is presented to demonstrate the availability of the designed control scheme.

Disturbance Observer-Based Minimum Entropy Control for a Class of Disturbed Non-Gaussian Stochastic Systems

In this article, a novel control algorithm is developed for a class of nonlinear stochastic systems subject to multiple disturbances, including exogenous dynamic disturbance and general non-Gaussian noise. An observer is designed to estimate the exogenous disturbance, and then the disturbance compensation is incorporated into a feedback control strategy for the non-Gaussian system. Considering the ability of entropy in randomness quantification, a performance index is established based on the generalized entropy optimization principle. Furthermore, it is adjusted to be available for the controller solution, which also solves the coupling between two kinds of disturbances. On this basis, the optimal controller is provided in a recursive way, with which the closed-loop stability and good antidisturbance ability can be guaranteed simultaneously. Compared with the existing studies on the non-Gaussian stochastic systems, the proposed control algorithm has merits in multiple disturbances decoupling and enhanced antidisturbance performance. Finally, a simulation example is given to demonstrate the effectiveness of theoretical results.

H∞ Tracking Control of Uncertain Markovian Hybrid Switching Systems: A Fuzzy Switching Dynamic Adaptive Control Approach

This article investigates the H_∞ stochastic tracking control problem for uncertain fuzzy Markovian hybrid switching systems by using a fuzzy switching dynamic adaptive control approach. The long and the short is to construct multiple piecewise stochastic Lyapunov functions which provide an effective tool for designing hybrid switching law and fuzzy switching dynamic adaptive law. A hybrid switching law, including both stochastic switching and deterministic switching, is designed to represent more general switching scenarios, which can improve the H_∞ adaptive tracking performance through offering a running time before stochastic switching for the adaptive control strategy to work well. A fuzzy switching dynamic adaptive control technique is developed such that all signals of the tracking error equation are bounded, and the system state trajectory tracks the reference model state trajectory under a disturbance attenuation level as closely as possible. Finally, an application study verifies the effectiveness of the acquired methods.

Composite Learning Control of Overactuated Manned Submersible Vehicle With Disturbance/Uncertainty and Measurement Noise

In this article, a novel composite learning control scheme based on nonlinear disturbance observer (NDOB), neural network (NN), and model-based state observer (MSOB) is investigated for the manned submersible vehicle. First, an MSOB is employed to reconstruct the real output signals from noise-contained measurements. Second, a composite estimation is developed where an NDOB is designed to estimate external disturbance and an NN is employed for model uncertainty. Furthermore, a control allocation technique is used to address the overactuated problem of the manned submersible vehicle. The rigorous stability analysis of the closed-loop manned submersible system is given via the Lyapunov theorem. Finally, several representative simulation results illustrate the superior control performance of the composite learning control scheme for the manned submersible vehicle.

Distributed Nesterov Gradient and Heavy-Ball Double Accelerated Asynchronous Optimization

In this article, we come up with a novel Nesterov gradient and heavy-ball double accelerated distributed synchronous optimization algorithm, called NHDA, and adopt a general asynchronous model to further propose an effective asynchronous algorithm, called ASY-NHDA, for distributed optimization problem over directed graphs, where each agent has access to a local objective function and computes the optimal solution via communicating only with its immediate neighbors. Our goal is to minimize a sum of all local objective functions satisfying strong convexity and Lipschitz continuity. Consider a general asynchronous model, where agents communicate with their immediate neighbors and start a new computation independently, that is, agents can communicate with their neighbors at any time without any coordination and use delayed information from their in-neighbors to compute a new update. Delays are arbitrary, unpredictable, and time-varying but bounded. The theoretical analysis of NHDA is based on analyzing the interaction among the consensus, the gradient tracking, and the optimization processes. As for the analysis of ASY-NHDA, we equivalently transform the asynchronous system into an augmented synchronous system without delays and prove its convergence through using the generalized small gain theorem. The results show that NHDA and ASY-NHDA converge to the optimal solution at a linear convergence as long as the largest step size is positive and less than an explicitly estimated upper bound, and the largest momentum parameter is nonnegative and less than an upper bound. Finally, we demonstrate the advantages of ASY-NHDA through simulations.

Decentralized Adaptive Neuro-Output Feedback Saturated Control for INS and Its Application to AUV

This article investigates the problem of the decentralized adaptive output feedback saturated control problem for interconnected nonlinear systems with strong interconnections. A decentralized linear observer is first established to estimate the unknown states. Then, an auxiliary system is constructed to offset the effect of input saturation. With the aid of graph theory and neural network technique, a decentralized adaptive neuro-output feedback saturated controller is designed in a nonrecursive manner. A sufficient criterion is established to achieve the uniform ultimate boundedness (UUB) of the closed-loop system. An application example of autonomous underwater vehicle (AUV) is provided to verify the effectiveness of the developed algorithm.

Synchronization for Quantized Semi-Markov Switching Neural Networks in a Finite Time

Finite-time synchronization (FTS) is discussed for delayed semi-Markov switching neural networks (S-MSNNs) with quantized measurement, in which a logarithmic quantizer is employed. The stochastic phenomena of structural and parametrical changes are modeled by a semi-Markov process whose transition rates are time-varying to depend on the sojourn time. Practical systems subject to unpredictable structural changes, such as quadruple-tank process systems, are described by delayed S-MSNNs. A key issue under the consideration is how to design a feedback controller to guarantee the FTS between the master system and the slave system. For this purpose, by using the weak infinitesimal operator, sufficient conditions are constructed to realize FTS of the resulting error system over a finite-time interval. Then, the solvability conditions for the desired finite-time controller can be determined under a linear matrix inequality framework. Finally, the theoretical findings are illustrated by the quadruple-tank process model.

Convergence Analysis of Adaptive Exponential Functional Link Network

The adaptive exponential functional link network (AEFLN) is a recently introduced novel linear-in-the-parameters nonlinear filter and is used in numerous nonlinear applications, including system identification, active noise control, and echo cancellation. The improved modeling accuracy offered by AEFLN for different nonlinear applications can be attributed to the exponentially varying sinusoidal basis functions used for nonlinear expansion. Even though AEFLN has been widely used for the identification of nonlinear systems, no theoretical analysis of AEFLN is available in the literature. Hence, in this article, a theoretical performance analysis of AEFLN trained using an adaptive exponential least mean square (AELMS) algorithm under the Gaussian input assumption is discussed. Expressions describing the mean as well as mean square behavior of the weight vector and adaptive exponential parameter are derived. Computer simulations are carried out, and the derived theoretical expressions show a close correspondence with simulation results.

Adaptive Neural Backstepping Sliding Mode Heading Control for Underactuated Ships with Drift Angle and Ship-Bank Interaction

In order to track the desired path under unknown parameters and environmental disturbances, an adaptive backstepping sliding mode control algorithm with a neural estimator is proposed for underactuated ships considering both ship-bank interaction effect and shift angle. Using the features of radial basis function neural network, which can approximate arbitrary function, the unknown parameters of the ship model and environmental disturbances are estimated. The trajectory tracking errors include stabilizing sway and surge velocities errors. Based on the Lyapunov stability theory, the tracking error will converge to zero and the system is asymptotically stable. The controlled trajectory is contractive and asymptotically tends to the desired position and attitude. The results show that compared with the basic sliding mode control algorithm, the overshoot of the adaptive backstepping sliding mode control with neural estimator is smaller and the regulation time of the system is shorter. The ship can adjust itself and quickly reach its desired position under disturbances. This shows that the designed RBF neural network observer can track both the mild level 3 sea state and the bad level 5 sea state, although the wave disturbance has relatively fast time-varying disturbance. The algorithm has good tracking performance and can realize the accurate estimation of wave disturbance, especially in bad sea conditions.