Global neural dynamic surface tracking control of strict-feedback systems with application to hypersonic flight vehicle

This paper studies both indirect and direct global neural control of strict-feedback systems in the presence of unknown dynamics, using the dynamic surface control (DSC) technique in a novel manner. A new switching mechanism is designed to combine an adaptive neural controller in the neural approximation domain, together with the robust controller that pulls the transient states back into the neural approximation domain from the outside. In comparison with the conventional control techniques, which could only achieve semiglobally uniformly ultimately bounded stability, the proposed control scheme guarantees all the signals in the closed-loop system are globally uniformly ultimately bounded, such that the conventional constraints on initial conditions of the neural control system can be relaxed. The simulation studies of hypersonic flight vehicle (HFV) are performed to demonstrate the effectiveness of the proposed global neural DSC design.

Dynamic Surface Control Using Neural Networks for a Class of Uncertain Nonlinear Systems With Input Saturation

In this paper, a dynamic surface control (DSC) scheme is proposed for a class of uncertain strict-feedback nonlinear systems in the presence of input saturation and unknown external disturbance. The radial basis function neural network (RBFNN) is employed to approximate the unknown system function. To efficiently tackle the unknown external disturbance, a nonlinear disturbance observer (NDO) is developed. The developed NDO can relax the known boundary requirement of the unknown disturbance and can guarantee the disturbance estimation error converge to a bounded compact set. Using NDO and RBFNN, the DSC scheme is developed for uncertain nonlinear systems based on a backstepping method. Using a DSC technique, the problem of explosion of complexity inherent in the conventional backstepping method is avoided, which is specially important for designs using neural network approximations. Under the proposed DSC scheme, the ultimately bounded convergence of all closed-loop signals is guaranteed via Lyapunov analysis. Simulation results are given to show the effectiveness of the proposed DSC design using NDO and RBFNN.

Adaptive neural network control of unknown nonlinear affine systems with input deadzone and output constraint

In this paper, we aim to solve the control problem of nonlinear affine systems, under the condition of the input deadzone and output constraint with the external unknown disturbance. To eliminate the effects of the input deadzone, a Radial Basis Function Neural Network (RBFNN) is introduced to compensate for the negative impact of input deadzone. Meanwhile, we design a barrier Lyapunov function to ensure that the output parameters are restricted. In support of the barrier Lyapunov method, we build an adaptive neural network controller based on state feedback and output feedback methods. The stability of the closed-loop system is proven via the Lyapunov method and the performance of the expected effects is verified in simulation.

Missile Guidance Law Based on Robust Model Predictive Control Using Neural-Network Optimization

In this brief, the utilization of robust model-based predictive control is investigated for the problem of missile interception. Treating the target acceleration as a bounded disturbance, novel guidance law using model predictive control is developed by incorporating missile inside constraints. The combined model predictive approach could be transformed as a constrained quadratic programming (QP) problem, which may be solved using a linear variational inequality-based primal-dual neural network over a finite receding horizon. Online solutions to multiple parametric QP problems are used so that constrained optimal control decisions can be made in real time. Simulation studies are conducted to illustrate the effectiveness and performance of the proposed guidance control law for missile interception.

Adaptive Neural Control of Nonaffine Systems With Unknown Control Coefficient and Nonsmooth Actuator Nonlinearities

This brief considers the asymptotic tracking problem for a class of high-order nonaffine nonlinear dynamical systems with nonsmooth actuator nonlinearities. A novel transformation approach is proposed, which is able to systematically transfer the original nonaffine nonlinear system into an equivalent affine one. Then, to deal with the unknown dynamics and unknown control coefficient contained in the affine system, online approximator and Nussbaum gain techniques are utilized in the controller design. It is proven rigorously that asymptotic convergence of the tracking error and ultimate uniform boundedness of all the other signals can be guaranteed by the proposed control method. The control feasibility is further verified by numerical simulations.

Approximation-Based Discrete-Time Adaptive Position Tracking Control for Interior Permanent Magnet Synchronous Motors

This paper considers the problem of discrete-time adaptive position tracking control for a interior permanent magnet synchronous motor (IPMSM) based on fuzzy-approximation. Fuzzy logic systems are used to approximate the nonlinearities of the discrete-time IPMSM drive system which is derived by direct discretization using Euler method, and a discrete-time fuzzy position tracking controller is designed via backstepping approach. In contrast to existing results, the advantage of the scheme is that the number of the adjustable parameters is reduced to two only and the problem of coupling nonlinearity can be overcome. It is shown that the proposed discrete-time fuzzy controller can guarantee the tracking error converges to a small neighborhood of the origin and all the signals are bounded. Simulation results illustrate the effectiveness and the potentials of the theoretic results obtained.

A direct self-constructing neural controller design for a class of nonlinear systems

This paper is concerned with the problem of adaptive neural control for a class of uncertain or ill-defined nonaffine nonlinear systems. Using a self-organizing radial basis function neural network (RBFNN), a direct self-constructing neural controller (DSNC) is designed so that unknown nonlinearities can be approximated and the closed-loop system is stable. The key features of the proposed DSNC design scheme can be summarized as follows. First, different from the existing results in literature, a self-organizing RBFNN with adaptive threshold is constructed online for DSNC to improve the control performance. Second, the control law and adaptive law for the weights of RBFNN are established so that the closed-loop system is stable in the term of Lyapunov stability theory. Third, the tracking error is guaranteed to uniformly asymptotically converge to zero with the aid of an additional robustifying control term. An example is finally given to demonstrate the design procedure and the performance of the proposed method. Simulation results reveal the effectiveness of the proposed method.

Generalized single-hidden layer feedforward networks for regression problems

In this paper, traditional single-hidden layer feedforward network (SLFN) is extended to novel generalized SLFN (GSLFN) by employing polynomial functions of inputs as output weights connecting randomly generated hidden units with corresponding output nodes. The significant contributions of this paper are as follows: 1) a primal GSLFN (P-GSLFN) is implemented using randomly generated hidden nodes and polynomial output weights whereby the regression matrix is augmented by full or partial input variables and only polynomial coefficients are to be estimated; 2) a simplified GSLFN (S-GSLFN) is realized by decomposing the polynomial output weights of the P-GSLFN into randomly generated polynomial nodes and tunable output weights; 3) both P- and S-GSLFN are able to achieve universal approximation if the output weights are tuned by ridge regression estimators; and 4) by virtue of the developed batch and online sequential ridge ELM (BR-ELM and OSR-ELM) learning algorithms, high performance of the proposed GSLFNs in terms of generalization and learning speed is guaranteed. Comprehensive simulation studies and comparisons with standard SLFNs are carried out on real-world regression benchmark data sets. Simulation results demonstrate that the innovative GSLFNs using BR-ELM and OSR-ELM are superior to standard SLFNs in terms of accuracy, training speed, and structure compactness.

Adaptive neural control of nonlinear MIMO systems with time-varying output constraints

In this paper, adaptive neural control is investigated for a class of unknown multiple-input multiple-output nonlinear systems with time-varying asymmetric output constraints. To ensure constraint satisfaction, we employ a system transformation technique to transform the original constrained (in the sense of the output restrictions) system into an equivalent unconstrained one, whose stability is sufficient to solve the output constraint problem. It is shown that output tracking is achieved without violation of the output constraint. More specifically, we can shape the system performance arbitrarily on transient and steady-state stages with the output evolving in predefined time-varying boundaries all the time. A single neural network, whose weights are tuned online, is used in our design to approximate the unknown functions in the system dynamics, while the singularity problem of the control coefficient matrix is avoided without assumption on the prior knowledge of control input's bound. All the signals in the closed-loop system are proved to be semiglobally uniformly ultimately bounded via Lyapunov synthesis. Finally, the merits of the proposed controller are verified in the simulation environment.

Adaptive NN controller design for a class of nonlinear MIMO discrete-time systems

An adaptive neural network tracking control is studied for a class of multiple-input multiple-output (MIMO) nonlinear systems. The studied systems are in discrete-time form and the discretized dead-zone inputs are considered. In addition, the studied MIMO systems are composed of N subsystems, and each subsystem contains unknown functions and external disturbance. Due to the complicated framework of the discrete-time systems, the existence of the dead zone and the noncausal problem in discrete-time, it brings about difficulties for controlling such a class of systems. To overcome the noncausal problem, by defining the coordinate transformations, the studied systems are transformed into a special form, which is suitable for the backstepping design. The radial basis functions NNs are utilized to approximate the unknown functions of the systems. The adaptation laws and the controllers are designed based on the transformed systems. By using the Lyapunov method, it is proved that the closed-loop system is stable in the sense that the semiglobally uniformly ultimately bounded of all the signals and the tracking errors converge to a bounded compact set. The simulation examples and the comparisons with previous approaches are provided to illustrate the effectiveness of the proposed control algorithm.

Consensus-based distributed cooperative learning from closed-loop neural control systems

In this paper, the neural tracking problem is addressed for a group of uncertain nonlinear systems where the system structures are identical but the reference signals are different. This paper focuses on studying the learning capability of neural networks (NNs) during the control process. First, we propose a novel control scheme called distributed cooperative learning (DCL) control scheme, by establishing the communication topology among adaptive laws of NN weights to share their learned knowledge online. It is further proved that if the communication topology is undirected and connected, all estimated weights of NNs can converge to small neighborhoods around their optimal values over a domain consisting of the union of all state orbits. Second, as a corollary it is shown that the conclusion on the deterministic learning still holds in the decentralized adaptive neural control scheme where, however, the estimated weights of NNs just converge to small neighborhoods of the optimal values along their own state orbits. Thus, the learned controllers obtained by DCL scheme have the better generalization capability than ones obtained by decentralized learning method. A simulation example is provided to verify the effectiveness and advantages of the control schemes proposed in this paper.

Backstepping fuzzy-neural-network control design for hybrid maglev transportation system

This paper focuses on the design of a backstepping fuzzy-neural-network control (BFNNC) for the online levitated balancing and propulsive positioning of a hybrid magnetic levitation (maglev) transportation system. The dynamic model of the hybrid maglev transportation system including levitated hybrid electromagnets to reduce the suspension power loss and the friction force during linear movement and a propulsive linear induction motor based on the concepts of mechanical geometry and motion dynamics is first constructed. The ultimate goal is to design an online fuzzy neural network (FNN) control methodology to cope with the problem of the complicated control transformation and the chattering control effort in backstepping control (BSC) design, and to directly ensure the stability of the controlled system without the requirement of strict constraints, detailed system information, and auxiliary compensated controllers despite the existence of uncertainties. In the proposed BFNNC scheme, an FNN control is utilized to be the major control role by imitating the BSC strategy, and adaptation laws for network parameters are derived in the sense of projection algorithm and Lyapunov stability theorem to ensure the network convergence as well as stable control performance. The effectiveness of the proposed control strategy for the hybrid maglev transportation system is verified by experimental results, and the superiority of the BFNNC scheme is indicated in comparison with the BSC strategy and the backstepping particle-swarm-optimization control system in previous research.

Reinforcement learning design-based adaptive tracking control with less learning parameters for nonlinear discrete-time MIMO systems

Based on the neural network (NN) approximator, an online reinforcement learning algorithm is proposed for a class of affine multiple input and multiple output (MIMO) nonlinear discrete-time systems with unknown functions and disturbances. In the design procedure, two networks are provided where one is an action network to generate an optimal control signal and the other is a critic network to approximate the cost function. An optimal control signal and adaptation laws can be generated based on two NNs. In the previous approaches, the weights of critic and action networks are updated based on the gradient descent rule and the estimations of optimal weight vectors are directly adjusted in the design. Consequently, compared with the existing results, the main contributions of this paper are: 1) only two parameters are needed to be adjusted, and thus the number of the adaptation laws is smaller than the previous results and 2) the updating parameters do not depend on the number of the subsystems for MIMO systems and the tuning rules are replaced by adjusting the norms on optimal weight vectors in both action and critic networks. It is proven that the tracking errors, the adaptation laws, and the control inputs are uniformly bounded using Lyapunov analysis method. The simulation examples are employed to illustrate the effectiveness of the proposed algorithm.

Neural network-based motion control of an underactuated wheeled inverted pendulum model

In this paper, automatic motion control is investigated for one of wheeled inverted pendulum (WIP) models, which have been widely applied for modeling of a large range of two wheeled modern vehicles. First, the underactuated WIP model is decomposed into a fully actuated second order subsystem Σa consisting of planar movement of vehicle forward and yaw angular motions, and a nonactuated first order subsystem Σb of pendulum motion. Due to the unknown dynamics of subsystem Σa and the universal approximation ability of neural network (NN), an adaptive NN scheme has been employed for motion control of subsystem Σa . The model reference approach has been used whereas the reference model is optimized by the finite time linear quadratic regulation technique. The pendulum motion in the passive subsystem Σb is indirectly controlled using the dynamic coupling with planar forward motion of subsystem Σa , such that satisfactory tracking of a set pendulum tilt angle can be guaranteed. Rigours theoretic analysis has been established, and simulation studies have been performed to demonstrate the developed method.

Contact-force distribution optimization and control for quadruped robots using both gradient and adaptive neural networks

This paper investigates optimal feet forces' distribution and control of quadruped robots under external disturbance forces. First, we formulate a constrained dynamics of quadruped robots and derive a reduced-order dynamical model of motion/force. Consider an external wrench on quadruped robots; the distribution of required forces and moments on the supporting legs of a quadruped robot is handled as a tip-point force distribution and used to equilibrate the external wrench. Then, a gradient neural network is adopted to deal with the optimized objective function formulated as to minimize this quadratic objective function subjected to linear equality and inequality constraints. For the obtained optimized tip-point force and the motion of legs, we propose the hybrid motion/force control based on an adaptive neural network to compensate for the perturbations in the environment and approximate feedforward force and impedance of the leg joints. The proposed control can confront the uncertainties including approximation error and external perturbation. The verification of the proposed control is conducted using a simulation.

Performance limitations in the tracking and regulation problem for discrete-time systems

In this paper, the optimal tracking and regulation performance of discrete-time, multi-input multi-output, linear time-invariant systems is investigated. The control signal is influenced by the external disturbance, and the output feedback is subjected to an additive white Gaussian noise (AWGN) corruption. The tracking error with channel input power constraint and the output regulation with control energy constraint are adopted as the measure of tracking and regulation performance respectively, which can be obtained by searching through all stabilizing two-parameter controllers. Both results demonstrate that the performance is closely related to locations and directions of the nonminimum phase zeros, unstable poles of the plant and may be badly degraded by external disturbance and AWGN.

Reinforcement learning output feedback NN control using deterministic learning technique

In this brief, a novel adaptive-critic-based neural network (NN) controller is investigated for nonlinear pure-feedback systems. The controller design is based on the transformed predictor form, and the actor-critic NN control architecture includes two NNs, whereas the critic NN is used to approximate the strategic utility function, and the action NN is employed to minimize both the strategic utility function and the tracking error. A deterministic learning technique has been employed to guarantee that the partial persistent excitation condition of internal states is satisfied during tracking control to a periodic reference orbit. The uniformly ultimate boundedness of closed-loop signals is shown via Lyapunov stability analysis. Simulation results are presented to demonstrate the effectiveness of the proposed control.

Adaptive Control Using Fully Online Sequential‐Extreme Learning Machine and a Case Study on Engine Air‐Fuel Ratio Regulation

Most adaptive neural control schemes are based on stochastic gradient‐descent backpropagation (SGBP), which suffers from local minima problem. Although the recently proposed regularized online sequential‐extreme learning machine (ReOS‐ELM) can overcome this issue, it requires a batch of representative initial training data to construct a base model before online learning. The initial data is usually difficult to collect in adaptive control applications. Therefore, this paper proposes an improved version of ReOS‐ELM, entitled fully online sequential‐extreme learning machine (FOS‐ELM). While retaining the advantages of ReOS‐ELM, FOS‐ELM discards the initial training phase, and hence becomes suitable for adaptive control applications. To demonstrate its effectiveness, FOS‐ELM was applied to the adaptive control of engine air‐fuel ratio based on a simulated engine model. Besides, controller parameters were also analyzed, in which it is found that large hidden node number with small regularization parameter leads to the best performance. A comparison among FOS‐ELM and SGBP was also conducted. The result indicates that FOS‐ELM achieves better tracking and convergence performance than SGBP, since FOS‐ELM tends to learn the unknown engine model globally whereas SGBP tends to “forget” what it has learnt. This implies that FOS‐ELM is more preferable for adaptive control applications.

Nonlinear systems identification and control via dynamic multitime scales neural networks

This paper deals with the adaptive nonlinear identification and trajectory tracking via dynamic multilayer neural network (NN) with different timescales. Two NN identifiers are proposed for nonlinear systems identification via dynamic NNs with different timescales including both fast and slow phenomenon. The first NN identifier uses the output signals from the actual system for the system identification. In the second NN identifier, all the output signals from nonlinear system are replaced with the state variables of the NNs. The online identification algorithms for both NN identifier parameters are proposed using Lyapunov function and singularly perturbed techniques. With the identified NN models, two indirect adaptive NN controllers for the nonlinear systems containing slow and fast dynamic processes are developed. For both developed adaptive NN controllers, the trajectory errors are analyzed and the stability of the systems is proved. Simulation results show that the controller based on the second identifier has better performance than that of the first identifier.

Delay-dependent global exponential robust stability for delayed cellular neural networks with time-varying delay

This paper investigates a class of delayed cellular neural networks (DCNN) with time-varying delay. Based on the Lyapunov-Krasovski functional and integral inequality approach (IIA), a uniformly asymptotic stability criterion in terms of only one simple linear matrix inequality (LMI) is addressed, which guarantees stability for such time-varying delay systems. This LMI can be easily solved by convex optimization techniques. Unlike previous methods, the upper bound of the delay derivative is taken into consideration, even if larger than or equal to 1. It is proven that results obtained are less conservative than existing ones. Four numerical examples illustrate efficacy of the proposed methods.

ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF PERTURBED NONLINEAR TIME-VARYING DELAYS SYSTEMS WITH UNKNOWN CONTROL DIRECTION

An adaptive fuzzy control scheme with only one adjusted parameter is developed for a class of nonlinear time-varying delays systems. Three kinds of uncertainties: time-varying delays, control directions, and nonlinear functions are all assumed to be completely unknown, which is different from the previous work. During the controller design procedure, appropriate Lyapunov-Krasovskii functionals are used to compensate the unknown time-varying delays terms and the Nussbaum-type function is used to detect the unknown control direction. It is proved that the proposed controller guarantees that all the signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood around zero. The two main advantages of the developed scheme are that (i) by combining the appropriate Lyapunov-Krasovskii functionals with the Nussbaum-gain technique, the control scheme is proposed for a class of nonlinear time-varying delays systems with unknown control directions, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the computational burden greatly. Finally, two examples are used to show the effectiveness of the proposed approach.

Direct Adaptive Neural Control for a Class of Uncertain Nonaffine Nonlinear Systems Based on Disturbance Observer

In this paper, the direct adaptive neural control is proposed for a class of uncertain nonaffine nonlinear systems with unknown nonsymmetric input saturation. Based on the implicit function theorem and mean value theorem, both state feedback and output feedback direct adaptive controls are developed using neural networks (NNs) and a disturbance observer. A compounded disturbance is defined to take into account of the effect of the unknown external disturbance, the unknown nonsymmetric input saturation, and the approximation error of NN. Then, a disturbance observer is developed to estimate the unknown compounded disturbance, and it is established that the estimate error converges to a compact set if appropriate observer design parameters are chosen. Both state feedback and output feedback direct adaptive controls can guarantee semiglobal uniform boundedness of the closed-loop system signals as rigorously proved by Lyapunov analysis. Numerical simulation results are presented to illustrate the effectiveness of the proposed direct adaptive neural control techniques.

Dynamics of random Boolean networks under fully asynchronous stochastic update based on linear representation

A novel algebraic approach is proposed to study dynamics of asynchronous random Boolean networks where a random number of nodes can be updated at each time step (ARBNs). In this article, the logical equations of ARBNs are converted into the discrete-time linear representation and dynamical behaviors of systems are investigated. We provide a general formula of network transition matrices of ARBNs as well as a necessary and sufficient algebraic criterion to determine whether a group of given states compose an attractor of length[Formula: see text] in ARBNs. Consequently, algorithms are achieved to find all of the attractors and basins in ARBNs. Examples are showed to demonstrate the feasibility of the proposed scheme.