Neural adaptive chaotic control with constrained input using state and output feedback

This paper presents neural adaptive control methods for a class of chaotic nonlinear systems in the presence of constrained input and unknown dynamics. To attenuate the influence of constrained input caused by actuator saturation, an effective auxiliary system is constructed to prevent the stability of closed loop system from being destroyed. Radial basis function neural networks（RBF-NNs） are used in the online learning of the unknown dynamics, which do not require an off-line training phase. Both state and output feedback control laws are developed. In the output feedback case, high-order sliding mode（HOSM） observer is utilized to estimate the unmeasurable system states. Simulation results are presented to verify the effectiveness of proposed schemes.

Dynamic Event-Triggered Consensus Control for Input Constrained Multi-Agent Systems With a Designable Minimum Inter-Event Time

This paper investigates the consensus control of multi-agent systems(MASs) with constrained input using the dynamic event-triggered mechanism(ETM).Consider the MASs with small-scale networks where a centralized dynamic ETM with global information of the MASs is first designed.Then,a distributed dynamic ETM which only uses local information is developed for the MASs with large-scale networks.It is shown that the semi-global consensus of the MASs can be achieved by the designed bounded control protocol where the Zeno phenomenon is eliminated by a designable minimum inter-event time.In addition,it is easier to find a trade-off between the convergence rate and the minimum inter-event time by an adjustable parameter.Furthermore,the results are extended to regional consensus of the MASs with the bounded control protocol.Numerical simulations show the effectiveness of the proposed approach.

STABILIZATION OF SWITCHED LINEAR SYSTEMS WITH CONSTRAINED INPUTS

The stabilization of switched linear systems with constrained inputs （SLSCI） is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time （MDT） to stabilized the system. First, for each subsystem with constrained inputs, a stabilizing linear state feedback and an invariant set of the closed-loop system are simultaneously constructed, such that the input constraints are satisfied if and only if the closed-loop system＇s states lie inside this set. Then, by constructing a quadratic Lyapunov function for each closed-loop subsystem, an MDT is deduced and an MDT-based switching strategy is presented to ensure the stability of the switched system.

Neural-Network-Based Control for Discrete-Time Nonlinear Systems with Input Saturation Under Stochastic Communication Protocol

In this paper,an adaptive dynamic programming(ADP)strategy is investigated for discrete-time nonlinear systems with unknown nonlinear dynamics subject to input saturation.To save the communication resources between the controller and the actuators,stochastic communication protocols(SCPs)are adopted to schedule the control signal,and therefore the closed-loop system is essentially a protocol-induced switching system.A neural network(NN)-based identifier with a robust term is exploited for approximating the unknown nonlinear system,and a set of switch-based updating rules with an additional tunable parameter of NN weights are developed with the help of the gradient descent.By virtue of a novel Lyapunov function,a sufficient condition is proposed to achieve the stability of both system identification errors and the update dynamics of NN weights.Then,a value iterative ADP algorithm in an offline way is proposed to solve the optimal control of protocol-induced switching systems with saturation constraints,and the convergence is profoundly discussed in light of mathematical induction.Furthermore,an actor-critic NN scheme is developed to approximate the control law and the proposed performance index function in the framework of ADP,and the stability of the closed-loop system is analyzed in view of the Lyapunov theory.Finally,the numerical simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

Event-triggered H_(∞) consensus control for input-constrained multi-agent systems via reinforcement learning

This article presents an event-triggered H_(∞) consensus control scheme using reinforcement learning (RL) for nonlinear second-order multi-agent systems (MASs) with control constraints. First, considering control constraints, the constrained H_(∞) consensus problem is transformed into a multi-player zero-sum game with non-quadratic performance functions. Then, an event-triggered control method is presented to conserve communication resources and a new triggering condition is developed for each agent to make the triggering threshold independent of the disturbance attenuation level. To derive the optimal controller that can minimize the cost function in the case of worst disturbance, a constrained Hamilton–Jacobi–Bellman (HJB) equation is defined. Since it is difficult to solve analytically due to its strongly non-linearity, reinforcement learning (RL) is implemented to obtain the optimal controller. In specific, the optimal performance function and the worst-case disturbance are approximated by a time-triggered critic network;meanwhile, the optimal controller is approximated by event-triggered actor network. After that, Lyapunov analysis is utilized to prove the uniformly ultimately bounded (UUB) stability of the system and that the network weight errors are UUB. Finally, a simulation example is utilized to demonstrate the effectiveness of the control strategy provided.

Neural network solution for finite-horizon H-infinity constrained optimal control of nonlinear systems

In this paper, neural networks are used to approximately solve the finite-horizon constrained input H-infinity state feedback control problem. The method is based on solving a related Hamilton-Jacobi-Isaacs equation of the corresponding finite-horizon zero-sum game. The game value function is approximated by a neural network with time- varying weights. It is shown that the neural network approximation converges uniformly to the game-value function and the resulting almost optimal constrained feedback controller provides closed-loop stability and bounded L2 gain. The result is an almost optimal H-infinity feedback controller with time-varying coefficients that is solved a priori off-line. The effectiveness of the method is shown on the Rotational/Translational Actuator benchmark nonlinear control problem.

Receding horizon H_∞ control for constrained time-delay systems

A receding horizon Hoo control algorithm is presented for linear discrete time-delay system in the presence of constrained input and disturbances. Disturbance attenuation level is optimized at each time instant, and the receding optimization problem includes several linear matrix inequality constraints. When the convex hull is applied to denote the saturating input, the algorithm has better performance. The numerical example can verify this result.