Event-Triggered Robust Adaptive Dynamic Programming for Multiplayer Stackelberg-Nash Games of Uncertain Nonlinear Systems.

This paper addresses the problem of decentralized global stabilization by output feedback for a class of uncertain large-scale nonlinear systems. A new design method based on the homogeneous domination approach and finite-time stabilization technique is developed, which leads to global output feedback stabilization for large-scale uncertain nonlinear systems under a homogeneous growth condition. Firstly, a homogeneous observer and controller is constructed for the nominal system without the perturbing nonlinearities for each subsystem. Then, a scaling gain is introduced into the homogeneous observers and controllers to globally stabilize the uncertain nonlinear systems.

An adaptive command filtered backstepping control design strategy in the presence of quantized states is presented for uncertain nonlinear systems in the strict-feedback form. A uniform quantizer quantizes all state variables, and the quantized state variables are only available for feedback. The existing quantized feedback recursive control design is only applicable to systems with nonlinearities matched to the control input because of its restriction that the partial derivatives of the virtual control laws with respect to state variables should be constants. Compared with the existing result, the primary contribution of this paper is to develop a quantized feedback recursive design using the command filtered backstepping technique for dealing with unmatched nonlinearities without this restriction. An adaptive tracking scheme using quantized states is constructed to compensate for quantization effects, and a new stability analysis strategy is established by analyzing the boundedness of the quantization errors of signals in the command filtered backstepping design framework. The stability of the closed-loop system is analyzed in the sense of uniform ultimate boundedness.

This paper presents a novel decentralized control strategy for a class of uncertain nonlinear large-scale systems with mismatched interconnections. First, it is shown that the decentralized controller for the overall system can be represented by an array of optimal control policies of auxiliary subsystems. Then, within the framework of adaptive dynamic programming, a simultaneous policy iteration (SPI) algorithm is developed to solve the Hamilton–Jacobi–Bellman equations associated with auxiliary subsystem optimal control policies. The convergence of the SPI algorithm is guaranteed by an equivalence relationship. To implement the present SPI algorithm, actor and critic neural networks are applied to approximate the optimal control policies and the optimal value functions, respectively. Meanwhile, both the least squares method and the Monte Carlo integration technique are employed to derive the unknown weight parameters. Furthermore, by using Lyapunov’s direct method, the overall system with the obtained decentralized controller is proved to be asymptotically stable. Finally, the effectiveness of the proposed decentralized control scheme is illustrated via simulations for nonlinear plants and unstable power systems.

Distributed robust event-triggered adaptive control for a class of uncertain nonlinear multi-agent systems with actuator saturation

In this paper, an infinite horizon optimal robust guaranteed cost control scheme of a class of continuous-time uncertain nonlinear systems is established based on adaptive dynamic programming. The main idea lies in that the optimal robust guaranteed cost control problem can be transformed into an optimal control problem. Actually, the optimal cost function of the nominal system is nothing but the optimal guaranteed cost of the original uncertain system. A critic neural network is constructed to help solving the modified Hamilton-Jacobi-Bellman equation corresponding to the nominal system. Then, an additional stabilizing term is introduced to reinforce the updating process of the weight vector and reduce the requirement of an initial stabilizing control. An example is provided to illustrate the effectiveness of the present control approach.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

This article addresses the robust stability for a class of nonlinear uncertain discrete-time systems with convex polytopic of uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic-type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established in terms of linear matrix inequalities. An application to robust stabilization of nonlinear uncertain discrete-time control systems is given. Numerical examples are included to illustrate the effectiveness of our results. MSC:15A09, 52A10, 74M05, 93D05.

This study presents a near‐optimal learning‐based approach for sliding‐mode control of uncertain nonsquare nonlinear systems subject to output constraints. To achieve a compromise between safety and optimality, a reinforcement learning algorithm is proposed to compute the near‐optimal values of the sliding manifold coefficients. In the reinforcement learning algorithm, only measured input‐output data obtained by experiments or simulations are employed. Furthermore, the presented method does not require partial knowledge of the system dynamics to initialize the reinforcement learning process. By employing the tuned sliding vector, an adaptive fuzzy sliding‐mode control (AFSMC) input, including a fuzzy term and a robust term, is generated. The fuzzy term is used to approximate an unknown nonlinear function and the robust term is designed for mismatch compensation. To guarantee that the output constraints are not violated, the adaptation laws for obtaining the fuzzy singletons and the bounds of the approximation errors are designed based on the barrier Lyapunov functions (BLF) theorem. The closed loop asymptotic stability is theoretically analyzed in the article, while the effectiveness of the method is assessed in simulation.

Problem of delay-dependent stability analysis and stabilization for a class of T-S uncertain nonlinear delay systems is dealt with. By constructing new Lyapunov functions based on fuzzy membership functions, the fuzzy weighing matrices and double integrals are introduced. Based on the feasibility solutions of some linear matrix inequalities, the delay-dependent stability criteria and the new stabilization design scheme are derived. Finally, numerical examples are given to show the effectiveness of the results.

Due to the under-actuated feature, the reference signals using the combination of the system outputs, whose number is larger than that of reference signal, are designed so that the number of control inputs and sliding surfaces is the same, and that the uncontrollable mode is indirectly controlled. Under the uncertain environment, the sliding-mode under-actuated control (SMUC) with the satisfaction of suitable condition is designed to asymptotically track the reference signal. Otherwise, a bounded tracking result is obtained for the mild condition. In this situation, an on-line fuzzy modeling for the uncertainty is employed to design a fuzzy model-based sliding-mode under-actuated control (FSMUC) to improve the system performance; e.g., the bounded tracking result of SMUC becomes an asymptotical tracking. The proposed hybrid fuzzy sliding-mode under-actuated control (HFSMUC) combining SMUC and FSMUC with a transition can be applied to a class of generalized, under-actuated and uncertain nonlinear systems, e.g., the trajectory tracking control of a differential mobile robot (DMR). Finally, the simulations of the HFSMUC system are presented to confirm the efficiency and effectiveness of the proposed control.

Distributed adaptive output feedback containment control for time-delay nonlinear multiagent systems

Dual-Condition event-Triggered distributed adaptive neural control for multi-Agent systems with nonlinear fault

A novel theorem for prescribed-time control of nonlinear uncertain time-delay systems

In this paper, we introduce a novel extended sliding mode control algorithm for a class of uncertain nonlinear system through a lumped disturbance estimator. The fundamental concept of this approach is to use multiple proportional-integral sliding surfaces to estimate the lumped disturbances generated by arbitrary matched/mismatched uncertainties. Following, an effectively extended sliding mode controller integrated with the estimated values is designed through the proposed series of sliding-surfaces to deal with the control problem of an uncertain nonlinear engineering model. The stability of both closed-loop control system and lumped disturbance estimator is achieved by Lyapunov theorem. The effectiveness of the proposed approach is demonstrated through simulation results of an illustrative example.

A novel neural network approximation scheme that is especially appropriate for adaptive control of nonlinear dynamical systems is proposed. In light of the new function approximation characterization, a neuro adaptive control framework for continuous- and discrete-time nonlinear uncertain dynamical systems is also presented. Specifically, the proposed neural network control framework is Lyapunov-based and, unlike standard neural network controllers guaranteeing ultimate boundedness, the framework guarantees partial asymptotic stability of the closed-loop system, that is, asymptotic stability with respect to part of the closed-loop system states associated with the system plant dynamics. The neuro adaptive controllers are constructed without requiring explicit knowledge of the system dynamics other than the assumption that the plant dynamics are continuous and piecewise continuously differentiable, and that the approximation error of uncertain system nonlinearities lie in a small gain-type norm bounded conic sector. This allows us to show that the standard neural network controllers are in fact capable of achieving partial asymptotic stability around the system equilibrium point for continuous-and discrete-time uncertain systems.