State-of-the-art in artificial neural network applications: A survey

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L2 Gain And Passivity Techniques In Nonlinear Control

This paper is concerned with a new discrete-time policy iteration adaptive dynamic programming (ADP) method for solving the infinite horizon optimal control problem of nonlinear systems. The idea is to use an iterative ADP technique to obtain the iterative control law, which optimizes the iterative performance index function. The main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete-time nonlinear systems for the first time. It shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the Hamilton-Jacobi-Bellman equation. It is also proven that any of the iterative control laws can stabilize the nonlinear systems. Neural networks are used to approximate the performance index function and compute the optimal control law, respectively, for facilitating the implementation of the iterative ADP algorithm, where the convergence of the weight matrices is analyzed. Finally, the numerical results and analysis are presented to illustrate the performance of the developed method.

http://www.derongliu.org/papers/liu-wei-TNNLS-mar-2014.pdf

Policy Iteration Adaptive Dynamic Programming Algorithm for Discrete-Time Nonlinear Systems

Optimal tracking control of nonlinear partially-unknown constrained-input systems using integral reinforcement learning

In order to stabilize a class of uncertain nonlinear strict-feedback systems with full-state constraints, an adaptive neural network control method is investigated in this paper. The state constraints are frequently emerged in the real-life plants and how to avoid the violation of state constraints is an important task. By introducing a barrier Lyapunov function (BLF) to every step in a backstepping procedure, a novel adaptive backstepping design is well developed to ensure that the full-state constraints are not violated. At the same time, one remarkable feature is that the minimal learning parameters are employed in BLF backstepping design. By making use of Lyapunov analysis, we can prove that all the signals in the closed-loop system are semiglobal uniformly ultimately bounded and the output is well driven to follow the desired output. Finally, a simulation is given to verify the effectiveness of the method.

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

The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem The constrained-input coupled with the inability to identify accurately the uncertainties motivates the design of stabilizing controller based on reinforcement-learning (RL) methods In this paper, a novel RL-based robust adaptive control algorithm is developed for a class of continuous-time uncertain nonlinear systems subject to input constraints The robust control problem is converted to the constrained optimal control problem with appropriately selecting value functions for the nominal system Distinct from typical action-critic dual networks employed in RL, only one critic neural network (NN) is constructed to derive the approximate optimal control Meanwhile, unlike initial stabilizing control often indispensable in RL, there is no special requirement imposed on the initial control By utilizing Lyapunov’s direct method, the closed-loop optimal control system and the estimated weights of the critic NN are proved to be uniformly ultimately bounded In addition, the derived approximate optimal control is verified to guarantee the uncertain nonlinear system to be stable in the sense of uniform ultimate boundedness Two simulation examples are provided to illustrate the effectiveness and applicability of the present approach

Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints

In this paper, the infinite horizon optimal robust guaranteed cost control of continuous-time uncertain nonlinear systems is investigated using neural-network-based online solution of Hamilton–Jacobi–Bellman (HJB) equation. By establishing an appropriate bounded function and defining a modified cost function, the optimal robust guaranteed cost control problem is transformed into an optimal control problem. It can be observed that 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 facilitate the solution of the modified HJB equation corresponding to the nominal system. More importantly, an additional stabilizing term is introduced for helping to verify the stability, which reinforces the updating process of the weight vector and reduces the requirement of an initial stabilizing control. The uniform ultimate boundedness of the closed-loop system is analyzed by using the Lyapunov approach as well. Two simulation examples are provided to verify the effectiveness of the present control approach.

Neural-Network-Based Online HJB Solution for Optimal Robust Guaranteed Cost Control of Continuous-Time Uncertain Nonlinear Systems

In this paper, an adaptive reinforcement learning-based solution is developed for the infinite-horizon optimal control problem of constrained-input continuous-time nonlinear systems in the presence of nonlinearities with unknown structures. Two different types of neural networks (NNs) are employed to approximate the Hamilton-Jacobi-Bellman equation. That is, an recurrent NN is constructed to identify the unknown dynamical system, and two feedforward NNs are used as the actor and the critic to approximate the optimal control and the optimal cost, respectively. Based on this framework, the action NN and the critic NN are tuned simultaneously, without the requirement for the knowledge of system drift dynamics. Moreover, by using Lyapunov's direct method, the weights of the action NN and the critic NN are guaranteed to be uniformly ultimately bounded, while keeping the closed-loop system stable. To demonstrate the effectiveness of the present approach, simulation results are illustrated.

Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints

In this paper, a new iterative adaptive dynamic programming (ADP) algorithm is developed to solve optimal control problems for infinite horizon discrete-time nonlinear systems with finite approximation errors. First, a new generalized value iteration algorithm of ADP is developed to make the iterative performance index function converge to the solution of the Hamilton–Jacobi–Bellman equation. The generalized value iteration algorithm permits an arbitrary positive semi-definite function to initialize it, which overcomes the disadvantage of traditional value iteration algorithms. When the iterative control law and iterative performance index function in each iteration cannot accurately be obtained, for the first time a new “design method of the convergence criteria” for the finite-approximation-error-based generalized value iteration algorithm is established. A suitable approximation error can be designed adaptively to make the iterative performance index function converge to a finite neighborhood of the optimal performance index function. Neural networks are used to implement the iterative ADP algorithm. Finally, two simulation examples are given to illustrate the performance of the developed method.

Finite-Approximation-Error-Based Discrete-Time Iterative Adaptive Dynamic Programming

In this paper, a novel iterative adaptive dynamic programming (ADP)-based infinite horizon self-learning optimal control algorithm, called generalized policy iteration algorithm, is developed for nonaffine discrete-time (DT) nonlinear systems. Generalized policy iteration algorithm is a general idea of interacting policy and value iteration algorithms of ADP. The developed generalized policy iteration algorithm permits an arbitrary positive semidefinite function to initialize the algorithm, where two iteration indices are used for policy improvement and policy evaluation, respectively. It is the first time that the convergence, admissibility, and optimality properties of the generalized policy iteration algorithm for DT nonlinear systems are analyzed. Neural networks are used to implement the developed algorithm. Finally, numerical examples are presented to illustrate the performance of the developed algorithm.

Xiong Yang

Papers

Reinforcement-Learning-Based Robust Controller Design for Continuous-Time Uncertain Nonlinear Systems Subject to Input Constraints

Neural-Network-Based Online HJB Solution for Optimal Robust Guaranteed Cost Control of Continuous-Time Uncertain Nonlinear Systems

Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints

Finite-Approximation-Error-Based Discrete-Time Iterative Adaptive Dynamic Programming

Infinite Horizon Self-Learning Optimal Control of Nonaffine Discrete-Time Nonlinear Systems