Abstract
In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.
Highlights
It is ineluctable to contain uncertain parameters and disturbances in practical systems due to modeling errors, external disturbances, and so on [1]
The neural network is utilized to approximate the optimal cost in policy iteration (PI) algorithm, which fulfilled a difficult task of solving the Hamilton Jacobi Bellman (HJB) equation
In order to solve the robust control problem by using Algorithm 1, it is assumed that the optimal cost function V∗(x) has a neural network structure: V∗(x) = WTφ(x), where W = [W1, W2, W3]T, φ(x) = [x12, x1x2, x22]T
Summary
It is ineluctable to contain uncertain parameters and disturbances in practical systems due to modeling errors, external disturbances, and so on [1]. Based on network structure approximation, an online PI algorithm was developed to solve robust control of a class of nonlinear discrete-time uncertain systems in [23]. The online PI algorithms are proposed to calculate robust control by approximating the optimal cost with neural network. For the matched and the mismatched uncertain systems, it is proved that the robust control can be converted into calculating an optimal controller. The neural network is utilized to approximate the optimal cost in PI algorithm, which fulfilled a difficult task of solving the HJB equation. Solving the robust control problem is converted to calculate an optimal control law of a nominal or auxiliary system in Sections 3 and 4. We consider the robust control problem of nonlinear system (1) with matched and mismatched conditions, respectively
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