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Model-Free Adaptive Near-Optimal Tracking Control

  • Yinyan Zhang
  • Shuai LiEmail author
  • Xuefeng Zhou
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 265)

Abstract

In this chapter, the receding-horizon near-optimal tracking control problem about a class of continuous-time nonlinear systems with fully unknown dynamics are considered. The main challenges of this problem lie in two aspects: (1) Most existing systems only restrict their considerations to the state feedback part while the input channel parameters are assumed to be known. This chapter considers fully unknown system dynamics in both the state feedback channel and the input channel. (2) The optimal control of nonlinear systems requires the solution of nonlinear Hamilton–Jacobi–Bellman equations. Up to today, there are no systematic approaches in the existing literature to solve it accurately. A novel model-free adaptive near-optimal control method is presented to solve this problem by utilizing the Taylor expansion based problem relaxation, the universal approximation property of sigmoid neural networks, and the concept of sliding mode control. By making an approximation for the performance index, it is first relaxed to a quadratic program, and then a linear algebraic equation with unknown terms. An auxiliary system is designed to reconstruct the input-to-output property of the control systems with unknown dynamics, so as to tackle the difficulty caused by the unknown terms. Then, by considering the property of the sliding mode surface, an explicit adaptive near-optimal control law is derived from the linear algebraic equation. Theoretical analysis shows that the auxiliary system is convergent, the resultant closed-loop system is asymptotically stable, and the performance index asymptomatically converges to optimal. An illustrative example and experimental results are presented, which substantiate the efficacy of the presented method and verify the theoretical results.

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.College of Cyber SecurityJinan UniversityGuangzhouChina
  2. 2.School of Information Science and EngineeringLanzhou UniversityLanzhouChina
  3. 3.Guangdong Institute of Intelligent ManufacturingGuangdong Academy of ScienceGuangzhouChina

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