Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 29, Issue 12, Pages 6227-6241Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2018.2828114
Keywords
Model-free adaptive control; neural network; optimal control; sliding mode control; universal approximation
Categories
Funding
- NSERC of Canada
- National Natural Science Foundation of China [61401385]
- Hong Kong Research Grants Council Early Career Scheme [25214015]
- Departmental General Research Fund of Hong Kong Polytechnic University [G.61.37.UA7L]
- PolyU Central Research under Grant G-YBMU
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In this paper, the receding horizon near-optimal tracking control problem about a class of continuous-time nonlinear systems with fully unknown dynamics is 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 paper considers fully unknown system dynamics in both the state feedback channel and the input channel and 2) the optimal control of nonlinear systems requires the solution of nonlinear Hamilton-Jacobi-Bellman equations. Up to date, there are no systematic approaches in the existing literature to solve it accurately. A novel model-free adaptive near-optimal control method is proposed to solve this problem via utilizing the Taylor expansion-based problem relaxation, the universal approximation property of sigmoid neural networks, and the concept of sliding mode control. By making 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 proposed method and verify the theoretical results.
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