Constrained Optimal Control for Nonlinear Multi-Input Safety-Critical Systems with Time-Varying Safety Constraints

Jinguang Wang, Chunbin Qin, Xiaopeng Qiao, Dehua Zhang, Zhongwei Zhang, Ziyang Shang and Heyang Zhu
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Jinguang Wang: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Chunbin Qin: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Xiaopeng Qiao: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Dehua Zhang: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Zhongwei Zhang: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Ziyang Shang: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China
Heyang Zhu: School of Artificial Intelligence, Henan University, Zhengzhou 450000, China

Mathematics, 2022, vol. 10, issue 15, 1-22

Abstract: In this paper, we investigate the constrained optimal control problem of nonlinear multi-input safety-critical systems with uncertain disturbances and time-varying safety constraints. By utilizing a barrier function transformation, together with a new disturbance-related term and a smooth safety boundary function, a nominal system-dependent multi-input barrier transformation architecture is developed to deal with the time-varying safety constraints and uncertain disturbances. Based on the obtained transformation system, the coupled Hamilton–Jacobi–Bellman (HJB) function is established to obtain the constrained Nash equilibrium solution. In addition, due to the fact that it is difficult to solve the HJB function directly, the single critic neural network (NN) is constructed to approximate the optimal performance index function of different control inputs, respectively. It is proved theoretically that, under the influence of uncertain disturbances and time-varying safety constraints, the system states and neural network parameters can be uniformly ultimately bounded (UUB) by the proposed neural network approximation method. Finally, the effectiveness of the proposed method is verified by two nonlinear simulation examples.

Keywords: barrier function; time-varying safety constraints; adaptive dynamic programming; multi-input system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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