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Event-Triggered Nonlinear \(H_{\infty }\) Control Design via an Improved Critic Learning Strategy

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Adaptive Critic Control with Robust Stabilization for Uncertain Nonlinear Systems

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 167))

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Abstract

In this chapter, we aim at improving the critic learning criterion to cope with the event-based nonlinear \(H_{\infty }\) state feedback control design. First of all, the \(H_{\infty }\) control problem is regarded as a two-player zero-sum game and the adaptive critic mechanism is used to achieve the minimax optimization under event-based environment. Then, based on an improved updating rule, the event-based optimal control law and the time-based worst-case disturbance law are obtained approximately by training a single critic neural network. The initial stabilizing control is no longer required during the implementation process of the new algorithm. Next, the closed-loop system is formulated as an impulsive model and its stability issue is handled by incorporating the improved learning criterion. The infamous Zeno behavior of the present event-based design is also avoided through theoretical analysis on the lower bound of the minimal inter-sample time. Finally, the applications to an aircraft dynamics and a robot arm plant are carried out to verify the efficient performance of the present novel design method.

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Authors and Affiliations

  1. The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing, China

    Ding Wang

  2. School of Electrical and Information Engineering, Tianjin University, Tianjin, China

    Chaoxu Mu

Authors
  1. Ding Wang
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  2. Chaoxu Mu
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Correspondence to Ding Wang .

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Wang, D., Mu, C. (2019). Event-Triggered Nonlinear \(H_{\infty }\) Control Design via an Improved Critic Learning Strategy. In: Adaptive Critic Control with Robust Stabilization for Uncertain Nonlinear Systems. Studies in Systems, Decision and Control, vol 167. Springer, Singapore. https://doi.org/10.1007/978-981-13-1253-3_8

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