As the core of modern control, the optimal control with the objective of optimizing the performance index function has always been the focus of mathematicians and engineers. However, due to the complexity of practical systems and the uncertainty of the practical environment, such as input constraints and external disturbances, the formula of the optimal controller cannot always be explicitly expressed. In addition, the optimal control problem in the infinite time domain relies on solving the partial differential equations: Hamilton-Jacobi-Bellman (HJB) equation, which is a complex partial differential equation that cannot be explicitly solved so far. The practice’s uncertainty and the HJB equation’s complexity make the optimal controller’s analytical solutions almost unsolvable. Therefore, this paper proposes an evolutionary pre-trained optimal feedback control method: the evolutionary optimal constraint control (EOCC) algorithm. The EOCC algorithm learns and identifies the uncertainty of the system online by constructing neural networks and auxiliary states, and then calculates the optimal learning rate by optimizing a finite time domain optimal control problem using our proposed improved evolutionary algorithms operator. The experimental results indicate that the infinite time domain performance index function can be well optimized if the pre-trained time domain includes the relatively long stable phase of the system.

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Evolutionary Approach for Infinite Time Domain Optimal Control Problems Under Multiple Constraints and Uncertainty

  • Xinyu Qiu

摘要

As the core of modern control, the optimal control with the objective of optimizing the performance index function has always been the focus of mathematicians and engineers. However, due to the complexity of practical systems and the uncertainty of the practical environment, such as input constraints and external disturbances, the formula of the optimal controller cannot always be explicitly expressed. In addition, the optimal control problem in the infinite time domain relies on solving the partial differential equations: Hamilton-Jacobi-Bellman (HJB) equation, which is a complex partial differential equation that cannot be explicitly solved so far. The practice’s uncertainty and the HJB equation’s complexity make the optimal controller’s analytical solutions almost unsolvable. Therefore, this paper proposes an evolutionary pre-trained optimal feedback control method: the evolutionary optimal constraint control (EOCC) algorithm. The EOCC algorithm learns and identifies the uncertainty of the system online by constructing neural networks and auxiliary states, and then calculates the optimal learning rate by optimizing a finite time domain optimal control problem using our proposed improved evolutionary algorithms operator. The experimental results indicate that the infinite time domain performance index function can be well optimized if the pre-trained time domain includes the relatively long stable phase of the system.