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Optimal control for multistage uncertain random dynamic systems with multiple time delays.

Xin Chen¹, Yuanguo Zhu¹

¹School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China.

ISA Transactions

|February 27, 2022

Summary

This summary is machine-generated.

This study introduces uncertain random dynamic systems and proposes a novel method to solve time-delayed optimal control problems. The approach converts delayed problems into non-delayed ones, offering a unified framework for various control types.

Keywords:

Discrete-time dynamic system Optimal control Recursion equations Time delays Uncertain random matrix

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Area of Science:

Control Theory
Stochastic Systems
Dynamic Systems

Background:

Complex systems often exhibit both uncertainty and randomness, termed uncertain random dynamic systems.
Optimal control problems in these systems are challenging, especially with time delays.
Existing methods may not provide a unified framework for discrete-time uncertain random optimal control with time delays.

Purpose of the Study:

To introduce the concept of uncertain random matrices.
To formulate and address time-delayed optimal control problems in uncertain random dynamic systems.
To develop a unified framework and algorithms for solving these problems.

Main Methods:

Formulation of time-delayed uncertain random dynamic systems.
Translation of time-delayed problems into equivalent non-delayed optimization problems.
Application of dynamic programming to solve converted problems via recursion equations.

Main Results:

A novel method is proposed to solve discrete-time uncertain random optimal control problems with time delays.
Three algorithms are developed for linear, quadratic, and cubic controls.
Optimal solutions for numerical examples and a turbofan engine application were obtained.

Conclusions:

The proposed approach provides a unified framework for discrete-time uncertain random optimal control problems with time delays.
The developed algorithms are effective in finding optimal solutions for various control types.
The methodology is applicable to real-world engineering problems, such as turbofan engine control.