Indefinite LQ optimal control with process state inequality constraints for discrete-time uncertain systems

Yuefen Chen; Yuanguo Zhu

doi:10.3934/jimo.2017082

Article Contents

2018, Volume 14, Issue 3: 913-930. Doi: 10.3934/jimo.2017082

This issue Previous Article On optimality conditions and duality for non-differentiable interval-valued programming problems with the generalized (F, ρ)-convexity Next Article Analysis of the Newsboy Problem subject to price dependent demand and multiple discounts

Indefinite LQ optimal control with process state inequality constraints for discrete-time uncertain systems

Yuefen Chen^1, and
Yuanguo Zhu^2, ,

1.
School of Mathematics and Statistics, Xinyang Normal University, Xinyang, Henan 464000, China
2.
School of Science, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China

* Corresponding author: ygzhu@njust.edu.cn
* Corresponding author: ygzhu@njust.edu.cn

Received: February 2016

Revised: August 2017

Early access: August 2017

Published: June 2018

This work is supported by the National Natural Science Foundation of China (No.61673011), the Nanhu Scholars Program for Young Scholars of XYNU and the Key Scientific Research Project for Colleges and Universities of Henan Province (No.17A120013).

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Abstract

Uncertainty theory is a branch of axiomatic mathematics that deals with human uncertainty. Based on uncertainty theory, this paper discusses linear quadratic (LQ) optimal control with process state inequality constraints for discrete-time uncertain systems, where the weighting matrices in the cost function are assumed to be indefinite. By means of the maximum principle with mixed inequality constraints, we present a necessary condition for the existence of optimal state feedback control that involves a constrained difference equation. Moreover, the existence of a solution to the constrained difference equation is equivalent to the solvability of the indefinite LQ problem. Furthermore, the well-posedness of the indefinite LQ problem is proved. Finally, an example is provided to demonstrate the effectiveness of our theoretical results.

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Mathematics Subject Classification: Primary: 49N10, 49L20; Secondary: 65K05.

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