Discounted-cost linear quadratic regulation of switched linear systems. Issue 14 (26th October 2022)

• Record Type: Journal Article
• Authors: Xiang, Aoxue; Wang, Siqi; Ma, Ruicheng
• Is Part Of: International journal of systems science. Volume 53:Issue 14(2022)
• Page Start: 3070
• Page End: 3080
• Publication Date: 2022-10-26
• Subjects: Switched linear systems -- linear quadratic regulator -- discounted-cost -- switching signal -- Riccati equation; System analysis -- Periodicals; 003.3
• DOI: 10.1080/00207721.2022.2070791
• Languages: English
• ISSNs: 0020-7721

Abstract

Abstract : This paper investigates the design of discounted-cost linear quadratic regulator for a class of switched linear systems. The distinguishing feature of the proposed method is that the designed discounted-cost linear quadratic regulator achieves not only the desired optimisation index but also the exponentially convergent of the state trajectory of the closed-loop switched linear systems. First, the studied problem is transformed into a quadratic-programming problem by embedding transformation. Then, the bang-bang type solution of the embedded optimal control problem on a finite-time horizon is derived, which is the optimal solution to the original problems. The computable sufficient conditions on discounted-cost linear quadratic regulator are proposed for finite-time and infinite-time horizon cases, respectively. Finally, two examples are provided to demonstrate the effectiveness of the proposed method.