Abstract
The indefinite linear quadratic (ILQ) optimal control problem has many important applications in financial, economic systems, etc., which has been widely researched in stochastic systems and descriptor systems, etc. However, for ILQ problem of rectangular descriptor Markov jump systems (DMJSs), because there are impulses simultaneously in descriptor subsystems and at the switching time, it is theoretically difficult to research and there is no result yet. This paper discusses the ILQ optimal control problem for continuous-time linear rectangular DMJSs. Firstly, under some rank conditions and inequality conditions, the ILQ problem for rectangular DMJSs can be equivalently transformed into standard LQ problem for Markov jump systems (MJSs) by using elementary linear algebra method. Then based on the LQ theory of MJSs, the solvable sufficient condition of the ILQ problem for rectangular DMJSs and the non-negative optimal cost value are obtained. The optimal control can be synthesised as state feedback, and the resulting optimal closed-loop system has the stochastically stable solution. In addition, with some rank inequality assumptions, the differential subsystem of the resulting optimal closed-loop system can be ensured to have a unique solution. Finally, two numerical examples are provided to illustrate the effectiveness of the methods proposed in this paper.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
