Regulation of Markov Jump Linear Systems Subject to Polytopic Uncertainties

Author(s)

Bueno, Jose Nuno A. D. ; Marcos, Lucas B. ; Rocha, Kaio D. T. ; Terra, Marco H.

• Document type: Journal article
• Source: IEEE Transactions on Automatic Control; v. 67, n. 11, p. 8-pg., 2022-11-01.

Abstract

When discrete-time Markov jump linear systems are prone to the damaging effects of polytopic uncertainties, it is necessary to address all the vertices of each Markov mode in order to properly design robust controllers. To this end, we propose a robust recursive linear-quadratic regulator for this class of systems. We define a quadratic min-max optimization problem by combining least-squares and penalty functions in a unified framework. We design a one-step cost function to encompass the entire set of vertices of each mode altogether, while maintaining its quadratic structure and the convexity of the problem. The solution is then obtained recursively and does not require numerical optimization packages. We establish conditions for convergence and stability by extending the matrix structure of the recursive solution. In addition, we provide numerical and real-world application examples to validate our method and to emphasize recursiveness and diminished computational effort. (AU)

• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 21/08103-0 - Cooperative autonomous control of heterogeneous vehicle systems
• Grantee: Lucas Barbosa Marcos
• Support Opportunities: Scholarships in Brazil - Technical Training Program - Technical Training
• FAPESP's process: 17/16346-4 - Communication network fault tolerant control for coordinated movement of heterogeneous robots
• Grantee: Kaio Douglas Teófilo Rocha
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)