Regulation of Markov Jump Linear Systems Subject to Polytopic Uncertainties

• 成果类型: Article
• 署名作者: Bueno, Jose Nuno A. D.; Marcos, Lucas B.; Rocha, Kaio D. T.; Terra, Marco H.
• 署名单位: Universidade de Sao Paulo
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3181567
• 发表日期: 2022
• 页码: 6279-6286
• 关键词: uncertainty; Markov processes; regulation; Numerical stability; Linear systems; CONVERGENCE; Power system stability; discrete-time systems; Markov jump systems; optimization; polytopic uncertainties; Robust control

摘要

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.