Model Predictive Control of Switched Linear Systems With Persistent Dwell-Time Constraints: Recursive Feasibility and Stability

• Published in: IEEE transactions on automatic control Vol. 68; no. 12; pp. 1 - 8
• Main Authors: Zhuang, Songlin, Gao, Huijun, Shi, Yang
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Control systems; Dwell time; Feasibility; Linear systems; Mixed integer; Model predictive control; Nonlinear programming; Numerical stability; Optimization; persistent dwell-time; Polynomials; Predictive control; recursive feasibility and stability; Stability criteria; switched system; Switched systems; Switches; Switching sequences; Time factors
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3248279

This paper develops a model predictive control (MPC) framework to co-optimize switching sequences and control inputs for switched linear systems subject to persistent dwell-time (PDT) constraints. As a class of time constraints, PDT has been demonstrated to be more general and flexible than others like dwell-time or average dwell-time. Although time constraints are widely used in applications for safety and stability concerns, MPC of switched systems with time constraints often formulates a mixed- integer nonlinear program which cannot obtain the optimal solution in polynomial time, and thus suffers from the loss of recursive feasibility and stability. To address this problem, we propose several novel techniques: (i) the construction of the terminal sets based on two constraint admissible PDT contractive sets, (ii) the introduction of PDT and historical constraints, (iii) the use of two non-globally optimal solutions, and (iv) the prolonged prediction horizon. It is the first time that MPC approaches are applied to the co-optimization problem of switched systems under time constraints with guaranteed recursive feasibility and stability.