Optimal control of discrete-time switched linear systems via continuous parameterization
This work addresses the high computational cost of optimal control for switched linear systems, which is a key bottleneck in control theory.
The paper introduces a continuous parameterization method for optimal control of discrete-time switched linear systems, reducing computational complexity by avoiding exhaustive exploration of switching sequences. The method solves a non-smooth block-sparsity optimization problem to jointly optimize mode and input sequences.
The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly minimize a quadratic performance index. State-of-art methods for solving such a control problem suffer in general from a high computational requirement due to the fact that an exponential number of switching sequences must be explored. The method of this paper addresses the challenge of the switching law design by introducing auxiliary continuous input variables and then solving a non-smooth block-sparsity inducing optimization problem.