Switching time optimization for nonlinear switched systems: direct optimization and the time-scaling transformation. (English) Zbl 1305.49042

Loxton, Ryan; Lin, Qun; Teo, Kok Lay

Pac. J. Optim. 10, No. 3, 537-560 (2014).

This important work investigates the problem of choosing optimal values for the switching times so that the switched system under consideration operates in the best possible manner. The STO problem is a type of nonlinear optimization problem in which a finite number of decision variables (the switching times) need to be chosen to minimize a given cost function (typically a function of the final state reached by the system). In principle the proposed problem can be solved using standard nonlinear optimization methods, e.g. sequential quadratic programming. But such methods rely on the gradient of the cost function, which is difficult to compute in the STO problem because of the presence of dynamic constraints. A typical nonlinear switched system in described mathematically in the presented paper.

Reviewer: Jan Lovíšek (Bratislava)

MSC:

49M37	Numerical methods based on nonlinear programming
93C30	Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
90C30	Nonlinear programming
93C65	Discrete event control/observation systems
93B51	Design techniques (robust design, computer-aided design, etc.)

Keywords:

switched system; switching times; time-scaling transformation; gradient-based optimization; STO problem; variational method; indirect optimization; numerical comuptation; Gronwal-Bellman inequality