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Liu, Chongyang; Loxton, Ryan; Teo, Kok Lay

Switching time and parameter optimization in nonlinear switched systems with multiple time-delays. (English) Zbl 1304.49063

J. Optim. Theory Appl. 163, No. 3, 957-988 (2014).
Summary: In this paper, we consider a dynamic optimization problem involving a general switched system that evolves by switching between several subsystems of nonlinear delay-differential equations. The optimization variables in this system consist of: (1) the times at which the subsystem switches occur; and (2) a set of system parameters that influence the subsystem dynamics. We first establish the existence of the partial derivatives of the system state with respect to both the switching times and the system parameters. Then, on the basis of this result, we show that the gradient of the cost function can be computed by solving the state system forward in time followed by a costate system backward in time. This gradient computation procedure can be combined with any gradient-based optimization method to determine the optimal switching times and parameters. We propose an effective optimization algorithm based on this idea. Finally, we consider three numerical examples, one involving the 1,3-propanediol fed-batch production process, to illustrate the effectiveness and applicability of the proposed algorithm.

Cited in 18 Documents

MSC:

49M37 Numerical methods based on nonlinear programming
65K10 Numerical optimization and variational techniques
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
92E20 Classical flows, reactions, etc. in chemistry

Keywords:

switched systems; time-delay system; nonlinear optimization

Software:

NLPQLP
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\textit{C. Liu} et al., J. Optim. Theory Appl. 163, No. 3, 957--988 (2014; Zbl 1304.49063)
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