Switching Time and Parameter Optimization in Nonlinear Switched Systems with Multiple Time-Delays

Chongyang Liu (), Ryan Loxton () and Kok Lay Teo ()
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Chongyang Liu: Shandong Institute of Business and Technology
Ryan Loxton: Curtin University
Kok Lay Teo: Zhejiang University

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 3, No 15, 957-988

Abstract: Abstract 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.

Keywords: Switched system; Time-delay system; Switching times; Nonlinear optimization; 49M07; 49M37; 65K10 (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-014-0533-7

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