Towards global solutions of optimal discrete‐valued control problems

Abstract

This paper proposes a new heuristic approach for solving optimal discrete-valued control problems. We illustrate the approach with an existing hybrid power system model. The problem of choosing an operating schedule to minimize generator, battery, and switching costs is first posed as a mixed discrete dynamic optimization problem. Then, a discrete filled function method is employed in conjunction with a computational optimal control technique to solve this problem. Computational results indicate that this approach is robust, efficient, and can successfully identify a near-global solution for this complex applied optimization problem despite the presence of multiple local optima.

Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

“…Strictly speaking, the standard control parameterization and time-scaling techniques are not applicable to optimal control problems governed by internally forced switched systems, as the dynamics in such systems depend discontinuously on the system state. Nevertheless, many researchers, including the authors of this paper, have ignored this restriction and applied control parameterization and the time-scaling transformation directly to optimal control problems subject to internally forced switched systems; see [41,47,64] for example. An interesting avenue for future research would be to study the ramifications of this (potentially invalid) approach.…”

“…In the bilevel optimization approach [63,64,68], the switched system optimal control problem is decomposed into the following bilevel form: u, ζ , τ , v). (5.8) There are two levels of minimization in (5.8): in the outer level, the switching sequence is optimized; in the inner level, the switching sequence is fixed, while the control function, parameter vector, and subsystem switching times are optimized subject to the canonical constraints (2.6) and the continuous inequality constraints (2.7).…”

“…To minimize J (v) in the outer level minimization, discrete optimization techniques, such as particle swarm optimization [13] or the filled function method [65,74], must be applied. For more details, see [63,64,68].…”

Global Uniform Asymptotic Stability of a Class of Switched Linear Systems with an Infinite Number of Subsystems

“…Since switched systems are used in many applications such as robotics, integrated circuit design, manufacturing, power electronics, switched-capacitor networks, chaos generators, and automated highway systems, some applications for linear or nonlinear switched systems have been further investigated, and many valuable results and simulations have been obtained; see [17][18][19][20] and some references therein.…”

“…In [19] an approach with an existing hybrid power system model was explained. The problem of choosing an operating schedule to minimize generator, battery, and switching costs was first posed as a mixed discrete dynamic optimization problem.…”