Optimal fixed-levels control for nonlinear systems with quadratic cost-functionals

Abstract

SUMMARYThis paper is devoted to general optimal control problems (OCPs) associated with a family of nonlinear continuous-time switched systems in the presence of some specific control constraints. The stepwise (fixed-level type) control restrictions we consider constitute a common class of admissible controls in many real-world engineering systems. Moreover, these control restrictions can also be interpreted as a result of a quantization procedure appglied to the inputs of a conventional dynamic system. We study control systems with a priori given time-driven switching mechanism in the presence of a quadratic cost functional. Our aim is to develop a practically implementable control algorithm that makes it possible to calculate approximating solutions for the class of OCPs under consideration. The paper presents a newly elaborated linear quadratic-type optimal control scheme and also contains illustrative numerical examples.

A separation based optimization approach to Dynamic Maximal Covering Location Problems with switched structure

“…Here z opt j (•), j = 1, ..., n is the j-component of z opt (•). The obtained condition (13) implies that z opt (•) is an admissible solution of the auxiliary problem (5). Sinceẑ is an optimal solution of (5), we get…”

“…Introduction. Applications of diverse methods from the modern Mathematical Optimization Theory and the corresponding numerical techniques are nowadays a usual and efficient approach to the development of engineering applications (see e.g., [7,4,3,5,2,10,11,23,27,33,34]). Optimal facility location methodology, amongst others, plays an important role in a success of Supply Chains and provides an important analytic tool for many real-world manufacturing and service problems [6,8,13,15,17,20,22,25,31,36].…”

“…Note that the existence of optimal solutions to the auxiliary problems (4) and ( 5) is a direct consequence of the general results from [10,23,27]. Let us also underline here that every problem from P r S can be solved independently from problem (5). Therefore, we next define a total optimal vectorŷ(t) ∈ B l for P r S determined by the natural composition…”

“…Byẑ(•), whereẑ(t) ∈ B n andẑ(•) := (ẑ 1 (•), ...,ẑ n (•)) T , we next denote an optimal solution to the auxiliary problem (5). It is easy to see that problem (5) coincides with the originally given DMCLP (1) for the specific case y(•) =ŷ(•).…”

Decentralized finite-horizon suboptimal control for nonlinear interconnected dynamic systems using SDRE approach

“…Optimal control of nonlinear systems is one of the most challenging subjects in control theories (Azhmyakov et al, 2016; Babaie and Ehyaie, 2017; Banks and Mhana, 1992; Kamocki, 2016; Mracek and Cloutier, 1998; Nguyen and Chibani et al, 2016; Gajic, 2010; Primbs et al, 1999; Vamvoudakis and Lewis, 2010; Yucelen et al, 2007). Indeed, the classical problems of optimal control are based on the resolution of the Hamilton–Jacobi equation.…”