2026· The Bulletin of Irkutsk State University. Series Mathematics· 0 citations
Abstract
A linear-quadratic problem of optimal control in a discrete-time formulation and multi-objective setting is considered: a linear system, a set of quadratic objective functions in state and control variables, multi-objective optimization, and Pareto-optimal solutions. Based on a linear scalarization of criteria, a reduction to a parametric scalar optimization problem is performed, requiring a global solution without any convexity assumptions. The dependence of the aggregate objective function on state variables is eliminated. Using extremal eigenvalues, conditions on the parameters that ensure the convexity property in the scalar problem are formulated. Furthermore, two optimization problems with respect to the parameters are announced; these problems improve the defining matrix of the resulting quadratic form in terms of conditioning and convergence. As a result of the proposed regularization procedure, a family of multi-extremal problems is reduced to convex programming problems with a quadratic objective function that admit a guaranteed solution. This solution constitutes a Pareto-optimal control for the original non-convex linear-quadratic problem.
The main purpose of this paper is to establish the local quadratic convergence of Newton's method for nonlinear optimal control problems. Under suitable smoothness assumptions, the cost functional is first shown to be twice G{\^a}teaux differentiable with respect to the control. An explicit operator representation of i...
This article addresses a linear‐quadratic (LQ) optimal control problem over the infinite horizon for discrete‐time deterministic systems, where the dynamic system contains the control and state variables. For classical deterministic LQ optimal control problems, it is commonly assumed to be
regular
, that is, the...
Chen-Chen Peng, Ze-He Lu, An-Qing Yang et al.· Optimal control applications...· 0 citations
In this work, the well-posedness and attainability of a finite horizon time linear quadratic (LQ) optimal control problem for a class of McKean–Vlasov stochastic linear differential equations controlled by impulses are addressed. No assumption regarding the sign of the weighting matrices involved in the performance cri...
We study an inverse optimal-control problem for identifying nonnegative weights in a convex-feature lower-level objective. The resulting model is an optimistic bilevel optimal-control problem whose lower level is a strongly convex, linearly constrained control problem with box constraints in \(L^2\). For the reduced re...
An analytical and numerical solution of the optimal controlling of a linear dynamic system with quadratic functional, fixed endpoints, constraint on control and quadratic phase constraint are obtained. The difficulties of studying and numerical solving such problems are related, firstly, to the problem of matching sect...
E. Shipilova, A. Tarakanov· Modeling of systems and proc...· 0 citations
This work studies a regularization procedure whose goal is the approximation of a solution to a bilevel optimization problem where the lower-level problem is formulated as an optimal control problem. This is done by regularizing the lower-level problem in such a way that an optimal control to the regularized problem ca...
T. Bayen, F. Mairet· Journal of Convex Analysis· 0 citations
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