Related papers: Relaxation Methods for Mixed-Integer Optimal Contr…
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
In this paper we study the approximate controllability and existence of optimal control of impulsive fractional semilinear delay differential equations with non-local conditions. We use Sadovskii's fixed point theorem, semigroup theory of…
This paper studies an optimal control problem governed by a semilinear elliptic equation, in which the control acts in a multiplicative or bilinear way as the reaction coefficient of the equation. We focus on the numerical discretization of…
We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the…
We consider a class of (ill-posed) optimal control problems in which a distributed vector-valued control is enforced to pointwise take values in a finite set $\mathcal{M}\subset\mathbb{R}^m$. After convex relaxation, one obtains a…
The relaxation complexity rc(X) of the set of integer points X contained in a polyhedron is the minimal number of inequalities needed to formulate a linear optimization problem over X without using auxiliary variables. Besides its relevance…
We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
The present paper deals with the data-driven design of regularizers in the form of artificial neural networks, for solving certain inverse problems formulated as optimal control problems. These regularizers aim at improving accuracy,…
It is well-known that by adding integrality constraints to the semidefinite programming (SDP) relaxation of the max-cut problem, the resulting integer semidefinite program is an exact formulation of the problem. In this paper we show…
In this paper we investigate an adaptive discretization strategy for ill-posed linear prob- lems combined with a regularization from a class of semiiterative methods. We show that such a discretization approach in combination with a…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
We consider constrained bilinear optimal control of second-order linear evolution partial differential equations (PDEs) with a reaction term on the half line, where control arises as a time-dependent reaction coefficient and constraints are…
Mixed integer predictive control deals with optimizing integer and real control variables over a receding horizon. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this…
This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…
This paper deals with distributed control of microgrids composed of storages, generators, renewable energy sources, critical and controllable loads. We consider a stochastic formulation of the optimal control problem associated to the…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
Several dynamical systems in fields such as engineering, chemistry, biology, and physics show impulsive behavior by reason of unexpected changes at specific times. These behaviors are described by differential systems under impulse effects.…