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In this work, we consider optimality conditions of an optimal control problem governed by an obstacle problem. Here, we focus on introducing a, matrix valued, control variable as the coefficients of the obstacle problem. As it is well…
The main goal of this paper is to investigate strong duality of non-convex semidefinite programming problems (SDPs). In the optimization community, it is well-known that a convex optimization problem satisfies strong duality if the Slater's…
We present a unified treatment to control problems on an arbitrary time scale by introducing the study of forward-backward optimal control problems. Necessary optimality conditions for delta-nabla isoperimetric problems are proved, and…
In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and…
This paper is concerned with providing the maximum principle for a control problem governed by a stochastic evolution system on a separable Hilbert space. In particular, necessary conditions for optimality for this stochastic optimal…
This paper explores a class of fully coupled nonlinear forward-backward stochastic difference equations (FBS$\Delta$Es). Building on insights from linear quadratic optimal control problems, we introduce a more relaxed framework of…
We describe the relation between block Jacobi matrices and minimization problems for discrete time optimal control problems. Using techniques developed for the continuous case, we provide new algorithms to compute spectral invariants of…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…
This work concentrates on a class of optimal control problems for semilinear parabolic equations subject to control constraint of the form $\|u(t)\|_{L^1(\Omega)} \le \gamma$ for $t \in (0,T)$. This limits the total control that can be…
This paper is devoted to the study, for the first time in the literature, of optimal control problems for sweeping processes governed by integro-differential inclusions of the Volterra type with different classes of control functions acting…
Finite-time linear-quadratic control of partial differential-algebraic equations (PDAEs) is considered. The discussion is restricted to those that are radial with index $0$; this corresponds to a nilpotency degree of 1. We establish the…
In this paper, we provide conditions under which one can take derivatives of the solution to convex optimization problems with respect to problem data. These conditions are (roughly) that Slater's condition holds, the functions involved are…
This paper introduces the notion of state constraints for optimal control problems governed by fractional elliptic PDEs of order $s \in (0,1)$. There are several mathematical tools that are developed during the process to study this…
We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
Reliable optimal control is challenging when the dynamics of a nonlinear system are unknown and only infrequent, noisy output measurements are available. This work addresses this setting of limited sensing by formulating a Bayesian prior…
We consider a broker who has to place a large order which consumes a sizable part of average daily trading volume. The broker's aim is thus to minimize execution costs he incurs from the adverse impact of his trades on market prices. By…
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
Optimality is a critical aspect of Model Predictive Control (MPC), especially in economic MPC. However, achieving optimality in MPC presents significant challenges, and may even be impossible, due to inherent inaccuracies in the predictive…