Related papers: Optimal L2-control problem in coefficients for a l…
This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
We study unconstrained and constrained linear quadratic problems and investigate the suboptimality of the model predictive control (MPC) method applied to such problems. Considering MPC as an approximate scheme for solving the related fixed…
In this study, we propose a novel gap-constraint-based reformulation for optimal control problems with equilibrium constraints (OCPECs). We show that the proposed reformulation generates a new constraint system equivalent to the original…
This paper aims to study the convergence of adaptive finite element method for control constrained elliptic optimal control problems under $L^2$-norm. We prove the contraction property and quasi-optimal complexity for the $L^2$-norm errors…
Solving optimal control problems (OCPs) of autonomous agents operating under spatial and temporal constraints fast and accurately is essential in applications ranging from eco-driving of autonomous vehicles to quadrotor navigation. However,…
In this work, new theoretical results on functional type a posteriori estimates for elliptic optimal control problems with control constraints are presented. More precisely, we derive new, sharp, guaranteed and fully computable lower bounds…
We consider an optimal control problem where the state is governed by a free boundary problem called the two-phase membrane problem and the control appears in the coefficients of the characteristic function of the positivity and negativity…
This paper is concerned with a linear quadratic (LQ, for short) optimal control problem with fixed terminal states and integral quadratic constraints. A Riccati equation with infinite terminal value is introduced, which is uniquely solvable…
In this paper, elliptic optimal control problems involving the $L^1$-control cost ($L^1$-EOCP) is considered. To numerically discretize $L^1$-EOCP, the standard piecewise linear finite element is employed. However, different from the finite…
We consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…
We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
In this paper we present explicit bounds for optimal control in a Lagrange problem without end-point constraints. The approach we use is due to Gamkrelidze and is based on the equivalence of the Lagrange problem and a time-optimal problem…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
In this paper we study an optimal control problem that is affine in two-dimensional bounded control. The problem is related to the stabilization of an inverted spherical pendulum in the vicinity of the upper unstable equilibrium. We find…
Finite element methods for a model elliptic distributed optimal control problem with pointwise state constraints are considered from the perspective of fourth order boundary value problems.
This work develops a rigorous numerical framework for solving time-dependent Optimal Control Problems (OCPs) governed by partial differential equations, with a particular focus on biomedical applications. The approach deals with…