Related papers: Relaxation Methods for Mixed-Integer Optimal Contr…
In this paper, we study numerical approximations for optimal control of a class of stochastic partial differential equations with partial observations. The system state evolves in a Hilbert space, whereas observations are given in…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
We present and analyze a new method for solving optimal control problems for Volterra integral equations, based on approximating the controlled Volterra integral equations by a sequence of systems of controlled ordinary differential…
This paper addresses the optimal covariance steering problem for stochastic discrete-time linear systems subject to probabilistic state and control constraints. A method is presented for efficiently attaining the exact solution of the…
This paper studies constrained optimal impulse control problems of a deterministic system described by a (semi)flow, where the performance measures are the discounted total costs including both the costs incurred with applying impulses as…
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general,…
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…
A general maximum principle is proved for optimal controls of abstract semilinear stochastic evolution equations. The control variable, as well as linear unbounded operators, acts in both drift and diffusion terms, and the control set need…
This paper introduces a discrete relaxation for the class of combinatorial optimization problems which can be described by a set partitioning formulation under packing constraints. We present two combinatorial relaxations based on computing…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
An optimization problem considering AC power flow constraints and integer decision variables can usually be posed as a mixed-integer quadratically constrained quadratic program (MIQCQP) problem. In this paper, first, a set of valid linear…
The problem of computing an exact experimental design that is optimal for the least-squares estimation of the parameters of a regression model is considered. We show that this problem can be solved via mixed-integer linear programming…
We consider a nonlinear ordinary differential equation and want to control its behavior so that it reaches a target by minimizing a cost function. Our approach is to use hybrid systems to solve this problem: the complex dynamic is replaced…
Controlling the evolution of nonequilibrium systems to minimize dissipated heat or work is a key goal for designing nanodevices, both in nanotechnology and biology. Progress in computing optimal protocols has thus far been limited to either…
Nonlinear optimal control problems for trajectory planning with obstacle avoidance present several challenges. While general-purpose optimizers and dynamic programming methods struggle when adopted separately, their combination enabled by a…
We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…
We consider optimal control problems involving nonlinear ordinary differential equations with uncertain inputs. Using the sample average approximation, we obtain optimal control problems with ensembles of deterministic dynamical systems.…
A method of optimal control computation is proposed for problems with control and state constraints. It uses a sequence of control structure adjustments in the form of generations and reductions of nodes and arcs, which do not change the…
A classic result of Cook et al. (1986) bounds the distances between optimal solutions of mixed-integer linear programs and optimal solutions of the corresponding linear relaxations. Their bound is given in terms of the number of variables…
As we move to increasingly complex cyber-physical systems (CPS), new approaches are needed to plan efficient state trajectories in real-time. In this paper, we propose an approach to significantly reduce the complexity of solving optimal…