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In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…
Trajectory optimization is a fundamental stochastic optimal control problem. This paper deals with a trajectory optimization approach for dynamical systems subject to measurement noise that can be fitted into linear time-varying stochastic…
We introduce an alternative approach for the analysis and numerical approximation of the optimal feedback control mapping. It consists in looking at a typical optimal control problem in such a way that feasible controls are mappings…
In this paper, we consider controlled linear dynamical systems in which the controller has only access to a compressed version of the system state. The technical problem we investigate is that of allocating compression resources over time…
Positive linear systems on arbitrary time scales are studied. The theory developed in the paper unifies and extends concepts and results known for continuous-time and discrete-time systems. A necessary and sufficient condition for a linear…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values…
This paper studies symmetric constrained linear-quadratic optimal control problems and their parametric solutions. The parametric solution of such a problem is a piecewise-affine feedback law that can be equivalently expressed as a set of…
This paper studies a time optimal control problem with control constraints of the rectangular type for the linear multi-input time-varying ordinary differential equations. The aims of this study are to establish certain necessary and…
We consider the problem of robotic planning under uncertainty in this paper. This problem may be posed as a stochastic optimal control problem, a solution to which is fundamentally intractable owing to the infamous "curse of…
We consider an optimal control problem for a system of local continuity equations on a space of probability measures. Such systems can be viewed as macroscopic models of ensembles of non-interacting particles or homotypic individuals,…
This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being…
We consider the decentralized control of a discrete-time, linear system subject to exogenous disturbances and polyhedral constraints on the state and input trajectories. The underlying system is composed of a finite collection of…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at…
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…
An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control…
In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…