Related papers: Optimal Control of Moving Sets
Existence of optimal solutions and necessary optimality conditions for a controlled version of Moreau's sweeping process are derived. The control is a measurable ingredient of the dynamics and the constraint set is a polyhedron. The novelty…
The paper extends an impulsive control-theoretical framework towards dynamic systems in the space of measures. We consider a transport equation describing the time-evolution of a conservative "mass" (probability measure), which represents…
State-space models (SSMs) are effective architectures for sequential modeling, but a rigorous theoretical understanding of their training dynamics is still lacking. In this work, we formulate the training of SSMs as an ensemble optimal…
This work addresses the optimal birth control problem for invasive species in a spatial environment. We apply the method of semigroups to qualitatively analyze a size-structured population model in which individuals occupy a position in a…
In this paper we combine two main topics in mechanics and optimal control theory: contact Hamiltonian systems and Pontryagin Maximum Principle. As an important result, among others, we develop a contact Pontryagin Maximum Principle that…
The paper presents necessary and sufficient conditions for the order reduction of optimal control systems. Exploring the corresponding Hamiltonian system allows to solve the order reduction problem in terms of dynamical systems,…
How to free a road from vehicle traffic as efficiently as possible and in a given time, in order to allow for example the passage of emergency vehicles? We are interested in this question which we reformulate as an optimal control problem.…
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem converge globally and practically asymptotically to the set…
A coordinate-free proof of the Maximum Principle is provided in the specific case of an optimal control problem with fixed time. Our treatment heavily relies on a special notion of variation of curves that consist of a concatenation of…
The purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints. The control acts both in the drift and…
Optimal control theory is a promising candidate for a drastic improvement of the performance of quantum information tasks. We explore its ultimate limit in paradigmatic cases, and demonstrate that it coincides with the maximum speed limit…
Through the Pontryagin maximum principle, we solve a minimal-time problem for a linear control system on a cylinder, considered as a homogeneous space of the solvable Lie group of dimension two. The main result explicitly shows the…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
This paper treats an optimal scheduling problem of control nodes in networked systems. We newly introduce both the L0 and l0 constraints on control inputs to extract a time-varying small number of effective control nodes. As the cost…
We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a…
Robotic locomotion often relies on sequenced gaits to efficiently convert control input into desired motion. Despite extensive studies on gait optimization, achieving smooth and efficient gait transitions remains challenging. In this paper,…
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…
Relying on the careful study of a related problem in the calculus of variations, we study a class of optimal control problems in which the control lies on the acceleration, with state constraints on the position variable. In dimension one,…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
We investigate optimal control of dynamical systems which are affine, i.e., linear in control, but nonlinear in state. The control task is to enforce the system state to follow a prescribed desired trajectory as closely as possible, a task…