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In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
This paper aims to address the nonlinear optimal guidance problem with impact-time and impact-angle constraints, which is fundamentally important for multiple pursuers to collaboratively achieve a target. Addressing such a guidance problem…
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…
We study a stochastic control problem for nonlinear systems governed by stochastic differential equations with irregular drift. The drift coefficient is assumed to decompose as $b(t,x,a)=b_1(t,x)+b_2(x)b_3(t,a)$, where $b_1$ is bounded and…
In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…
A family of optimal control problems for a single and two coupled spinning particles in the Euler-Lagrange formalism is discussed. A characteristic of such problems is that the equations controlling the system are implicit and a reduction…
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…
We consider linear model reduction in both the control and state variables for unconstrained linear-quadratic optimal control problems subject to time-varying parabolic PDEs. The first-order optimality condition for a state-space reduced…
In this paper, we study the necessary and sufficient conditions for ensuring the well-posedness of the stochastic singular systems. Moreover, we investigate the stochastic singular linear-quadratic control problems, considering both finite…
We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…
The turnpike phenomenon stipulates that the solution of an optimal control problem in large time, remains essentially close to a steady-state of the dynamics, itself being the optimal solution of an associated static optimal control…
In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying. We take into account this aspect by considering Markov jump linear systems where the…
The finite state semi-Markov process is a generalization over the Markov chain in which the sojourn time distribution is any general distribution. In this article we provide a sufficient stochastic maximum principle for the optimal control…
We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…
We provide verification theorems (at different levels of generality) for infinite horizon stochastic control problems in continuous time for semimartingales. The control framework is given as an abstract "martingale formulation", which…
Quantum optimal control is a set of methods for designing time-varying electromagnetic fields to perform operations in quantum technologies. This tutorial paper introduces the basic elements of this theory based on the Pontryagin maximum…
Time scale separation is a natural property of many control systems that can be ex- ploited, theoretically and numerically. We present a numerical scheme to solve optimal control problems with considerable time scale separation that is…