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In this article, we explore two distinct issues. Initially, we examine the utilization of the Pontriagin maximum principle in relation to fractional delay differential equations. Additionally, we discuss the optimal approach for solving the…
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…
We obtain a method to compute effective first integrals by combining Noether's principle with the Kozlov-Kolesnikov integrability theorem. A sufficient condition for the integrability by quadratures of optimal control problems with controls…
In this paper, we study the optimal singular controls for stochastic recursive systems, in which the control has two components: the regular control, and the singular control. Under certain assumptions, we establish the dynamic programming…
This paper is dedicated to the elementary proof of Pontryagin's maximum principle for problems with free right end point. The proof for the standard problem is taken from the monography of Ioffe and Tichomirov. We assume piecewise…
We consider optimal control problems for systems governed by mean-field stochastic differential equations, where the control enters both the drift and the diffusion coefficient. We study the relaxed model, in which admissible controls are…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
Distributed control problems under some specific information constraints can be formulated as (possibly infinite dimensional) convex optimization problems. The underlying motivation of this work is to develop an understanding of the optimal…
Solutions to optimal control problems can be discontinuous, even if all the functionals defining the problem are smooth. This can cause difficulties when numerically computing solutions to these problems. While conventional numerical…
It is a longstanding unsolved problem to characterize the optimal feedbacks for general SLQs (i.e., stochastic linear quadratic control problems) with random coefficients in infinite dimensions; while the same problem but in finite…
In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…
This paper is concerned with a linear quadratic optimal control problem of delayed backward stochastic differential equations. An explicit representation is derived for the optimal control, which is a linear feedback of the entire past…
Hybrid quantum-classical algorithms hold great promise for solving quantum control problems on near-term quantum computers. In this work, we employ the hybrid framework that integrates digital quantum simulation with classical optimization…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
We study the Pontryagin maximum principle by deriving necessary and sufficient conditions for a class of optimal control problems arising in non exchangeable mean field systems, where agents interact through heterogeneous and asymmetric…
An optimal control problem for the continuity equation is considered. The aim of a controller is to maximize the total mass within a target set at a given type moment. An iterative numerical algorithm for solving this problem is presented.
The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient…
We consider the class of control systems where the differential equation, state and control system are described by polynomials. Given a set of trajectories and a class of Lagrangians, we are interested to find a Lagrangian in this class…
The paper considers the suboptimal H-infinity control problem for a general discrete-time system (whose transfer function matrix is allowed to be improper or polynomial). The parametrization of output feedback controllers is given in a…
We study the problem of optimal inside control of a stochastic Volterra equation driven by a Brownian motion and a Poisson random measure. We prove a sufficient and a necessary maximum principle for the optimal control when the trader has…