相关论文: Generic uniqueness and conjugate points for optima…
We consider continuous-state and continuous-time control problems where the admissible trajectories of the system are constrained to remain on a union of half-planes which share a common straight line. This set will be named a junction. We…
We generalize the Maximum Principle for free end point optimal control problems involving sweeping systems derived in [9] to cover the case where the end point is constrained to take values in a certain set. As in [9], an ingenious smooth…
We consider a stochastic control problem which is composed of a controlled stochastic differential equation, and whose associated cost functional is defined through a controlled backward stochastic differential equation. Under appropriate…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
This paper investigates the optimal control problem for a class of nonlinear fully coupled forward-backward stochastic difference equations (FBS$\Delta$Es). Under the convexity assumption of the control domain, we establish a variational…
We consider optimal control problems involving two constraint sets: one comprised of linear ordinary differential equations with the initial and terminal states specified and the other defined by the control variables constrained by simple…
This paper considers the problem of steering an arbitrary initial probability density function to an arbitrary terminal one, where the system dynamics is governed by a first-order linear stochastic difference equation. It is a…
In this paper, a general stochastic model with controls applied at the moments when the random process hits the boundary of a given subset of the state set is proposed and studied. The general concept of the model is formulated and its…
A decentralized control system with linear dynamics, quadratic cost, and Gaussian disturbances is considered. The system consists of a finite number of subsystems whose dynamics and per-step cost function are coupled through their…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
We study a class of backward stochastic differential equations (BSDEs) driven by a random measure or, equivalently, by a marked point process. Under appropriate assumptions we prove well-posedness and continuous dependence of the solution…
We study the regularity properties of the value function associated with an affine optimal control problem with quadratic cost plus a potential, for a fixed final time and initial point. Without assuming any condition on singular…
We study controllability and constructive synthesis for control-affine systems. We introduce trajectory-dependent Gramian maps that extend the linear time-varying Gramian and yield explicit fixed-point synthesis maps. On feasible coercivity…
We consider a steady-state heat conduction problem in a multidimensional bounded domain Omega for the Poisson equation with constant internal energy g and mixed boundary conditions given by a constant temperature b in the portion Gamma_1 of…
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…
We study a constrained optimal control problem with possibly degenerate coefficients arising in models of optimal portfolio liquidation under market impact. The coefficients can be random in which case the value function is described by a…
In this paper, we consider ensembles of control-affine systems in $\mathbb{R}^d$, and we study simultaneous optimal control problems related to the worst-case minimization. After proving that such problems admit solutions, denoting with…
We study a finite horizon optimal control problem for the continuity equation under a weighted integral state constraint on the mass outside a fixed set. The model is cast in a Hilbert framework for densities. On a suitable invariant…
The consensus control with optimal cost remains major challenging although consensus control problems have been well studied in recent years. In this paper, we study the consensus control of multi-agent system associated with a given cost…
Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…