Related papers: Minimal-time nonlinear control via semi-infinite p…
We consider a finite-time stochastic drift control problem with the assumption that the control is bounded and the system is controlled until the state process leaves the half-line. Assuming general conditions, it is proved that the…
We present safe control of partially-observed linear time-varying systems in the presence of unknown and unpredictable process and measurement noise. We introduce a control algorithm that minimizes dynamic regret, i.e., that minimizes the…
We consider discrete-time infinite horizon deterministic optimal control problems with nonnegative cost per stage, and a destination that is cost-free and absorbing. The classical linear-quadratic regulator problem is a special case. Our…
We introduce a new numerical method to approximate the solutions of a class of stationary Hamilton-Jacobi (HJ) partial differential equations arising from minimum time optimal control problems. We rely on nested grid approximations, and…
We study a specific class of finite-horizon mean field optimal stopping problems by means of the dynamic programming approach. In particular, we consider problems where the state process is not affected by the stopping time. Such problems…
This paper is concerned with stochastic impulse control problems in which the running cost changes depending on the impulse control. Because of such a dependence, it brings several difficulties when the usual dynamic programming principle…
We propose a new numerical method for solving the Hamilton-Jacobi-Bellman quasi-variational inequality associated with the combined impulse and stochastic optimal control problem over a finite time horizon. Our method corresponds to an…
We propose two new optimistic planning algorithms for nonlinear hybrid-input systems, in which the input has both a continuous and a discrete component, and the discrete component must respect a dwell-time constraint. Both algorithms select…
The considered optimal control problem of a stochastic power system, is to select the set of power supply vectors which infimizes the probability that the phase-angle differences of any power flow of the network, endangers the transient…
Conditions are established under which the optimal control of processes having both absolutely continuous and singular (with respect to time) controls are equivalent to linear programs over a space of measures on the state and control…
In this paper, we address the problem of closed-loop control of nonlinear dynamical systems subjected to probabilistic uncertainties. More precisely, we design time-varying polynomial feedback controllers to follow the given nominal…
Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse optimality property since each passivating state feedback controller is optimal with respect to some specific performance index. Due to the nonlinear…
Verification theorems are key results to successfully employ the dynamic programming approach to optimal control problems. In this paper we introduce a new method to prove verification theorems for infinite dimensional stochastic optimal…
This paper considers the infinite horizon optimal control problem for nonlinear systems. Under the condition of nonlinear controllability of the system to any terminal set containing the origin and forward invariance of the terminal set, we…
A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and…
We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…
In this paper we estimate the minimal controllability time for a class of non-linear control systems with a bounded convex state constraint. An explicit expression is given for the controllability time if the image of the control matrix is…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. We establish that these problems are related to certain infinite-dimensional linear…