Related papers: The Minkowski-Bellman Equation
In this paper, we consider discrete-time infinite horizon problems of optimal control to a terminal set of states. These are the problems that are often taken as the starting point for adaptive dynamic programming. Under very general…
This article is a continuation of a previous work where we studied infinite horizon control problems for which the dynamic, running cost and control space may be different in two half-spaces of some euclidian space $\R^N$. In this article…
We consider a class of closed loop stochastic optimal control problems in finite time horizon, in which the cost is an expectation conditional on the event that the process has not exited a given bounded domain. An important difficulty is…
Controlling systems of ordinary differential equations (ODEs) is ubiquitous in science and engineering. For finding an optimal feedback controller, the value function and associated fundamental equations such as the Bellman equation and the…
We develop the dynamic programming approach for a family of infinite horizon boundary control problems with linear state equation and convex cost. We prove that the value function of the problem is the unique regular solution of the…
Adaptive optimal control of nonlinear dynamic systems with deterministic and known dynamics under a known undiscounted infinite-horizon cost function is investigated. Policy iteration scheme initiated using a stabilizing initial control is…
In this paper we consider an infinite time horizon risk-sensitive optimal stopping problem for a Feller--Markov process with an unbounded terminal cost function. We show that in the unbounded case an associated Bellman equation may have…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
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 minimization of energy-like cost functionals is addressed in the context of optimal control problems. For a general class of dynamical systems, with possibly unstable and nonlinear free dynamics, it is shown that a sequence of solutions…
We propose a machine learning algorithm for solving finite-horizon stochastic control problems based on a deep neural network representation of the optimal policy functions. The algorithm has three features: (1) It can solve…
This paper proposes a method to compute lower performance bounds for discrete-time infinite-horizon min-max control problems with input constraints and bounded disturbances. Such bounds can be used as a performance metric for control…
We present a theory of optimal control for McKean-Vlasov stochastic differential equations with infinite time horizon and discounted gain functional. We first establish the well-posedness of the state equation and of the associated control…
In this paper we consider a broad class of infinite horizon discrete-time optimal control models that involve a nonnegative cost function and an affine mapping in their dynamic programming equation. They include as special cases classical…
The objective of this work is to study continuous-time Markov decision processes on a general Borel state space with both impulsive and continuous controls for the infinite-time horizon discounted cost. The continuous-time controlled…
We analyze the consequences that the so-called turnpike property has on the long-time behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
The Bellman equation and its continuous-time counterpart, the Hamilton-Jacobi-Bellman (HJB) equation, serve as necessary conditions for optimality in reinforcement learning and optimal control. While the value function is known to be 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…
An abstract framework guaranteeing the local continuous differentiability of the value function associated with optimal stabilization problems subject to abstract semilinear parabolic equations subject to a norm constraint on the controls…