Related papers: Symmetry reduction for dynamic programming
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming…
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…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
This paper studies stochastic optimization problems and associated Bellman equations in formats that allow for reduced dimensionality of the cost-to-go functions. In particular, we study stochastic control problems in the…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…
This article proposes an improved trajectory optimization approach for stochastic optimal control of dynamical systems affected by measurement noise by combining optimal control with maximum likelihood techniques to improve the reduction of…
In this paper, we consider a class of continuous-time, continuous-space stochastic optimal control problems. Building upon recent advances in Markov chain approximation methods and sampling-based algorithms for deterministic path planning,…
We present a method of computing backward reachable sets for nonlinear discrete-time control systems possessing continuous symmetries. The starting point is a dynamic game formulation of reachability analysis where control inputs aim to…
We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…
Optimal control problems driven by evolutionary partial differential equations arise in many industrial applications and their numerical solution is known to be a challenging problem. One approach to obtain an optimal feedback control is…
In this paper, we focus on a method based on optimal control to address the optimization problem. The objective is to find the optimal solution that minimizes the objective function. We transform the optimization problem into optimal…
We present an accelerated algorithm for the solution of static Hamilton-Jacobi-Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure, which is known to have superlinear…
A method of optimal control computation is proposed for problems with control and state constraints. It uses a sequence of control structure adjustments in the form of generations and reductions of nodes and arcs, which do not change the…
This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional…
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a…
This paper presents a constrained adaptive dynamic programming (CADP) algorithm to solve general nonlinear nonaffine optimal control problems with known dynamics. Unlike previous ADP algorithms, it can directly deal with problems with state…
A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…