An Algorithm to Warm Start Perturbed (WASP) Constrained Dynamic Programs

TL;DR

This paper introduces a novel algorithm that efficiently approximates solutions to perturbed constrained dynamic programming problems, reducing computational effort in real-time control scenarios where boundary conditions change marginally.

Contribution

The paper develops a method to compute closed-form first-order perturbations for optimal strategies and Lagrange multipliers, enabling quick initialization of solution algorithms for perturbed problems.

Findings

Significant reduction in computational burden for near-constant boundary conditions

Closed-form expressions for first-order perturbations derived

Method facilitates real-time implementation of constrained dynamic programming

Abstract

Receding horizon optimal control problems compute the solution at each time step to operate the system on a near-optimal path. However, in many practical cases, the boundary conditions, such as external inputs, constraint equations, or the objective function, vary only marginally from one time step to the next. In this case, recomputing the optimal solution at each time represents a significant burden for real-time applications. This paper proposes a novel algorithm to approximately solve a perturbed constrained dynamic program that significantly improves the computational burden when the objective function and the constraints are perturbed slightly. The method hinges on determining closed-form expressions for first-order perturbations in the optimal strategy and the Lagrange multipliers of the perturbed constrained dynamic programming problem are obtained. This information can be used to initialize any algorithm (such as the method of Lagrange multipliers, or the augmented Lagrangian method) to solve the perturbed dynamic programming problem with minimal computational resources.