An efficient method for multiobjective optimal control and optimal control subject to integral constraints

TL;DR

This paper presents a novel, efficient numerical method for multiobjective and constrained optimal control problems, leveraging an extended state space and a semi-Lagrangian approach to solve the augmented Hamilton-Jacobi-Bellman PDE.

Contribution

The paper introduces a causality-based, semi-Lagrangian numerical method for solving multiobjective and integral-constrained optimal control problems, improving computational efficiency.

Findings

Method outperforms weighted sum algorithms in efficiency

Successfully applied to flight path planning and robotic navigation

Demonstrates accurate solutions for complex control scenarios

Abstract

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget" remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian "marching" method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced "weighted sum" based algorithm for the same problem. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.