Work

A generalization of Bellman’s equation with application to path planning, obstacle avoidance and invariant set estimation

Year: 2021

Type: article

Abstract: The standard Dynamic Programming (DP) formulation can be used to solve Multi-Stage Optimization Problems (MSOP’s) with additively separable objective functions. In this paper we consider a larger class of MSOP’s with monotonically backward separable objective functions; additively separable functions being a special case of monotonically backward separable functions. We propose a necessary and sufficient condition, utilizing a generalization of Bellman’s equation, for a solution of a MSOP, with a monotonically backward separable cost function, to be optimal. Moreover, we show that this proposed condition can be used to efficiently compute optimal solutions for two important MSOP’s; the optimal path for Dubin’s car with obstacle avoidance, and the maximal invariant set for discrete time systems.

Source: Automatica

DOI: 10.1016/j.automatica.2021.109510

Authors: Morgan Jones, Matthew M. Peet

Institution: Arizona State University

Language: English

Topic: Advanced Control Systems Optimization

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,010

Funders: National Science Foundation, Division of Civil, Mechanical and Manufacturing Innovation