Near-Optimal Constrained Feedback Control of Nonlinear Systems via Approximate HJB and Control Barrier Functions

TL;DR

This paper introduces a two-stage control framework combining approximate HJB solutions with control barrier functions to achieve near-optimal constrained feedback control for nonlinear systems, allowing online constraint modifications.

Contribution

The paper proposes a novel decoupled approach that separates performance optimization from constraint enforcement, enabling flexible online constraint adjustments without recomputing the value function.

Findings

Demonstrates near-optimal performance on a linear hovercraft model.

Achieves superior results compared to control Lyapunov function-based controllers.

Validates effectiveness on a nonlinear spacecraft attitude control problem.

Abstract

This paper presents a two-stage framework for constrained near-optimal feedback control of input-affine nonlinear systems. An approximate value function for the unconstrained control problem is computed offline by solving the Hamilton--Jacobi--Bellman equation. Online, a quadratic program is solved that minimizes the associated approximate Hamiltonian subject to safety constraints imposed via control barrier functions. Our proposed architecture decouples performance from constraint enforcement, allowing constraints to be modified online without recomputing the value function. Validation on a linear 2-state 1D hovercraft and a nonlinear 9-state spacecraft attitude control problem demonstrates near-optimal performance relative to open-loop optimal control benchmarks and superior performance compared to control Lyapunov function-based controllers.