Near-Optimal Constrained Feedback Control of Nonlinear Systems via Approximate HJB and Control Barrier Functions
This work addresses safety-critical control problems in robotics and aerospace, offering an incremental improvement by enabling online constraint modifications without recomputing value functions.
The paper tackles constrained near-optimal feedback control for nonlinear systems by developing a two-stage framework that decouples performance from safety constraints, achieving near-optimal performance relative to benchmarks and superior results compared to control Lyapunov function-based methods.
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.