An Adjoint-based Neural Regulator for Real-Time Optimal Control with State Constraints

Abstract: This paper introduces a learning-based control framework for real-time constrained optimal control of nonlinear systems with safety guarantees based on the Pontryagin's Minimum Principle. The approach learns a neural co-state (adjoint) policy that encodes optimality through the system Hamiltonian, rather than directly approximating a control law. Feasibility is enforced separately at runtime through an efficient convex projection that incorporates actuator limits and safety constraints expressed as control barrier functions. We refer to this framework as an adjoint-based neural regulator (ANR) as it yields a controller that satisfies constraints while retaining the optimality structure encoded by the learned adjoint. We demonstrate the effectiveness of the proposed framework on nonlinear constrained control tasks using a unicycle model. The ANR achieves performance at par with nonlinear model predictive control at more than two orders of magnitude lower computational cost, while exhibiting near-invariant performance across unseen scenarios, thus, significantly outperforming reinforcement learning methods in out-of-training-distribution regimes.