Infinite-Horizon Differentiable Model Predictive Control
This addresses safe controller learning for robotics or autonomous systems, but it is incremental as it builds on existing MPC and differentiable methods.
The paper tackled the problem of safe imitation learning by proposing a differentiable linear quadratic Model Predictive Control (MPC) framework with an infinite-horizon cost, ensuring closed-loop stability and enforcing hard constraints. The result demonstrated learning capabilities in numerical studies, though no concrete numbers were provided.
This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic Riccati equation (DARE), so that the learned controller can be proven to be stabilizing in closed-loop. A central contribution is the derivation of the analytical derivative of the solution of the DARE, thereby allowing the use of differentiation-based learning methods. A further contribution is the structure of the MPC optimization problem: an augmented Lagrangian method ensures that the MPC optimization is feasible throughout training whilst enforcing hard constraints on state and input, and a pre-stabilizing controller ensures that the MPC solution and derivatives are accurate at each iteration. The learning capabilities of the framework are demonstrated in a set of numerical studies.