Continuous-Time Approximated Parametric Output-Feedback Nonlinear Model Predictive Control

Designing predictive controllers for systems with computationally limited embedded hardware, e.g. for autonomous vehicles, requires solving an optimization problem in real-time taking the vehicle dynamics and constraints into account. Furthermore, often the controller needs to be available in explicit form for verification and validation purposes and should only exploit the available output measurement. We propose an approximation of a special nonlinear model predictive output-feedback formulation considering the infinite-horizon case. The main idea is to offline derive an approximated explicit solution of the underlying Hamilton–Jacobi–Bellman equation. The resulting feedback control law is polynomial in terms of the measurements and estimated parameters. Therefore, the online evaluation can be efficiently implemented. The optimal control law is parameterized in terms of the varying parameters which can be updated/learned online. We provide a proof of convergence and existence of the explicit solution and compare the proposed approximated nonlinear controller to a finite-horizon nonlinear model predictive controller considering the control of a quadcopter subject to wind disturbances.