Observed Control -- Linearly Scalable Nonlinear Model Predictive Control with Adaptive Horizons

Abstract: This work highlights the duality between state estimation methods and model predictive control. A predictive controller, observed control, is presented that uses this duality to efficiently compute control actions with linear time-horizon length scalability. The proposed algorithms provide exceptional computational efficiency, adaptive time horizon lengths, and early optimization termination criteria. The use of Kalman smoothers as the backend optimization framework provides for a straightforward implementation supported by strong theoretical guarantees. Additionally, a formulation is presented that separates linear model predictive control into purely reactive and anticipatory components, enabling any-time any-horizon observed control while ensuring controller stability for short time horizons. Finally, numerical case studies confirm that nonlinear filter extensions, i.e., the extended Kalman filter and unscented Kalman filter, effectively extend observed control to nonlinear systems and objectives.