A Kalman Filter for Online Calibration of Optimal Controllers

This paper proposes an approach for the calibration of the cost function of optimization-based controllers. The approach uses a Kalman filter that estimates the cost function parameters using data of closed-loop system operation. It adapts the parameters online and robustly, provides safety guarantees, is computationally efficient, has low data storage requirements, and is easy to implement making it appealing for many real-time applications. The approach provides a data-efficient alternative to Bayesian optimization and an automated alternative to learning from demonstrations. Simulation results show that the approach is able to learn cost function parameters quickly (approximately 95% faster than Bayesian optimization), is able to adapt the parameters to compensate for disturbances (approximately 25% improvement on tracking precision), and is robust to noise.