Model predictive control with tracking error bound and an influence function approach to moving horizon estimation
Date of Issue2017-01-04
School of Electrical and Electronic Engineering
Model Predictive Control (MPC) and constrained Moving Horizon Estimation (MHE) are both optimization-based method where a constrained optimization problem is solved at each time instant. Recursive feasibility of the constrained optimization problem plays a key role in MPC as it ensures that the state is not driven into a "blind alley" where the constrained problem could become infeasible. For MHE the constrained optimization problem can become infeasible when erroneous measurements occur. In this thesis, we showed relationship between a trajectory advisor for MPC with tracking error bound and a measurement checker for constrained MHE. Akin to the concept of reference governor, the trajectory advisor can supply a new feasible reference signal to recover the feasibility of the MPC problem if the original reference signal makes the MPC problem infeasible. The measurement checker could be used to determine the admissibility of the measurements before the MHE is solved. MPC requires state feedback and if the full state is not measurable, a state estimator is required. Gaussian noise is often assumed in state estimation and the optimality of the estimators based on this assumption may be lost when the assumption is violated. Constrained MHE offers an approach to handle non Gaussian noise by using constraints. In this thesis, a novel moving horizon Maximum Likelihood Estimation (MLE) is proposed for Autoregressive-Moving-Average with eXogenous (ARMAX) process with t-distribution noise model. The thick tail property of t-distribution downs weigh outliers in the likelihood function so that the proposed estimator is robust to outliers. Instead of solving the maximization problem numerically, the Influence Function (IF), an analysis tool in robust statistics, is used to formulate a computationally efficient recursive solution to the maximization problem approximately. As expected, the recursive estimator is reduced to the traditional Moving Window Least-Squares Estimation when the noise is Gaussian. The moving horizon N can be used as tuning parameter for the proposed estimator. The formula for the variance of the estimate is derived. This formula shows explicitly how the variance of estimate is affected by the number of measurements and noise variance. In addition, a formula which predicts the effect of an outlier on estimate is derived. The simulations show the advantages of the proposed estimator over Moving Horizon Least-Squares Estimation in the sense of estimation variance and robustness to outlier, and the advantage over Kalman filter when model mismatch happens. The proposed estimator is applied to liquid level estimation of a Coupled-Tank Control Apparatus and indoor environment localization which show that the proposed estimator gives smaller estimation variance and is more robust to outlier than Moving Window Least-Squares Estimation.