Design of state observers for discretely controlled continuous systems

This paper describes an observer design procedure for a class of hybrid systems, in which a continuous plant with nonlinear dynamics is controlled by a logic controller that processes discrete measurements. The task of the observer is to estimate the continuous state values of the system from the sequence of partial discrete measurements. The proposed observer design procedure, the Constrained Hybrid Kalman filter (CHKF), is an adapted version of the Constrained Extend Kalman filter (CEKF). In between measurement events, the prediction stage propagates the states according to the known nonlinear dynamics and inputs, and the covariance matrix of the estimation error is computed by means of a simplified continuous Riccati equation. When a measurement event occurs, the correction stage updates the states by solving a constrained optimization problem, and the predicted covariance matrix using the EKF update. Constraints are embedded into the optimization problem by considering the knowledge of the intervals of states. The approach is illustrated for a simple example.