A gain-scheduled observer under transmissions without delivery acknowledgment

Abstract

This paper addresses the estimation problem for discrete-time systems where both measurements and control commands are sent to a central station through a lossy network without delivery acknowledgment. The central unit implements the estimation and control algorithms. We propose a jump observer that uses the expected value of the unknown control input at the actuator to run an open loop estimation. Then, the absence of acknowledgment in the control input transmission is dealt with through the introduction of an unknown disturbance. The observer update is performed by means of jumping gains when there are available measurements. We employ an statistic of the control error (new disturbance), i.e., the difference between the control inputs at the plant and at the observer, to schedule the observer gains in real time. The observer is designed to minimize the H∞ norm from disturbances, measurement noises and control input errors, to estimation error. The infinite-dimensional design problem is turn into an optimization problem over polynomials using sum-of-squares decomposition techniques. Benefits of the proposal are shown in a simulation example.