Robust estimation of uncertain linear systems using a moving horizon approach (2013)
Abstract: Since the famous contributions of Kalman at the middle of the last century, the state estimation became a special issue related to the control theory. Countless modern control strategies, or statespace control approaches, assume the partial or overall knowledge of the system state. However, this is far to be found in practice, because the direct measurement of every state is not always possible. The state estimators solve the previous issue by using tools form the control theory. Roughly speaking, an state estimator uses both a system model and some measurements to build the dynamical behaviour of the system state. Regarding the type of dynamic system, there exist an important amount of state estimation designs. For instance, the well-known Kalman filter solves the optimal state estimation problem of a linear system with stochastic inputs modeled by white noises with known statistics. The optimization is with respect to the minimization of the estimation error variance. Robust filters in turn, solve a different problem. The most used assumptions are about the uncertainty of the disturbing noises and the parameters of the system. However, there is not enough evidence of contributions about robust filters using additional information in form of constraints. The present contribution is about a novel estimation scheme robust to unknown inputs and able to use a priori information of the system in form of constraints. The proposed scheme uses an alternative formulation of the MHE (moving horizon estimator) with the game-theoretical formulation of the Hinf filtering. On one hand, the MHE-based scheme gives a way to address constraints. On the other hand, a cost function in a form of a disturbance attenuation function offers a ‘worst-case’ framework. Following the classic MHE formulation, first the full information estimator based on the Hinf theory is proposed, namely, the Hinf-FIE. Then, an approximation is provided by means of the Hinf-MHE to avoid numerical feasibility problems. Different examples show the effectiveness of the proposed filter. The filter is also compared with respect the classic MHE and some robust schemes. A numerical approximation is used to provide a solution of the minimax optimization associated to the constrained Hinf-MHE.