Assessment and Future Directions of Nonlinear Model Predictive ...

Minimum-Distance Receding-Horizon StateEstimation for Switching Discrete-Time LinearSystemsAngelo Alessandri 1 , Marco Baglietto 2 , and Giorgio Battistelli 31 Department of Production Engineering, Thermoenergetics, and MathematicalModels, DIPTEM–University of Genoa, P.le Kennedy Pad. D, 16129 Genova, Italyalessandri@diptem.unige.it2 Department of Communications, Computer and System Sciences, DIST–Universityof Genoa, Via Opera Pia 13, 16145 Genova, Italymbaglietto@dist.unige.it3 Dipartimento di Sistemi e Informatica, DSI-Universit‘a di Firenze, Via S. Marta 3,50139, Firenze Italybattistelli@dsi.unifi.itSummary. State estimation is addressed for a class of discrete-time systems that mayswitch among different modes taken from a finite set. The system and measurementequations of each mode are assumed to be linear and perfectly known, but the currentmode of the system is unknown and is regarded as a discrete state to be estimated ateach time instant together with the continuous state vector. A new computationally efficientmethod for the estimation of the system mode according to a minimum-distancecriterion is proposed. The estimate of the continuous state is obtained according to areceding-horizon approach by minimizing a quadratic least-squares cost function. Inthe presence of bounded noises and under suitable observability conditions, an explicitexponentially converging sequence provides an upper bound on the estimation error.Simulation results confirm the effectiveness of the proposed approach.1 IntroductionThe literature on state estimation for systems that may undergo switching amongvarious modes includes, among others, methods based on the use of banks offilters and hidden finite-state Markov chains [5]. In this contribution, a differentapproach is presented that is based on the idea of using only a limited amountof the most recent information and is usually referred to as receding-horizon ormoving-horizon.Recently, after the success of model predictive control [8], many researches onreceding-horizon state estimation appeared [1, 3, 6, 9]. The first investigations onsuch techniques date back to the late sixties (see, e.g., [7]), when it was proposedto reduce the effects of the uncertainties by determining estimates that dependonly on a batch of the most recent measurements.In this contribution, we focus on a receding-horizon state estimator with alower computation effort with respect to that required by the method describedR. Findeisen et al. (Eds.): Assessment and Future Directions, LNCIS 358, pp. 347–358, 2007.springerlink.com c○ Springer-Verlag Berlin Heidelberg 2007