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Moving horizon estimation and fault detection for hybrid systems


M. Morari

AIChE Annual Meeting, Los Angeles, USA

Many practical control, estimation and fault detection problems involve hybrid systems, here loosely defined as systems involving both continuous and discrete variables. Various approaches have been proposed for modeling hybrid systems. Often engineering systems include "logic" components (eg. if-then-else rules, finite state machine, etc.) which are conveniently described via propositional logic. Moreover, in addition to a quantitative system description there might be some available qualitative information about the behavior of the system, for instance in terms of heuristic knowledge. Recently it was shown by Bemporad and Morari (1999) that expressing logical propositions in the form of linear constraints on integer variables leads to a powerful modeling framework, the so-called mixed logic dynamical (MLD) form. It allows to describe a broad number of important classes of systems, like piecewise linear systems, systems with mixed discrete/continuous inputs and states, and many others more (Bemporad and Morari, 1999). The framework permits to include and prioritize constraints, and incorporate heuristic rules in the description of the model. In this work we first show that the MLD form can be used as a new tool to model systems with faults. Next we formulate the moving horizon estimation (MHE) problem for MLD systems, which can be considered dual to (receding horizon) model predictive control. At each time step we solve a least squares estimation problem over a finite horizon extending backwards from the current time. The resulting optimization problem is a mixed-integer quadratic program (MIQP), for which efficient solvers exist. We propose to use this moving horizon estimation formulation to estimate states and faults of hybrid systems in the MLD form. Next we propose a state smoothing algorithm based on MHE. Based on the results by Rao and Rawlings (1998) we provide sufficient conditions on the time horizon and the additional penalties in the MHE cost function to guarantee asymptotic convergence of the MHE scheme. Moreover we propose an algorithm for the computation of the additional penalties that allows to implement MHE by solving Mixed-Integer Quadratic Programs. Finally we consider some aspects of the numerical problems involved in the estimation procedure.


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