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State estimation for hybrid systems



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Hybrid Systems State estimation for hybrid systems applications to aircraft tracking I Hwang H Balakrishnan and C Tomlin Abstract The problem of estimating the discrete and continuous state of a stochastic linear hybrid system given only the continuous system output data is studied Well established techniques for hybrid estimation known as the multiple model adaptive estimation algorithm and the interacting multiple model algorithm are first reviewed Conditions that must be satisfied to guarantee the convergence of these hybrid estimation algorithms are then presented These conditions also provide a means to predict as a function of the system parameters which transitions in a hybrid system are relatively easy to detect A new variant of hybrid estimation algorithms called the residual mean interacting multiple model RMIMM algorithm is then proposed and analysed The performance of RMIMM is demonstrated through multi modal aircraft trajectory tracking examples 1 Introduction Hybrid systems are dynamical systems that combine continuous dynamics modelled by differential or difference equations and discrete dynamics modelled by finite automata Since hybrid systems can suitably model the complex behaviour of varied embedded control systems such as robotic transportation and process control systems there has been considerable interest in the estimation and control of hybrid systems among researchers in both academic and industrial communities 1 4 The objective of hybrid estimation is to compute both the discrete and continuous state estimates of a hybrid system at any given time Hybrid estimators usually consist of the combination of a bank of continuous state estimators each one designed for a different discrete state or mode and a mode selecting algorithm How the correct mode is selected depends on the type of output data available The hybrid estimators analysed in this paper address a particularly challenging problem that of mode and continuous state estimation given



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