State Estimation for Control Systems with a Multiplicative Uncertainty through Polyhedral Techniques

Abstract : The paper deals with polyhedral estimates for reachable tubes of differential systems with a multiplicative uncertainty, namely linear systems with set-valued uncertainties in initial states, additive inputs and coefficients of the system. We present nonlinear parametrized systems of ordinary differential equations (ODE) which describe the evolution of the parallelotope-valued estimates for reachable sets (time cross-sections of the reachable tubes). The main results are obtained for internal estimates. In fact, a whole family of the internal estimates is introduced. The properties of the obtained ODE systems (such as existence and uniqueness of solutions, nondegeneracy of estimates) are investigated. Using some optimization procedure we also obtain a differential inclusion which provides nondegenerate internal estimates. Examples of numerically constructed external and internal estimates are presented.
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Communication dans un congrès
Dietmar Hömberg; Fredi Tröltzsch. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. Springer, IFIP Advances in Information and Communication Technology, AICT-391, pp.165-176, 2013, System Modeling and Optimization. 〈10.1007/978-3-642-36062-6_17〉
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Elena Kostousova. State Estimation for Control Systems with a Multiplicative Uncertainty through Polyhedral Techniques. Dietmar Hömberg; Fredi Tröltzsch. 25th System Modeling and Optimization (CSMO), Sep 2011, Berlin, Germany. Springer, IFIP Advances in Information and Communication Technology, AICT-391, pp.165-176, 2013, System Modeling and Optimization. 〈10.1007/978-3-642-36062-6_17〉. 〈hal-01347534〉

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