Geodesic
Estimates of reachable sets of multidimensional control systems with nonlinear interconnections
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 4, pp. 82-94

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The paper is devoted to the problem of constructing external estimates for the reachable set of a multidimensional control system by means of vector estimators. A system is considered that permits a decomposition into several independent subsystems with simple structure (for example, linear subsystems), which are connected to each other by means of nonlinear interconnections. For each of the subsystems, an external estimate of the reachable set is assumed to be known; this estimate is representable in the form of a level set of some function satisfying a differential inequality. An estimate for the reachable set of the united system is constructed with the use of estimates for subsystems. The method of deriving the estimates is based on constructing comparison systems for analogs of vector Lyapunov functions (cost functions).
Keywords: control system, reachable set, comparison principle, vector Lyapunov function. 
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     author = {M. I. Gusev},
     title = {Estimates of reachable sets of multidimensional control systems with nonlinear interconnections},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2009_15_4_a7/}
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M. I. Gusev. Estimates of reachable sets of multidimensional control systems with nonlinear interconnections. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 15 (2009) no. 4, pp. 82-94. http://geodesic.mathdoc.fr/item/TIMM_2009_15_4_a7/