The problems of construction of the reachable sets for stable oscillatory systems and its applications

“Reachable sets play a fundamental role in the theories of robust stability and the optimal control. The analysis of reachable sets gives a possibility to solve a wide class of problems related to the study of dynamic models in various elds of natural science. Specically, such analysis is widely used in rocket science [57], construction of automotive autopilots [26] or neural networks [73]. Therefore, researching and constructing the reachable sets is an actual problem nowadays. This work provides an algorithm which is a symbiosis of these two methods. On the one hand, this algorithm is a new method for constructing reachable sets for linear systems with variable coecients. On the other hand, it is possible to obtain an approximation of the reachable set for a nonlinear system. The sequence of reachable sets for a linear system, constructed in the neighborhood of the periodic attractor of a nonlinear system, is an approximation of the reachable set of nonlinear system.”
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