Reachable Sets of Nonlinear Control Systems: Estimation Approaches

  • Tatiana F. FilippovaEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)


The dynamical control systems of a special structure with a combined nonlinearity of quadratic and bilinear kinds presenting in state velocities are studied. The uncertainty in initial states and in system parameters is also assumed and it has a set-membership type when only the bounding sets for unknown items are given. The ellipsoidal estimates of reachable sets are derived using the special structure of studied control system. The techniques of generalized solutions of Hamilton-Jacobi-Bellman (HJB) equations and HJB inequalities together with previously established results of ellipsoidal calculus are applied to find the set-valued estimates of reachable sets as the level sets of a related cost functional. The computational algorithms and related numerical examples are also given.


Control system Nonlinearity Reachable set Uncertainty State estimation 


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Authors and Affiliations

  1. 1.Department of Optimal ControlKrasovskii Institute of Mathematics and Mechanics, Russian Academy of SciencesEkaterinburgRussian Federation
  2. 2.Ural Federal UniversityEkaterinburgRussian Federation

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