Dynamic optimization for reachability problems
Journal of Optimization Theory and Applications
Dynamic Programming and Optimal Control, Two Volume Set
Dynamic Programming and Optimal Control, Two Volume Set
Overapproximating Reachable Sets by Hamilton-Jacobi Projections
Journal of Scientific Computing
Estimates of trajectory tubes of uncertain nonlinear control systems
LSSC'09 Proceedings of the 7th international conference on Large-Scale Scientific Computing
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Consideration was given to formation of the external estimates of the reachability sets of the nonlinear controlled systems in the form of the level sets of the functions satisfying the differential Hamilton-Jacobi inequalities. The trajectories of the nonlinear system are estimated by modifying the estimates of its linear part. The constructions proposed are based on comparing the systems of differential inequalities. Applications of the reachability sets of the multivariable controlled systems with nonlinear cross connections to the ellipsoidal estimates were examined.