Control for Set-Valued Movements of Dynamical Systems Under Uncertainty with Applications

Abstract

The guaranteed control problems for nonlinear dynamical systems with uncertainty in initial states and parameters are studied. The case is investigate when only the bounding sets for initial system states and for system parameters are given without any additional statistical or probabilistic information on these values. Applying the previously developed approaches and new results developed here to evaluating trajectory tubes and reachable sets, we study the properties of optimal control that solves the problem of control for the trajectory tube of a dynamic system with uncertainty and nonlinearity of a quadratic type. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.