Simulation and Bisimulation of Nonlinear Control Systems with Admissible Classes of Inputs and Disturbances
Kevin A. Grasse · SIAM Journal on Control and Optimization · 2007
Motivated by analogous concepts in theoretical computer science, the concepts of simulation and bisimulation relations have recently been introduced in the study of the geometric theory of nonlinear control systems. Simulation relations generalize such notions as trajectory propagation and trajectory lifting, while bisimulation relations generalize such notions as system equivalence and state‐space reduction. This paper explores previously obtained necessary and sufficient conditions for the existence of (bi)simulation relations and determines to what extent those relations can be maintained if inputs and disturbances are restricted to specified “admissible” classes. We show how the results obtained here for general simulation relations extend prior results obtained for trajectory propagation and trajectory lifting. Also addressed briefly are some sufficient conditions for simulation relations to hold semiglobally in time.