Probabilistic ultimate bounds and invariant sets in nonlinear systems

This article extends the notions of probabilistic ultimate bounds (PUB) and probabilistic invariant sets (PIS) to nonlinear continuous-time systems providing tools for their characterization and for the usage of these concepts in control design. Two design strategies are proposed that allow finding a nonlinear control law which ensures that the closed loop system is probabilistically ultimate bounded to a desired region. These strategies are based on Lyapunov and stochastic feedback linearization, respectively. (C) 2021 Published by Elsevier Ltd.

Automated summary

This article extends the concepts of probabilistic ultimate bounds (PUB) and probabilistic invariant sets (PIS) to nonlinear continuous-time systems, providing tools for their characterization and control design. Two design strategies based on Lyapunov and stochastic feedback linearization are proposed to find a nonlinear control law ensuring probabilistic ultimate boundedness of the closed loop system to a desired region.