Sufficient Conditions for Temporal Logic Specifications in Hybrid Dynamical Systems.

In this paper, we introduce operators, semantics, and conditions that, when possible, are solution-independent to guarantee basic temporal logic specifications for hybrid dynamical systems. Employing sufficient conditions for forward invariance and finite time attractivity of sets for such systems, we derive such sufficient conditions for the satisfaction of formulas involving temporal operators and atomic propositions. Furthermore, we present how to certify formulas that have more than one operator. Academic examples illustrate the results throughout the paper

Forward Invariance of Sets for Hybrid Dynamical Systems (Part I)

In this paper, tools to study forward invariance properties with robustness to dis- turbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in terms of dif- ferential and difference inclusions with state and disturbance constraints, for whose definition only four objects are required. The proposed robust forward invariance notions allow for the diverse type of solutions to such systems (with and without dis- turbances), including solutions that have persistent flows and jumps, that are Zeno, and that stop to exist after finite amount of (hybrid) time. Sufficient conditions for sets to enjoy such properties are presented. These conditions are given in terms of the objects defining the hybrid inclusions and the set to be rendered robust forward invariant. In addition, as special cases, these conditions are exploited to state results on nominal forward invariance for hybrid systems without disturbances. Furthermore, results that provide conditions to render the sublevel sets of Lyapunov-like functions forward invariant are established. Analysis of a controlled inverter system is presented as an application of our results. Academic examples are given throughout the paper to illustrate the main ideas.Comment: 39 pages, 7 figures, accepted to TA

On notions and sufficient conditions for forward invariance of sets for hybrid dynamical systems

Forward invariance for hybrid dynamical systems modeled by differential and difference inclusions with state-depending conditions enabling flows and jumps is studied. Several notions of forward invariance are considered and sufficient conditions in terms of the objects defining the system are introduced. In particular, we study forward invariance notions that apply to systems with nonlinear dynamics for which not every solution is unique or may exist for arbitrary long hybrid time. Such behavior is very common in hybrid systems. Lyapunov-based conditions are also proposed for the estimation of invariant sets. Applications and examples are given to illustrate the results. In particular, the results are applied to the estimation of weakly forward invariant sets, which is an invariance property of interest when employing invariance principles to study convergence of solutions

On notions and sufficient conditions for forward invariance of sets for hybrid dynamical systems

Forward invariance for hybrid dynamical systems modeled by differential and difference inclusions with state-depending conditions enabling flows and jumps is studied. Several notions of forward invariance are considered and sufficient conditions in terms of the objects defining the system are introduced. In particular, we study forward invariance notions that apply to systems with nonlinear dynamics for which not every solution is unique or may exist for arbitrary long hybrid time. Such behavior is very common in hybrid systems. Lyapunov-based conditions are also proposed for the estimation of invariant sets. Applications and examples are given to illustrate the results. In particular, the results are applied to the estimation of weakly forward invariant sets, which is an invariance property of interest when employing invariance principles to study convergence of solutions