This paper presents a methodology for safety verification of continuous and hybrid systems
in the worst-case and stochastic settings. In the worst-case setting, a function of state termed …

Abstract Control Barrier Functions (CBFs) are a popular approach for safe control of
nonlinear systems. In CBF-based control, the desired safety properties of the system are …

This paper presents a novel method of global adaptive dynamic programming (ADP) for the
adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing …

Methods for model validation of continuous-time nonlinear systems with uncertain
parameters are presented in this paper. The methods employ functions of state-parameter …

We present a methodology for the algorithmic construction of Lyapunov functions for the
transient stability analysis of classical power system models. The proposed methodology …

We completely characterize sections of the cones of nonnegative polynomials, convex
polynomials and sums of squares with polynomials supported on circuits, a genuine class of …

A barrier certificate is an inductive invariant function which can be used for the safety
verification of a hybrid system. Safety verification based on barrier certificate has the benefit …

This paper proposes a compositional method for verifying the safety of a dynamical system,
given as an interconnection of subsystems. The safety verification is conducted by the use of …

A barrier certificate can separate the state space of a considered hybrid system (HS) into
safe and unsafe parts according to the safety property to be verified. Therefore this notion …

Inspired by the idea of multiple Lyapunov functions (MLFs), we use piecewise continuous
scalar functions to investigate the stabilizability of time-varying switched systems. Starting …