Related papers: Permissive Barrier Certificates for Safe Stabiliza…
Recently, barrier certificates have been introduced to prove the safety of continuous or hybrid dynamical systems. A barrier certificate needs to exhibit some barrier function, which partitions the state space in two subsets: the safe…
Sum of Squares programming has been used extensively over the past decade for the stability analysis of nonlinear systems but several questions remain unanswered. In this paper, we show that exponential stability of a polynomial vector…
This paper establishes the equivalence between robust safety and the existence of a barrier function certificate for differential inclusions. More precisely, for a robustly-safe differential inclusion, a barrier function is constructed as…
This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite-time horizon. We use stochastic control barrier functions as a means to quantify the probability that a system exits a given safe region of…
Stability certificates play a critical role in ensuring the safety and reliability of robotic systems. However, deriving these certificates for complex, unknown systems has traditionally required explicit knowledge of system dynamics, often…
We propose a novel approach to certify closed-loop stability and safety of a constrained polynomial system based on the combination of Control Lyapunov Functions (CLFs) and Control Barrier Functions (CBFs). For polynomial systems that are…
A barrier certificate often serves as an inductive invariant that isolates an unsafe region from the reachable set of states, and hence is widely used in proving safety of hybrid systems possibly over the infinite time horizon. We present a…
In this paper, we present a novel approach to determine the stability of switched linear and nonlinear systems using Sum of Squares optimisation. Particularly, we use Sum of Squares optimisation to search for a Lyapunov function that…
Established techniques that enable robots to learn from demonstrations are based on learning a stable dynamical system (DS). To increase the robots' resilience to perturbations during tasks that involve static obstacle avoidance, we propose…
This paper studies the problem of enforcing safety of a stochastic dynamical system over a finite time horizon. We use stochastic barrier functions as a means to quantify the probability that a system exits a given safe region of the state…
Control Lyapunov functions (CLFs) and control barrier functions (CBFs) are widely used tools for synthesizing controllers subject to stability and safety constraints. Paired with online optimization, they provide stabilizing control actions…
The goal of this paper is to present a systematic method to compute reference dependent positively invariant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent…
We study the safety verification problem for a class of distributed parameter systems described by partial differential equations (PDEs), i.e., the problem of checking whether the solutions of the PDE satisfy a set of constraints at a…
Traditional Lyapunov based transient stability assessment approaches focus on identifying the stability region (SR) of the equilibrium point under study. When trying to estimate this region using Lyapunov functions, the shape of the final…
In this paper, we address robust static anti-windup compensator design and performance analysis for saturated linear closed loops in the presence of nonlinear probabilistic parameter uncertainties via randomized techniques. The proposed…
This work estimates safe invariant subsets of the Region of Attraction (ROA) for a seven-state vehicle-with-driver system, capturing both asymptotic stability and the influence of state-safety bounds along the system trajectory. Safe sets…
Verifying stability and safety guarantees for nonlinear systems has received considerable attention in recent years. This property serves as a fundamental building block for specifying more complex system behaviors and control objectives.…
Barrier certificates are scalar functions over the state space of dynamical systems that separate all unsafe states from all reachable states. The existence of a barrier certificate formally verifies the safety of the dynamical system.…
Safe control with guarantees generally requires the system model to be known. It is far more challenging to handle systems with uncertain parameters. In this paper, we propose a generic algorithm that can synthesize and verify safe…
This paper addresses the challenge of safe stabilization, ensuring the system state reach the origin while avoiding unsafe regions. Existing approaches relying on smooth Lyapunov barrier functions often fail to guarantee a feasible…