Related papers: Sufficient Conditions for Robust Safety in Differe…
A dynamical system is strongly robustly safe provided that it remains safe in the presence of a continuous and positive perturbation, named robustness margin, added to both the argument and the image of the right-hand side (the dynamics).…
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 presents converse theorems for safety in terms of barrier functions for unconstrained continuous-time systems modeled as differential inclusions. Via a counterexample, we show the lack of existence of autonomous and continuous…
For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs.…
We study stochastic systems characterized by difference inclusions. Such stochastic differential inclusions are defined by set-valued maps involving the current state and stochastic input. For such systems, we investigate the problem of…
Providing finite-time probabilistic safety and reach-avoid guarantees is crucial for safety-critical stochastic systems. Existing state-of-the-art barrier methods often rely on a restrictive boundedness assumption for auxiliary functions,…
This paper studies set invariance and contractivity in hybrid systems modeled by hybrid inclusions using barrier functions. After introducing the notion of a multiple barrier functions, we investigate the tightest possible sufficient…
Guaranteeing safety for robotic and autonomous systems in real-world environments is a challenging task that requires the mitigation of stochastic uncertainties. Control barrier functions have, in recent years, been widely used for…
Safety-critical control is a crucial aspect of modern systems, and Control Barrier Functions (CBFs) have gained popularity as the framework of choice for ensuring safety. However, implementing a CBF requires exact knowledge of the true…
In this paper, we consider the problem of verifying safety constraint satisfaction for single-input single-output systems with uncertain transfer function coefficients. We propose a new type of barrier function based on a vector norm. This…
Verifying set invariance has classical solutions stemming from the seminal work by Nagumo, and defining sets via a smooth barrier function constraint inequality results in computable flow conditions for guaranteeing set invariance. While a…
When deployed in the real world, safe control methods must be robust to unstructured uncertainties such as modeling error and external disturbances. Typical robust safety methods achieve their guarantees by always assuming that the…
This paper studies the design of controllers that guarantee stability and safety of nonlinear control affine systems with parametric uncertainty in both the drift and control vector fields. To this end, we introduce novel classes of robust…
The need for robust control laws is especially important in safety-critical applications. We propose robust hybrid control barrier functions as a means to synthesize control laws that ensure robust safety. Based on this notion, we formulate…
In this paper, we address the problem of synthesizing safe and stabilizing controllers for nonlinear systems subject to complex safety specifications and input constraints. We introduce the Universal Barrier Function (UBF), a single…
Safety in dynamic systems with prevalent uncertainties is crucial. Current robust safe controllers, designed primarily for uni-modal uncertainties, may be either overly conservative or unsafe when handling multi-modal uncertainties. To…
This work applies universal adaptive control to control barrier functions to achieve forward invariance of a safe set despite the presence of unmatched parametric uncertainties. The approach combines two ideas. The first is to construct a…
Barrier functions (also called certificates) have been an important tool for the verification of hybrid systems, and have also played important roles in optimization and multi-objective control. The extension of a barrier function to a…
In this paper, we consider nonlinear control systems subject to bounded disturbances and to both state and input constraints. We introduce the definition of robust admissible set - the set of all initial states from which the state and…
In this paper, we study the robustness of safety properties of a linear dynamical system with respect to model uncertainties. Our paper involves three parts. In the first part, we provide symbolic (analytical) and numerical (representation…