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Stability and safety are two important aspects in safety-critical control of dynamical systems. It has been a well established fact in control theory that stability properties can be characterized by Lyapunov functions. Reachability…
Control Lyapunov functions (CLFs) and control barrier functions (CBFs) have been used to develop provably safe controllers by means of quadratic programs (QPs), guaranteeing safety in the form of trajectory invariance with respect to a…
This paper takes a step towards addressing the difficulty of constructing Control Barrier Functions (CBFs) for parallel safety boundaries. A single CBF for both boundaries has been reported to be difficult to validate for safety, and we…
The existence of a Control Barrier Function (CBF) for a control-affine system provides a powerful design tool to ensure safety. Any controller that satisfies the CBF condition and ensures that the trajectories of the closed-loop system are…
A combination of control Lyapunov functions (CLFs) and control barrier functions (CBFs) forms an efficient framework for addressing control challenges in safe stabilization. In our previous research, we developed an analytical control…
In a complex real-time operating environment, external disturbances and uncertainties adversely affect the safety, stability, and performance of dynamical systems. This paper presents a robust stabilizing safety-critical controller…
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…
We prove a robust converse barrier function theorem via the converse Lyapunov theory. While the use of a Lyapunov function as a barrier function is straightforward, the existence of a converse Lyapunov function as a barrier function for a…
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…
Control barrier functions (CBFs) provide a powerful tool for enforcing safety constraints in control systems, but their direct application to complex, high-dimensional dynamics is often challenging. In many settings, safety certificates are…
This paper studies control synthesis for a general class of nonlinear, control-affine dynamical systems under additive disturbances and state-estimation errors. We enforce forward invariance of static and dynamic safe sets and convergence…
Control Barrier Functions (CBFs) provide a powerful framework for ensuring safety in dynamical systems. However, their application typically relies on full state information, which is often violated in real-world due to the availability of…
In this paper we address the problem of control Lyapunov-barrier function (CLBF)-based safe stabilization for a class of nonlinear control-affine systems. A difficulty may arise for the case when a constraint has the relative degree larger…
Control barrier functions guarantee safety but typically require accurate system models. Parametric uncertainty invalidates these guarantees. Existing robust methods maintain safety via worst-case bounds, limiting performance, while modular…
Safety-critical whole-body robot control demands reactive methods that ensure collision avoidance in real-time. Complementarity constraints and control barrier functions (CBF) have emerged as core tools for ensuring such safety constraints,…
Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions…
Control Barrier Functions (CBFs) have emerged as a powerful tool in the design of safety-critical controllers for nonlinear systems. In modern applications, complex systems often involve the feedback interconnection of subsystems evolving…
Connected automated vehicles have shown great potential to improve the efficiency of transportation systems in terms of passenger comfort, fuel economy, stability of driving behavior and mitigation of traffic congestions. Yet, to deploy…
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…
Control barrier functions (CBFs) are a powerful tool for synthesizing safe control actions; however, constructing CBFs remains difficult for general nonlinear systems. In this work, we provide a constructive framework for synthesizing CBFs…