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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 article presents tools for the design of control laws inducing robust controlled forward invariance of a set for hybrid dynamical systems modeled as hybrid inclusions. A set has the robust controlled forward invariance property via a…
In this paper, we establish a connection between model predictive control (MPC) techniques and Control Barrier Functions (CBFs). Recognizing the similarity between CBFs and Control Lyapunov Functions (CLFs), we propose a MPC formulation…
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.…
Control barrier functions (CBFs) have emerged as a popular topic in safety critical control due to their ability to provide formal safety guarantees for dynamical systems. Despite their powerful capabilities, the determination of feasible…
This paper considers collision avoidance for vehicles with first-order nonholonomic constraints maintaining nonzero forward speeds, moving within dynamic environments. We leverage the concept of control barrier functions (CBFs) to…
This work proposes a hybrid framework for car-like robots with obstacle avoidance, global convergence, and safety, where safety is interpreted as path invariance, namely, once the robot converges to the path, it never leaves the path. Given…
Stability and safety are crucial in safety-critical control of dynamical systems. The reach-avoid-stay objectives for deterministic dynamical systems can be effectively handled by formal methods as well as Lyapunov methods with soundness…
Singularities in robotic and dynamical systems arise when the mapping from control inputs to task-space motion loses rank, leading to an inability to determine inputs. This limits the system's ability to generate forces and torques in…
While learning-based control techniques often outperform classical controller designs, safety requirements limit the acceptance of such methods in many applications. Recent developments address this issue through so-called predictive safety…
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 have been demonstrated to be a useful method of ensuring constraint satisfaction for a wide class of controllers, however existing results are mostly restricted to continuous time systems of relative degree one.…
In this paper, we present Lyapunov-based {\color{black}time varying} controllers for {\color{black}fast} stabilization of a perturbed chain of integrators with bounded uncertainties. We refer to such controllers as {\color{black}time…
In this letter we propose an optimization-based boundary controller for traffic flow dynamics capable of achieving both stability and invariance conditions. The approach is based on the definition of Boundary Control Barrier Functionals,…
This paper demonstrates that the safety override arising from the use of a barrier function can in some cases be needlessly restrictive. In particular, we examine the case of fixed-wing collision avoidance and show that when using a barrier…
In this paper, a method to achieve smooth transitions between sequential reachability tasks for a continuous time mobile robotic system is presented. Control barrier functions provide formal guarantees of forward invariance of safe sets and…
This paper presents a novel approach for ensuring safe operation of systems subject to input nonlinearities and time-varying safety constraints. We extend the time-varying barrier function framework to address time-varying safety…
This paper develops a control approach with correctness guarantees for the simultaneous operation of lane keeping and adaptive cruise control. The safety specifications for these driver assistance modules are expressed in terms of set…
Optimal stabilization of safety-critical nonlinear systems requires balancing long-term performance and strict safety constraints. Existing quadratic-programming-based control barrier function (CBF) safety filters are point-wise and may…
This paper presents novel theoretical results to guarantee multi-agent set invariance using Matrix Control Barrier Functions in sampled-data systems. More specifically, the paper presents conditions under which heterogeneous control-affine…