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This paper investigates necessary and sufficient barrier-like conditions for infinite-horizon safety and reach-avoid verification of stochastic discrete-time systems, derived via a relaxation of the Bellman equations. Unlike prior…
This paper presents a novel approach for the safe control design of systems with parametric uncertainties in both drift terms and control-input matrices. The method combines control barrier functions and adaptive laws to generate a safe…
Safety is a fundamental requirement of control systems. Control Barrier Functions (CBFs) are proposed to ensure the safety of the control system by constructing safety filters or synthesizing control inputs. However, the safety guarantee…
In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of…
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…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
This paper presents a strategy for control of a spacecraft docking with a non-maneuvering target in the presence of safety constraints and bounded disturbances. The presence of disturbances prevents convergence to a unique docking state, so…
This paper is motivated by controllers developed for autonomous vehicles which occasionally result into conditions where safety is no longer guaranteed. We develop an exact-time safety recovery framework for any control-affine nonlinear…
The existing control barrier function literature generally relies on precise mathematical models to guarantee system safety, limiting their applicability in scenarios with parametric uncertainties. While incremental control techniques have…
We provide a detailed proof of Proposition 3.1 in the paper titled ``Backstepping control of a class of space-time-varying linear parabolic PDEs via time invariant kernel functions''. In the paper titled ``Backstepping control of a class of…
Useful robot control algorithms should not only achieve performance objectives but also adhere to hard safety constraints. Control Barrier Functions (CBFs) have been developed to provably ensure system safety through forward invariance.…
Motivated by the result of invariance of regular-boundary open sets in \cite{CannarsaDaPratoFrankowska2009} and multi-stability issues in gene networks, our paper focuses on three closely related aims. First, we give a necessary local…
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…
Providing non-trivial certificates of safety for non-linear stochastic systems is an important open problem that limits the wider adoption of autonomous systems in safety-critical applications. One promising solution to address this problem…
Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust…
When deploying autonomous agents in unstructured environments over sustained periods of time, adaptability and robustness oftentimes outweigh optimality as a primary consideration. In other words, safety and survivability constraints play a…
In this work, we explore the application of barrier states (BaS) in the realm of safe nonlinear adaptive control. Our proposed framework derives barrier states for systems with parametric uncertainty, which are augmented into the uncertain…
Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning…
This paper presents two new control approaches for guaranteed safety (remaining in a safe set) subject to actuator constraints (the control is in a convex polytope). The control signals are computed using real-time optimization, including…
This paper proposes a safe reinforcement learning (RL) framework based on forward-invariance-induced action-space design. The control problem is cast as a Markov decision process, but instead of relying on runtime shielding or penalty-based…