Related papers: Piecewise Stochastic Barrier Functions
This paper proposes a new framework to compute finite-horizon safety guarantees for discrete-time piece-wise affine systems with stochastic noise of unknown distributions. The approach is based on a novel approach to synthesise a stochastic…
This paper presents a method for the simultaneous synthesis of a barrier certificate and a safe controller for discrete-time nonlinear stochastic systems. Our approach, based on piecewise stochastic control barrier functions, reduces the…
We present StochasticBarrier.jl, an open-source Julia-based toolbox for generating Stochastic Barrier Functions (SBFs) for safety verification of discrete-time stochastic systems with additive Gaussian noise. StochasticBarrier.jl certifies…
Stochastic Barrier Functions (SBFs) certify the safety of stochastic systems by formulating a functional optimization problem, which state-of-the-art methods solve using Sum-of-Squares (SoS) polynomials. This work focuses on polynomial SBFs…
A predictive control barrier function (PCBF) based safety filter is a modular framework to verify safety of a control input by predicting a future trajectory. The approach relies on the solution of two optimization problems, first computing…
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…
Obtaining control barrier functions (CBFs) with large safe sets for complex nonlinear systems and constraints is a challenging task. Predictive CBFs address this issue by using an online finite-horizon optimal control problem that…
Providing safety guarantees for stochastic dynamical systems is a central problem in various fields, including control theory, machine learning, and robotics. Existing methods either employ Stochastic Barrier Functions (SBFs) or rely on…
We develop efficient algorithms for optimizing piecewise smooth (PWS) functions where the underlying partition of the domain into smooth pieces is \emph{unknown}. For PWS functions satisfying a quadratic growth (QG) condition, we propose a…
We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…
Safe control designs for robotic systems remain challenging because of the difficulties of explicitly solving optimal control with nonlinear dynamics perturbed by stochastic noise. However, recent technological advances in computing devices…
Safety-critical control systems, such as spacecraft performing proximity operations, must provide formal safety guarantees despite stochastic uncertainties from state estimation and unmodeled dynamics. Although Control Barrier Functions…
Control barrier functions (CBFs) offer an efficient framework for designing real-time safe controllers. However, CBF-based controllers can be short-sighted, resulting in poor performance, a behaviour which is aggravated in uncertain…
This paper addresses the problem of optimizing partition functions in a stochastic learning setting. We propose a stochastic variant of the bound majorization algorithm that relies on upper-bounding the partition function with a quadratic…
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…
Control Barrier Functions (CBFs) are a practical approach for designing safety-critical controllers, but constructing them for arbitrary nonlinear dynamical systems remains a challenge. Recent efforts have explored learning-based methods,…
We introduce an optimal and nearly parameter-free algorithm for minimizing piecewise smooth (PWS) convex functions under the quadratic growth (QG) condition, where the locations and structure of the smooth regions are entirely…
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…
Control systems operating in the real world face countless sources of unpredictable uncertainties. These random disturbances can render deterministic guarantees inapplicable and cause catastrophic safety failures. To overcome this, this…
This manuscript presents an innovative framework for constructing barrier functions to bound reachability probabilities for continuous-time stochastic systems described by stochastic differential equations (SDEs). The reachability…