Related papers: Piecewise Stochastic Barrier Functions
We propose stochastic variance reduced algorithms for solving convex-concave saddle point problems, monotone variational inequalities, and monotone inclusions. Our framework applies to extragradient, forward-backward-forward, and…
Deploying safety-critical controllers in practice necessitates the ability to modulate uncertainties in control systems. In this context, robust control barrier functions -- in a variety of forms -- have been used to obtain safety…
In this paper, we consider the general non-oblivious stochastic optimization where the underlying stochasticity may change during the optimization procedure and depends on the point at which the function is evaluated. We develop Stochastic…
Many problems on signal processing reduce to nonparametric function estimation. We propose a new methodology, piecewise convex fitting (PCF), and give a two-stage adaptive estimate. In the first stage, the number and location of the change…
Control Barrier Functions (CBFs) have become a popular tool for enforcing set invariance in safety-critical control systems. While guaranteeing safety, most CBF approaches are myopic in the sense that they solve an optimization problem at…
Safe control with guarantees generally requires the system model to be known. It is far more challenging to handle systems with uncertain parameters. In this paper, we propose a generic algorithm that can synthesize and verify safe…
Safety of stochastic dynamic systems in environments with dynamic obstacles is studied in this paper through the lens of stochastic barrier functions. We introduce both time-invariant and time-varying barrier certificates for discrete-time,…
There are many significant applied contexts that require the solution of discontinuous optimization problems in finite dimensions. Yet these problems are very difficult, both computationally and analytically. With the functions being…
We design and analyze an algorithm for first-order stochastic optimization of a large class of functions on $\mathbb{R}^d$. In particular, we consider the \emph{variationally coherent} functions which can be convex or non-convex. The…
Control barrier function (CBF)-based methods provide the minimum modification necessary to formally guarantee safety in the context of quadratic programming, and strict safety guarantee for safety critical systems. However, most CBF-related…
In this paper we aim to construct piecewise-linear (PWL) approximations for functions of multiple variables and to build compact mixed-integer linear programming (MILP) formulations to represent the resulting PWL function. On the one hand,…
Most of machine learning approaches have stemmed from the application of minimizing the mean squared distance principle, based on the computationally efficient quadratic optimization methods. However, when faced with high-dimensional and…
We consider the problem of minimizing the sum of two convex functions: one is the average of a large number of smooth component functions, and the other is a general convex function that admits a simple proximal mapping. We assume the whole…
The paper proposes a method to obtain the optimal basis set for solving the self consistent field (SCF) equations for large atomic systems in order to calculate the energy barriers in tunneling structures, with higher accuracy and speed.…
One of the challenges encountered in optimization of mechanical structures, in particular in what is known as topology optimization, is the size of the problems, which can easily involve millions of variables. A basic example is the minimum…
Ensuring both performance and safety is critical for autonomous systems operating in real-world environments. While safety filters such as Control Barrier Functions (CBFs) enforce constraints by modifying nominal controllers in real time,…
Certifying the safety of nonlinear systems, through the lens of set invariance and control barrier functions (CBFs), offers a powerful method for controller synthesis, provided a CBF can be constructed. This paper draws connections between…
Control barrier functions (CBFs) have recently introduced a systematic tool to ensure system safety by establishing set invariance. When combined with a nominal control strategy, they form a safety-critical control mechanism. However, the…
Optimization problems involving sequential decisions in a stochastic environment were studied in Stochastic Programming (SP), Stochastic Optimal Control (SOC) and Markov Decision Processes (MDP). In this paper we mainly concentrate on SP…
We propose distributed iterative algorithms for safe control design and safety verification for networked multi-agent systems. These algorithms rely on distributing a control barrier function (CBF) related quadratic programming (QP) problem…