Related papers: Backward Reachability for Polynomial Systems on A …
There has been an increasing interest in using neural networks in closed-loop control systems to improve performance and reduce computational costs for on-line implementation. However, providing safety and stability guarantees for these…
Zonotopes are widely used for over-approximating forward reachable sets of uncertain linear systems for verification purposes. In this paper, we use zonotopes to achieve more scalable algorithms that under-approximate backward reachable…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…
In this paper, we present an analytical approach for the synthesis of ellipsoidal probabilistic reachable sets of saturated systems subject to unbounded additive noise. Using convex optimization methods, we compute a contraction factor of…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
The increasing prevalence of neural networks (NNs) in safety-critical applications calls for methods to certify their behavior and guarantee safety. This paper presents a backward reachability approach for safety verification of neural…
Accurately modeling and verifying the correct operation of systems interacting in dynamic environments is challenging. By leveraging parametric uncertainty within the model description, one can relax the requirement to describe exactly the…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Higher-order pushdown systems (PDSs) generalise pushdown systems through the use of higher-order stacks, that is, a nested "stack of stacks" structure. These systems may be used to model higher-order programs and are closely related to the…
While several classes of integer linear optimization problems are known to be solvable in polynomial time, far fewer tractability results exist for integer nonlinear optimization. In this work, we narrow this gap by identifying a broad…
In this paper, we consider the computational complexity of bounding the reachable set of a Linear Time-Invariant (LTI) system controlled by a Rectified Linear Unit (ReLU) Two-Level Lattice (TLL) Neural Network (NN) controller. In…
Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…
This paper considers the robust phase retrieval problem, which can be cast as a nonsmooth and nonconvex optimization problem. We propose a new inexact proximal linear algorithm with the subproblem being solved inexactly. Our contributions…
This paper considers an optimal radial reconfiguration problem in multi-source distribution networks, where the goal is to find a radial configuration that minimizes quadratic distribution costs while ensuring all sink demands are met. This…
In multirotor systems, guaranteeing safety while considering unknown disturbances is essential for robust trajectory planning. The Forward reachable set (FRS), the set of feasible states subject to bounded disturbances, can be utilized to…
We consider the problem of ensuring the safety of nonlinear control systems under adversarial signals. Using Lyapunov based reachability analysis, we first give sufficient conditions to assess safety, i.e., to guarantee that the states of…
We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main…
The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing…
Model predictive control allows solving complex control tasks with control and state constraints. However, an optimal control problem must be solved in real-time to predict the future system behavior, which is hardly possible on embedded…