Related papers: Scalable Zonotopic Under-approximation of Backward…

We present a method to overapproximate forward stochastic reach sets of discrete-time, stochastic nonlinear systems with interval geometry. This is made possible by extending the theory of mixed-monotone systems to incorporate stochastic…

A method is proposed to compute robust inner-approximations to the backward reachable set for uncertain nonlinear systems. It also produces a robust control law that drives trajectories starting in these sets to the target set. The method…

Data-driven reachability analysis using matrix zonotopes faces a fundamental challenge: the number of generators in the reachable set grows exponentially during propagation, while current order reduction yields overly conservative…

One often wishes for the ability to formally analyze large-scale systems---typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This work tries to further close this…

Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between…

In this paper, I propose a new framework for representing multidimensional incomplete preferences through zonotope-valued utilities, addressing the shortcomings of traditional scalar and vector-based models in decision theory. Traditional…

Backward reachability analysis computes the set of states that reach a target set under the competing influence of control input and disturbances. Depending on their interplay, the backward reachable set either represents all states that…

In this work, we perform safety analysis of linear dynamical systems with uncertainties. Instead of computing a conservative overapproximation of the reachable set, our approach involves computing a statistical approximate reachable set. As…

Forward reachability analysis is the predominant approach for verifying reach-avoid properties in neural feedback systems (dynamical systems controlled by neural networks). This dominance stems from the limited scalability of existing…

We propose a method to outer bound forward reachable sets on finite horizons for uncertain nonlinear systems with polynomial dynamics. This method makes use of time-dependent polynomial storage functions that satisfy appropriate dissipation…

We study the verification problem for closed-loop dynamical systems with neural-network controllers (NNCS). This problem is commonly reduced to computing the set of reachable states. When considering dynamical systems and neural networks in…

We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…

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…

In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable…

Learning-enabled planning and control algorithms are increasingly popular, but they often lack rigorous guarantees of performance or safety. We introduce an algorithm for computing underapproximate backward reachable sets of nonlinear…

Reachability analysis for hybrid nonaffine systems remains computationally challenging, as existing set representations--including constrained, polynomial, and hybrid zonotopes--either lose tightness under high-order nonaffine maps or…

Computing tight over-approximation of reach sets of a controlled uncertain dynamical system is a common practice in verification of safety-critical cyber-physical systems (CPS). While several algorithms are available for this purpose, they…

Reachability analysis is important for studying optimal control problems and differential games, which are powerful theoretical tools for analyzing and modeling many practical problems in robotics, aircraft control, among other application…

The probabilistic reachability problems of nondeterministic systems are studied. Based on the existing studies, the definition of probabilistic reachable sets is generalized by taking into account time-varying target set and obstacle. A…

This paper proposes a tractable family of remainder-form mixed-monotone decomposition functions that are useful for over-approximating the image set of nonlinear mappings in reachability and estimation problems. Our approach applies to a…