Related papers: Exact Safety Verification of Hybrid Systems Using …
Stability analysis tools are essential to understanding and controlling any engineering system. Recently sum-of-squares (SOS) based methods have been used to compute Lyapunov based estimates for the region-of-attraction (ROA) of polynomial…
Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finite-time asymptotic…
A common technique for verifying the safety of complex systems is the inductive invariant method. Inductive invariants are inductive formulas that overapproximate the reachable states of a system and imply a desired safety property.…
In this paper, we present an algorithm for synthesizing certificates---so-called barrier certificates---for safety of hybrid dynamical systems. Unlike the usual approach of using constraint solvers to compute the certificate from the system…
Certifying nonnegativity of polynomials is a well-known NP-hard problem with direct applications spanning non-convex optimization, control, robotics, and beyond. A sufficient condition for nonnegativity is the Sum of Squares (SOS) property,…
In this paper we give an overview of results on the analysis of parametric linear hybrid automata, and of systems of similar linear hybrid automata: We present possibilities of describing systems with a parametric (i.e. not explicitly…
Safety guarantee is essential in many engineering implementations. Reinforcement learning provides a useful way to strengthen safety. However, reinforcement learning algorithms cannot completely guarantee safety over realistic operations.…
This paper presents a novel algorithm for constructing a sum-of-squares (SOS) decomposition for positive semi-definite polynomials with rational coefficients. Unlike previous methods that typically yield SOS decompositions with…
This paper presents numerical methods for computing regions of finite-time invariance (funnels) around solutions of polynomial differential equations. First, we present a method which exactly certifies sufficient conditions for invariance…
In order to obtain the best-known guarantees, algorithms are traditionally tailored to the particular problem we want to solve. Two recent developments, the Unique Games Conjecture (UGC) and the Sum-of-Squares (SOS) method, surprisingly…
We consider the problem of coordinating a collection of switched subsystems under both local and global constraints for safe operation of the system. Although an invariant set can be leveraged to construct a safety-guaranteed controller for…
The integration of neural networks into safety-critical systems has shown great potential in recent years. However, the challenge of effectively verifying the safety of Neural Network Controlled Systems (NNCS) persists. This paper…
In order to address the imprecision often introduced by widening operators in static analysis, policy iteration based on min-computations amounts to considering the characterization of reachable value set of a program as an iterative…
We study sum of squares (SOS) relaxations to optimize polynomial functions over a set $V\cap R^n$, where $V$ is a complex algebraic variety. We propose a new methodology that, rather than relying on some algebraic description, represents…
Estimation is the computational task of recovering a hidden parameter $x$ associated with a distribution $D_x$, given a measurement $y$ sampled from the distribution. High dimensional estimation problems arise naturally in statistics,…
This work presents a computationally efficient approach to data-driven robust contracting controller synthesis for polynomial control-affine systems based on a sum-of-squares program. In particular, we consider the case in which a system…
In this paper, we address the risk estimation problem where one aims at estimating the probability of violation of safety constraints for a robot in the presence of bounded uncertainties with arbitrary probability distributions. In this…
Finding a controlled-invariant set for a system with state and control constraints is crucial for safety-critical applications. However, existing methods often produce overly conservative solutions. This paper presents a method for…
We demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (i) wireless…
This paper proposes a (control) barrier function synthesis and safety verification scheme for interconnected nonlinear systems based on assume-guarantee contracts (AGC) and sum-of-squares (SOS) techniques. It is well-known that the SOS…