相关论文: On Completeness of SDP-Based Barrier Certificate S…

This paper introduces the notion of control closure certificates to synthesize controllers for discrete-time control systems against $\omega$-regular specifications. Typical functional approaches to synthesize controllers against…

Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…

In recent years, techniques based on convex optimization and real algebra that produce converging hierarchies of lower bounds for polynomial minimization problems have gained much popularity. At their heart, these hierarchies rely crucially…

Adversarial training is well-known to produce high-quality neural network models that are empirically robust against adversarial perturbations. Nevertheless, once a model has been adversarially trained, one often desires a certification…

Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision…

In this article, the problem of synthesizing switching controllers is considered through the synthesis of a "control certificate". Control certificates include control barrier and Lyapunov functions, which represent control strategies, and…

Polarization, understood as a division into mutually hostile groups, is a common feature of social systems. It is studied in Structural Balance Theory (SBT) in terms of semicycles in signed networks. However, enumerating semicycles is…

We consider the class of polynomial optimization problems $\inf \{f(x):x\in K\}$ for which the quadratic module generated by the polynomials that define $K$ and the polynomial $c-f$ (for some scalar $c$) is Archimedean. For such problems,…

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…

We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…

This paper presents a novel approach for the safe control design of systems with parametric uncertainties in both drift terms and control-input matrices. The method combines control barrier functions and adaptive laws to generate a safe…

In this article we combine two developments in polynomial optimization. On the one hand, we consider nonnegativity certificates based on sums of nonnegative circuit polynomials, which were recently introduced by the second and the third…

In this work, we propose a data-driven scheme within a compositional framework with noisy data to design robust safety controllers in a fully decentralized fashion for large-scale interconnected networks with unknown mathematical dynamics.…

Among the biggest challenges in property-based testing (PBT) is the constrained random generation problem: given a predicate on program values, randomly sample from the set of all values satisfying that predicate, and only those values.…

This paper addresses the quantitative verification of constrained occupation time in stochastic discrete-time systems, focusing on the probability of visiting a target set at least $k$ times while maintaining safety. Such cumulative…

This paper introduces a new storage-optimal first-order method (FOM), CertSDP, for solving a special class of semidefinite programs (SDPs) to high accuracy. The class of SDPs that we consider, the exact QMP-like SDPs, is characterized by…

Bounded proofs are convenient to use due to the high degree of automation that exhaustive checking affords. However, they fall short of providing the robust assurances offered by unbounded proofs. We sketch how completeness thresholds serve…

Consider a convex set S defined by a matrix inequality of polynomials or rational functions over a domain. The set S is called semidefinite programming (SDP) representable or just semidefinite representable if it equals the projection of a…

This paper develops a semidefinite-programming-based method for online feedback control of nonlinear systems using a state-dependent representation. We formulate sequences of time-varying SDPs whose optimal solutions jointly yield a…

This work addresses the critical challenge of guaranteeing safety for complex dynamical systems where precise mathematical models are uncertain and data measurements are corrupted by noise. We develop a physics-informed, direct data-driven…