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

In this work, we propose a compositional scheme based on small-gain reasoning to synthesize safety controllers for interconnected stochastic hybrid systems. In our proposed setting, we first offer an augmented scheme that characterizes each…

Let $p_{\min}$ denote the minimum of a polynomial $p$ over a (general) compact semialgebraic set $S \subseteq \mathbb{R}^n$. A standard way to approximate $p_{\min}$ is via hierarchies built from Positivstellens\"atze, which certify…

This work is concerned with a formal approach for safety controller synthesis of stochastic control systems with both process and measurement noises while considering wireless communication networks between sensors, controllers, and…

In this paper we introduce a variant of the Syndrome Decoding Problem (SDP), that we call Restricted SDP (R-SDP), in which the entries of the searched vector are defined over a subset of the underlying finite field. We prove the…

In this draft article, we consider the problem of achieving safe control of a dynamic system for which the safety index or (control barrier function (loosely)) has relative degree equal to two. We consider parameter affine nonlinear dynamic…

A fundamental problem in quantum coding theory is to determine the maximum size of quantum codes of given block length and distance. A recent work introduced bounds based on semidefinite programming, strengthening the well-known quantum…

This work is concerned with developing a data-driven approach for learning control barrier certificates (CBCs) and associated safety controllers for discrete-time nonlinear polynomial systems with unknown mathematical models, guaranteeing…

Modern cyber-physical systems (CPS) integrate physics, computation, and learning, demanding modeling frameworks that are simultaneously composable, learnable, and verifiable. Yet existing approaches treat these goals in isolation: causal…

This paper introduces a method of identifying a maximal set of safe strategies from data for stochastic systems with unknown dynamics using barrier certificates. The first step is learning the dynamics of the system via Gaussian process…

Signature kernels have emerged as a powerful tool within kernel methods for sequential data. In the paper "The Signature Kernel is the solution of a Goursat PDE", the authors identify a kernel trick that demonstrates that, for continuously…

This paper generalizes the control barrier function framework by replacing scalar-valued functions with matrix-valued ones. Specifically, we develop barrier conditions for safe sets defined by matrix inequalities -- both semidefinite and…

Symmetry and dominance breaking can be crucial for solving hard combinatorial search and optimisation problems, but the correctness of these techniques sometimes relies on subtle arguments. For this reason, it is desirable to produce…

We introduce a hybrid (discrete--continuous) safety controller which enforces strict state and input constraints on a system---but only acts when necessary, preserving transparent operation of the original system within some safe region of…

Recent advances in Deep Machine Learning have shown promise in solving complex perception and control loops via methods such as reinforcement and imitation learning. However, guaranteeing safety for such learned deep policies has been a…

This paper studies the complexity of matrix Putinar's Positivstellens{\"a}tz on the semialgebraic set that is given by the polynomial matrix inequality. \rev{When the quadratic module generated by the constrained polynomial matrix is…

We investigate the problem of verifying different properties of discrete time dynamical systems, namely, reachability, safety and reach-while-avoid. To achieve this, we adopt a data driven perspective and, using past system trajectories as…

Certifying the safety or robustness of neural networks against input uncertainties and adversarial attacks is an emerging challenge in the area of safe machine learning and control. To provide such a guarantee, one must be able to bound the…

While conventional (k=1) discrete-time barrier certificate conditions impose strict safety constraints by requiring the function to be non-increasing at every step, k-inductive barrier certificates relax this by allowing a temporary…

Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…

Differential-algebraic equations (DAEs) arise in power networks, chemical processes, and multibody systems, where algebraic constraints encode physical conservation laws. The safety of such systems is critical, yet safe control is…