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Model checkers use automated state exploration in order to prove various properties such as reachability, non-reachability, and bisimulation over state transition systems. While model checkers have proved valuable for locating errors in…
Training-time safety violations have been a major concern when we deploy reinforcement learning algorithms in the real world. This paper explores the possibility of safe RL algorithms with zero training-time safety violations in the…
Learning-based methods provide a promising approach to solving highly non-linear control tasks that are often challenging for classical control methods. To ensure the satisfaction of a safety property, learning-based methods jointly learn a…
An emerging branch of control theory specialises in certificate learning, concerning the specification of a desired (possibly complex) system behaviour for an autonomous or control model, which is then analytically verified by means of a…
The second-order cone (SOC) is a class of simple convex cones and optimizing over them can be done more efficiently than with semidefinite programming. It is interesting both in theory and in practice to investigate which convex cones admit…
This paper offers a direct data-driven approach for learning robust control barrier certificates (R-CBCs) and robust safety controllers (R-SCs) for discrete-time input-affine polynomial systems with unknown dynamics under…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
The Hessian of a differentiable convex function is positive semidefinite. Therefore, checking the Hessian of a given function is a natural approach to certify convexity. However, implementing this approach is not straightforward since it…
Reach-avoid analysis is fundamental to reasoning about the safety and goal-reaching behavior of dynamical systems, and serves as a foundation for specifying and verifying more complex control objectives. This paper introduces a reach-avoid…
In (Davis and Papp, 2022), the authors introduced the concept of dual certificates of (weighted) sum-of-squares polynomials, which are vectors from the dual cone of weighted sums of squares (WSOS) polynomials that can be interpreted as…
Almost sure reachability refers to the property of a stochastic system whereby, from any initial condition, the system state reaches a given target set with probability one. In this paper, we study the problem of certifying almost sure…
The goal of this paper is certifying safety of dynamical systems subject to uncertainty. Existing approaches use trajectory data to estimate transition probabilities, and compute safety probabilities recursively via dynamic programming…
In this paper, vector optimization is considered in the framework of decision making and optimization in general spaces. Interdependencies between domination structures in decision making and domination sets in vector optimization are…
Given query access to a monotone function $f\colon\{0,1\}^n\to\{0,1\}$ with certificate complexity $C(f)$ and an input $x^{\star}$, we design an algorithm that outputs a size-$C(f)$ subset of $x^{\star}$ certifying the value of…
In recent years, various techniques have been explored for the verification of quantum circuits, including the use of barrier certificates, mathematical tools capable of demonstrating the correctness of such systems. These certificates…
We develop a general and unconditional framework for certifying the global nonnegativity of multivariate integer polynomials; based on rewriting them as sum of squares modulo their gradient ideals. We remove the two structural assumptions…
This paper develops an approach to learn a policy of a dynamical system that is guaranteed to be both provably safe and goal-reaching. Here, the safety means that a policy must not drive the state of the system to any unsafe region, while…
The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…
We show that existence of a global polynomial Lyapunov function for a homogeneous polynomial vector field or a planar polynomial vector field (under a mild condition) implies existence of a polynomial Lyapunov function that is a sum of…
The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…