Related papers: Quantitative Supermartingale Certificates
In this paper, we revisit the formal verification problem for stochastic dynamical systems over finite horizon using barrier certificates. Most existing work on this topic focuses on safety properties by constructing barrier certificates…
Control barrier certificates have proven effective in formally guaranteeing the safety of the control systems. However, designing a control barrier certificate is a time-consuming and computationally expensive endeavor that requires expert…
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…
We develop an assume-guarantee framework for control of large scale linear (time-varying) systems from finite-time reach and avoid or infinite-time invariance specifications. The contracts describe the admissible set of states and controls…
We establish finite sample certificates on the quality of solutions produced by data-based forward-backward (FB) operator splitting schemes. As frequently happens in stochastic regimes, we consider the problem of finding a zero of the sum…
In this paper, we present a provably correct controller synthesis approach for switched stochastic control systems with metric temporal logic (MTL) specifications with provable probabilistic guarantees. We first present the stochastic…
In this paper, we compute finite sample bounds for data-driven approximations of the solution to stochastic reachability problems. Our approach uses a nonparametric technique known as kernel distribution embeddings, and provides…
This paper addresses the problem of risk-aware fixed-time stabilization of a class of uncertain, output-feedback nonlinear systems modeled via stochastic differential equations. First, novel classes of certificate functions, namely…
The accurate characterization of quantum systems is essential for the advancement of quantum technologies. In particular, certifying convex functions of quantum states plays a central role in many applications. We present a certification…
We develop a theory of decidable inductive invariants for an infinite-state variant of the Applied pi-calculus, with applications to automatic verification of stateful cryptographic protocols with unbounded sessions/nonces. Since the…
Stochastic models are widely used to verify whether systems satisfy their reliability, performance and other nonfunctional requirements. However, the validity of the verification depends on how accurately the parameters of these models can…
In this paper, we present a computational approach to certify almost sure reachability for discrete-time polynomial stochastic systems by turning drift--variant criteria into sum-of-squares (SOS) programs solved with standard semidefinite…
This paper presents conditions for ensuring forward invariance of safe sets under sampled-data system dynamics with piecewise-constant controllers and fixed time-steps. First, we introduce two different metrics to compare the…
Mistrustful quantum cryptographic protocols encode information in incompatible observables, so that any attempt by a dishonest party to access multiple pieces of information necessarily involves a tradeoff. A natural class of such…
In this paper we consider the safety verification and safe controller synthesis problems for nonlinear control systems. The Control Barrier Certificates (CBC) approach is proposed as an extension to the Barrier certificates approach. Our…
Deciding termination is a fundamental problem in the analysis of probabilistic imperative programs. We consider the qualitative and quantitative probabilistic termination problems for an imperative programming model with discrete…
Infinite networks are complex interconnected systems comprising a countably infinite number of subsystems, for which no fixed upper bound on the number of participating subsystems is specified a priori since it may vary over time as agents…
In this paper, we associate, to any submartingale of class $(\Sigma)$, defined on a filtered probability space $(\Omega, \mathcal{F}, \mathbb{P}, (\mathcal{F}_t)_{t \geq 0})$, which satisfies some technical conditions, a $\sigma$-finite…
Model mismatches prevail in real-world applications. Ensuring safety for systems with uncertain dynamic models is critical. However, existing robust safe controllers may not be realizable when control limits exist. And existing methods use…
We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…