Related papers: Quantitative Supermartingale Certificates
We extend a template-based approach for synthesizing switching controllers for semi-algebraic hybrid systems, in which all expressions are polynomials. This is achieved by combining a QE (quantifier elimination)-based method for generating…
This paper presents a probabilistic model validation methodology for nonlinear systems in time-domain. The proposed formulation is simple, intuitive, and accounts both deterministic and stochastic nonlinear systems with parametric and…
This paper addresses the critical challenge of developing data-driven certificates for the stability and safety of unmodeled dynamical systems by leveraging a tree data structure and an upper bound of the system's Lipschitz constant.…
We study the problem of learning controllers for discrete-time non-linear stochastic dynamical systems with formal reach-avoid guarantees. This work presents the first method for providing formal reach-avoid guarantees, which combine and…
In many synthesis problems, it can be essential to generate implementations which not only satisfy functional constraints but are also randomized to improve variety, robustness, or unpredictability. The recently-proposed framework of…
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
This paper presents a synthesis approach aiming to guarantee a minimum upper-bound for the time taken to reach a target set of non-zero measure that encompasses the origin, while taking into account uncertainties and input and state…
We study time-inhomogeneous Markov chains to obtain quantitative results on their asymptotic behavior. We use Poincar\'e, Nash, and logarithmic-Sobolev inequalities. We assume that our Markov chain admits a finite invariant measure at each…
An approach is presented for robustness analysis and quantum (unitary) control synthesis based on the classic method of averaging. The result is a multicriterion optimization competing the nominal (uncertainty-free) fidelity with a well…
This paper investigates the algorithmic safety verification problem of infinite-state parameterized concurrent programs over a rich set of communication topologies. The goal is to automatically produce a proof of correctness in the form of…
In this paper, we present a generalization of the certainty equivalence principle of stochastic control. One interpretation of the classical certainty equivalence principle for linear systems with output feedback and quadratic costs is as…
This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…
Controllers for dynamical systems that operate in safety-critical settings must account for stochastic disturbances. Such disturbances are often modeled as process noise in a dynamical system, and common assumptions are that the underlying…
The Error-in-Variables model of system identification/control involves nontrivial input and measurement corruption of observed data, resulting in generically nonconvex optimization problems. This paper performs full-state-feedback…
This paper is concerned with the maximum principle of stochastic optimal control problems, where the coefficients of the state equation and the cost functional are uncertain, and the system is generally under Markovian regime switching.…
Let $L$ be a countable language. We characterize, in terms of definable closure, those countable theories $\Sigma$ of $\mathcal{L}_{\omega_1, \omega}(L)$ for which there exists an $S_\infty$-invariant probability measure on the collection…
Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal…
The number of times that we can access a system to extract information via quantum metrology is always finite, and possibly small, and realistic amounts of prior knowledge tend to be moderate. Thus theoretical consistency demands a…
Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide…
Safety is a critical property for control systems in medicine, transportation, manufacturing, and other applications, and can be defined as ensuring positive invariance of a predefined safe set. This paper investigates the problems of…