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We survey dynamic logics for specifying and verifying properties of dynamical systems, including hybrid systems, distributed hybrid systems, and stochastic hybrid systems. A dynamic logic is a first-order modal logic with a pair of…
In this paper we investigate formal verification problems for Neural Network computations. Of central importance will be various robustness and minimization problems such as: Given symbolic specifications of allowed inputs and outputs in…
We propose, analyze, and test new robust iterative solvers for systems of linear algebraic equations arising from the space-time finite element discretization of reduced optimality systems defining the approximate solution of hyperbolic…
We study the problem of detecting zeros of continuous functions that are known only up to an error bound, extending the earlier theoretical work with explicit algorithms and experiments with an implementation. More formally, the robustness…
In a paper by Willems and coauthors it was shown that persistently exciting data can be used to represent the input-output behavior of a linear system. Based on this fundamental result, we derive a parametrization of linear feedback systems…
Nonlinear ordinary differential equations (ODEs) are powerful tools for modeling real-world dynamical systems. However, propagating initial state uncertainty through nonlinear dynamics, especially when the ODE is unknown and learned from…
Symmetric matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
We consider the problem of learning the dynamics of autonomous linear systems (i.e., systems that are not affected by external control inputs) from observations of multiple trajectories of those systems, with finite sample guarantees.…
Consider an n-dimensional linear system where it is known that there are at most k<n non-zero components in the initial state. The observability problem, that is the recovery of the initial state, for such a system is considered. We obtain…
This paper investigates a series of optimization problems for one-counter Markov decision processes (MDPs) and integer-weighted MDPs with finite state space. Specifically, it considers problems addressing termination probabilities and…
We discuss different cases of dissipative Hamiltonian differential-algebraic equations and the linear algebraic systems that arise in their linearization or discretization. For each case we give examples from practical applications. An…
Results on the problem of stabilizing a nonlinear continuous-time system by a finite number of control or measurement values are presented. The basic tool is a discontinuous version of the so-called semi-global backstepping lemma. We derive…
In this paper, we consider the robust linear infinite programming problem $({\rm RLIP}_c) $ defined by \begin{eqnarray*} ({\rm RLIP}_c)\quad &&\inf\; \langle c,x\rangle \textrm{subject to } &&x\in X,\; \langle x^\ast,x \rangle \le r…
This paper studies the robustness of reinforcement learning algorithms to errors in the learning process. Specifically, we revisit the benchmark problem of discrete-time linear quadratic regulation (LQR) and study the long-standing open…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…
Implicit methods for the numerical solution of initial-value problems may admit multiple solutions at any given time step. Accordingly, their nonlinear solvers may converge to any of these solutions. Below a critical timestep, exactly one…
Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered…
We introduce a model of infinite horizon linear dynamic optimization and obtain results concerning existence of solution and satisfaction of the competitive condition and transversality condition being unconditionally sufficient for…