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We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received…
We introduce High-Relative Degree Stochastic Control Lyapunov functions and Barrier Functions as a means to ensure asymptotic stability of the system and incorporate state dependent high relative degree safety constraints on a non-linear…
We have developed a method for complementing an arbitrary classical dynamical system to a quantum system using the Lorenz and R\"ossler systems as examples. The Schr\"odinger equation for the corresponding quantum statistical ensemble is…
We propose to compute approximations to general invariant sets in dynamical systems by minimizing the distance between an appropriately selected finite set of points and its image under the dynamics. We demonstrate, through computational…
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most previous works consider numerical bounds over the whole…
In this paper, we present an analytical approach for the synthesis of ellipsoidal probabilistic reachable sets of saturated systems subject to unbounded additive noise. Using convex optimization methods, we compute a contraction factor of…
The threshold, or saturation phenomenon of spatially coupled systems is revisited in the light of Lyapunov's theory of dynamical systems. It is shown that an application of Lyapunov's direct method can be used to quantitatively describe the…
The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with…
Analyzing and reasoning about safety properties of software systems becomes an especially challenging task for programs with complex flow and, in particular, with loops or recursion. For such programs one needs additional information, for…
Recent advances in learning techniques have enabled the modelling of unknown dynamical systems directly from data. However, in many contexts, these learning-based methods are short of safety guarantee and strict stability verification. To…
In various fields of natural science, the chaotic systems of differential equations are considered more than 50 years. The correct prediction of the behaviour of solutions of dynamical model equations is important in understanding of…
General purpose intelligent learning agents cycle through (complex,non-MDP) sequences of observations, actions, and rewards. On the other hand, reinforcement learning is well-developed for small finite state Markov Decision Processes…
A method for constructing homogeneous Lyapunov functions of degree 1 from polynomial invariant sets is presented for linear time varying systems, homogeneous dynamic systems and the class of nonlinear systems that can be represented as…
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…
In this paper, we consider a control synthesis problem for a class of polynomial dynamical systems subject to bounded disturbances and with input constraints. More precisely, we aim at synthesizing at the same time a controller and an…
Control invariant sets play an important role in safety-critical control and find broad application in numerous fields such as obstacle avoidance for mobile robots. However, finding valid control invariant sets of dynamical systems under…
In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using…
We propose a new matrix pencil based approach for design of state-feedback and output-feedback stabilizing controllers for a general class of uncertain nonlinear strict-feedback-like systems. While the dynamic controller structure is based…
In this paper an autonomous analytical system of ordinary differential equations is considered. For an asymptotically stable steady state x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when…
We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…