Related papers: Invariants for Continuous Linear Dynamical Systems
Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions,…
Invariants are a set of properties over program attributes that are expected to be true during the execution of a program. Since developing those invariants manually can be costly and challenging, there are a myriad of approaches that…
A general expression for a relative invariant of a linear ordinary differential equations is given in terms of the fundamental semi-invariant and an absolute invariant. This result is used to established a number of properties of relative…
In this paper, we consider the problem of invariant set computation for black-box switched linear systems using merely a finite set of observations of system trajectories. In particular, this paper focuses on polyhedral invariant sets. We…
Contraction analysis is a stability theory for nonlinear systems where stability is defined incrementally between two arbitrary trajectories. It provides an alternative framework in which to study uncertain interconnections or systems with…
Assessing the robustness of perception models to covariate shifts and their ability to detect out-of-distribution (OOD) inputs is crucial for safety-critical applications such as autonomous vehicles. By nature of such applications, however,…
We survey the state of the art on the algorithmic analysis of discrete linear dynamical systems, focussing in particular on reachability, model-checking, and invariant-generation questions, both unconditionally as well as relative to…
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…
Ensuring software correctness remains a fundamental challenge in formal program verification. One promising approach relies on finding polynomial invariants for loops. Polynomial invariants are properties of a program loop that hold before…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
We investigate the integrals of motion of general conformal mechanical systems with and without confining harmonic potential as well as of the related angular subsystems, by employing the SL(2,R) algebra and its representations. In…
Infinite-state systems such as distributed protocols are challenging to verify using interactive theorem provers or automatic verification tools. Of these techniques, deductive verification is highly expressive but requires the user to…
In this paper, we consider an extended concept of invariant for polynomial dynamical system (PDS) with domain and initial condition, and establish a sound and complete criterion for checking semi-algebraic invariants (SAI) for such PDSs.…
We consider here systems with piecewise linear dynamics that are periodically sampled with a given period {\tau} . At each sampling time, the mode of the system, i.e., the parameters of the linear dynamics, can be switched, according to a…
We describe an algorithm for computing the maximal invariant set for a Markov chain with linear safety constraints on the distribution over states. We then propose a Markov chain synthesis method that guarantees finite determination of the…
Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…
There are recent shifts in demand for design controllers from simplified to complex model-based. Although simplification approaches are successful in many areas of engineering control systems, high-fidelity simulation-based control design,…
We consider learning underlying laws of dynamical systems governed by ordinary differential equations (ODE). A key challenge is how to discover intrinsic dynamics across multiple environments while circumventing environment-specific…
Invariants withstand transformations and, therefore, represent the essence of objects or phenomena. In mathematics, transformations often constitute a group action. Since the 19th century, studying the structure of various types of…