Related papers: On Recurrent Reachability for Continuous Linear Dy…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…
Synchronous dynamic systems are well-established models that have been used to capture a range of phenomena in networks, including opinion diffusion, spread of disease and product adoption. We study the three most notable problems in…
A new iterative method for solving large scale symmetric nonlinear eigenvalue problems is presented. We firstly derive an infinite dimensional symmetric linearization of the nonlinear eigenvalue problem, then we apply the indefinite Lanczos…
In this paper, we study networks of discrete-time linear time-invariant subsystems. Our focus is on situations where subsystems are connected to each other through a time-invariant topology and where there exists a base-station whose aim is…
We develop a numerical method for solving a system of nonlinear integral equations involving two integral terms: at the current time t, one integral is taken from 0 to t, and a different integral is taken from t to infinity. We prove the…
In this paper, we consider the solvability problems for the fully coupled forward-backward stochastic difference equations (FBS{\Delta}Es) on spaces related to discrete time, finite state processes. On one hand, we provide the necessary and…
In this work, we present a novel Koopman spectrum-based reachability verification method for nonlinear systems. Contrary to conventional methods that focus on characterizing all potential states of a dynamical system over a presupposed time…
We study the following reachability problem for piecewise affine maps: Given two vectors $\mathbf{s}, \mathbf{t} \in \mathbb{Q}^d$ and a piecewise affine map $f \colon \mathbb{Q}^d\rightarrow \mathbb{Q}^d$, does there exist $n\in…
The goal of this paper is to investigate new and simple convergence analysis of dynamic programming for linear quadratic regulator problem of discrete-time linear time-invariant systems. In particular, bounds on errors are given in terms of…
A non-deterministic recursion scheme recognizes a language of finite trees. This very expressive model can simulate, among others, higher-order pushdown automata with collapse. We show decidability of the diagonal problem for schemes. This…
The question is studied whether weak solutions of linear partial integrodifferential equations approach a constant spatial profile after rescaling, as time goes to infinity. The possible limits and corresponding scaling functions are…
Nearly linear recurrences are a generalisation of linear recurrences and are instances of linear time-invariant systems in control theory and linear constraint loops in program analysis. In this paper we formulate the Positivity Problem for…
This paper studies the solvability of a class of Dirichlet problem associated with non-linear integro-differential operator. The main ingredient is the probabilistic construction of continuous supersolution via the identification of the…
Shaping the reachable set of a dynamical system is a fundamental challenge in control design, with direct implications for both performance and safety. This paper considers the problem of selecting the optimal input matrix for a linear…
We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
We investigate the use of piecewise linear systems, whose coefficient matrix is a piecewise constant function of the solution itself. Such systems arise, for example, from the numerical solution of linear complementarity problems and in the…
The decidability of the reachability problem for finitary PCF has been used as a theoretical basis for fully automated verification tools for functional programs. The reachability problem, however, often becomes undecidable for a slight…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…