Related papers: Finite-Step Invariant Sets for Hybrid Systems with…
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…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
In this paper we study the robust invariant sets generation problem for discrete-time switched polynomial systems subject to disturbance inputs within the optimal control framework. A robust invariant set of interest is a set of states such…
Recurrence in the phase space of complex systems is a well-studied phenomenon, which has provided deep insights into the nonlinear dynamics of such systems. For dissipative systems, characteristics based on recurrence plots have recently…
Approximation of a continuous dynamics by discrete dynamics in the form of Poincare map is one of the fascinating mathematical tool, which can describe the approximate behaviour of the dynamics of the dynamical system in lesser dimension…
Successfully achieving bipedal locomotion remains challenging due to real-world factors such as model uncertainty, random disturbances, and imperfect state estimation. In this work, we propose a novel metric for locomotive robustness -- the…
We present a unified probabilistic framework for simultaneous trajectory estimation and planning (STEAP). Estimation and planning problems are usually considered separately, however, within our framework we show that solving them…
The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…
This paper investigates a class of generalized inverse mixed variational inequality problems (GIMVIPs), which consist in finding a vector $\overline{w}\in \R^d$ such that \[ F(\bar w)\in \Omega \quad \text{and} \quad \langle h(\bar w),…
The Poincare function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V.Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and…
Slow-fast dynamical systems have two time scales and an explicit parameter representing the ratio of these time scales. Locally invariant slow manifolds along which motion occurs on the slow time scale are a prominent feature of slow-fast…
In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new…
Study of continuous dynamical system through Poincare map is one of the most popular topics in nonlinear analysis. This is done by taking intersections of the orbit of flow by a hyper-plane parallel to one of the coordinate hyper-planes of…
In this paper, we propose a mass conservative semi-Lagrangian finite difference scheme for multi-dimensional problems without dimensional splitting. The semi-Lagrangian scheme, based on tracing characteristics backward in time from grid…
Recent years have witnessed the rapid advancement of understanding the control mechanism of networked dynamical systems (NDSs), which are governed by components such as nodal dynamics and topology. This paper reveals that the critical…
In this article, a posteriori error analysis of the elliptic obstacle problem is addressed using hybrid high-order methods. The method involve cell unknowns represented by degree-$r$ polynomials and face unknowns represented by degree-$s$…
Safe path and gait planning are essential for bipedal robots to navigate complex real-world environments. The prevailing approaches often plan the path and gait separately in a hierarchical fashion, potentially resulting in unsafe movements…
Accurate and robust localization and mapping are essential components for most autonomous robots. In this paper, we propose a SLAM system for building globally consistent maps, called PIN-SLAM, that is based on an elastic and compact…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…