相关论文: Computation of invariant sets via immersion for di…

In this paper a constructive method to determine and compute probabilistic reachable and invariant sets for linear discrete-time systems, excited by a stochastic disturbance, is presented. The samples of the disturbance signal are not…

For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…

The synthesis of robust invariant sets for nonlinear systems has traditionally been hindered by the inherent non convexity and a strict reliance on exact analytical models. This paper presents a purely data-driven framework to compute…

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,…

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…

Linear models with additive unknown-but-bounded input disturbances are extensively used to model uncertainty in robust control systems design. Typically, the disturbance set is either assumed to be known a priori or estimated from data…

We propose a convex-optimization-based framework for computation of invariant measures of polynomial dynamical systems and Markov processes, in discrete and continuous time. The set of all invariant measures is characterized as the feasible…

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…

In this work, we propose a new framework for reachable set computation through continuous evolution of a set of parameters and offsets which define a parametope, through the intersection of constraints. This results in a dynamical approach…

This work considers special types of interval linear systems - overdetermined systems. Simply said these systems have more equations than variables. The solution set of an interval linear system is a collection of all solutions of all…

Systems equipped with modern sensing modalities such as vision and lidar gain access to increasingly high-dimensional measurements with which to enact estimation and control schemes. In this article, we examine the continuum limit of…

We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We propose a semidefinite…

Entropy notions for $\varepsilon$-incremental practical stability and incremental stability of deterministic nonlinear systems under disturbances are introduced. The entropy notions are constructed via a set of points in state space which…

Reachable sets of nonlinear control systems can in general only be approximated numerically, and these approximations are typically very expensive to compute. In this paper, we explore a strategy for choosing the temporal and spatial…

Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…

In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…

Understanding when linear immersions of nonlinear dynamical systems exist is important since such immersions allow us to leverage the rich tools of linear system theory to analyze nonlinear dynamics. Recently, Liu et al. (2023) showed that…

We present two theoretical results on the computation of lambda-contractive sets for linear systems with state and input constraints. First, we show that it is possible to a priori compute a number of iterations that is sufficient to…

We propose a framework for inversion-based estimation of certain categories of faults in discrete-time linear systems. The fault signal, as an unknown input, is reconstructed from its projections onto two subspaces. One projection is…

Given a dynamical system with constrained outputs, the maximal admissible set (MAS) is defined as the set of all initial conditions such that the output constraints are satisfied for all time. It has been previously shown that for…