On sample-based computations of invariant sets
Sign Up to like & getrecommendations! Published in 2018 at "Nonlinear Dynamics"
DOI: 10.1007/s11071-018-4512-7
Abstract: In this paper, the classical problem of uncovering the maximal invariant set of a (discrete-time) dynamical system is illuminated from a novel perspective, which in particular leads to a novel sample-based computational procedure to compute… read more here.
Keywords: sample based; computations invariant; invariant set; invariant sets ... See more keywords
Invariant sets and Lyapunov pairs for differential inclusions with maximal monotone operators
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.04.059
Abstract: We give different conditions for the invariance of closed sets with respect to differential inclusions governed by a maximal monotone operator defined on Hilbert spaces, which is subject to a Lipschitz continuous perturbation depending on… read more here.
Keywords: maximal monotone; differential inclusions; sets lyapunov; lyapunov pairs ... See more keywords
Characterizations of Integral Input-to-State Stability for Systems With Multiple Invariant Sets
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DOI: 10.1109/tac.2016.2642782
Abstract: We extend the classical integral Input-to-State Stability (iISS) theory to systems evolving on complete Riemannian manifolds and admitting multiple disjoint invariant sets, so as to allow a much broader variety of dynamical behaviors of interest.… read more here.
Keywords: state stability; input; input state; invariant sets ... See more keywords
Computing Robust Controlled Invariant Sets of Linear Systems
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DOI: 10.1109/tac.2017.2672859
Abstract: We consider controllable linear discrete-time systems with bounded perturbations and present two methods to compute robust controlled invariant sets. The first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation… read more here.
Keywords: sets linear; robust controlled; controlled invariant; computing robust ... See more keywords
An Interval Approach to Compute Invariant Sets
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DOI: 10.1109/tac.2017.2685241
Abstract: This paper proposes an original interval-based method to compute an outer approximation of all invariant sets (such as limit cycles) of a continuous-time nonlinear dynamic system, which are included inside a prior set of the… read more here.
Keywords: interval approach; compute invariant; invariant sets; approach compute ... See more keywords
Scalable Computation of Robust Control Invariant Sets of Nonlinear Systems
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Automatic Control"
DOI: 10.1109/tac.2023.3275305
Abstract: —Ensuring robust constraint satisfaction for an infinite time horizon is a challenging, yet crucial task when deploying safety-critical systems. We address this issue by synthesizing robust control invariant sets for perturbed nonlinear sampled-data systems. This… read more here.
Keywords: computation robust; control; control invariant; robust control ... See more keywords
Formal Methods for Computing Hyperbolic Invariant Sets for Nonlinear Systems
Sign Up to like & getrecommendations! Published in 2020 at "IEEE Control Systems Letters"
DOI: 10.1145/3302504.3313350
Abstract: Hyperbolicity is a cornerstone of nonlinear dynamical systems theory. Hyperbolic dynamics are characterized by the presence of expanding and contracting directions for the derivative along the trajectories of the system. Hyperbolic dynamical systems enjoy many… read more here.
Keywords: system; methods computing; formal methods; hyperbolic invariant ... See more keywords
Using Interval Analysis to Compute the Invariant Set of a Nonlinear Closed-Loop Control System
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DOI: 10.3390/a12120262
Abstract: In recent years, many applications, as well as theoretical properties of interval analysis have been investigated. Without any claim for completeness, such applications and methodologies range from enclosing the effect of round-off errors in highly… read more here.
Keywords: closed loop; interval analysis; nonlinear closed; control ... See more keywords
Kleene Algebra to Compute Invariant Sets of Dynamical Systems
Sign Up to like & getrecommendations! Published in 2022 at "Algorithms"
DOI: 10.3390/a15030090
Abstract: In this paper, we show that a basic fixed point method used to enclose the greatest fixed point in a Kleene algebra will allow us to compute inner and outer approximations of invariant-based sets for… read more here.
Keywords: kleene algebra; compute invariant; dynamical systems; invariant sets ... See more keywords