1,976 research outputs found
Safe Stabilization for Stochastic Time-Delay Systems
This paper addresses the safe stabilization problem of stochastic nonlinear
time-delay systems. Based on the Krasovskii approach, we first propose a
stochastic control Lyapunov-Krasovskii functional to guarantee the
stabilization objective and a stochastic control barrier-Krasovskii functional
to ensure the safety objective. Both functionals are developed respectively for
each control objectives for the first time. Since the optimization problem is
not easy to be resolved for stochastic time-delay systems, we derive a sliding
mode based approach to combine the proposed two functionals and to meditate
stabilization and safety objectives, which allows to achieve the stabilization
objective under the safety requirement. The proposed approach is illustrated
via a numerical example.Comment: 7 pages, 4 figures, submitted. arXiv admin note: text overlap with
arXiv:2204.1210
Certifying Safety for Nonlinear Time Delay Systems via Safety Functionals: A Discretization Based Approach
In this paper, we consider the safety of continuous time control systems with input delays. Safety functionals are constructed that define safety sets in the infinite-dimensional state space. Time-discretization is used in order to compute safety sets in finite dimensions and it is shown that these sets approach an infinite-dimensional safety set as the time step is decreased. A simple example of a nonlinear scalar system is used to demonstrate the convergence of the proposed methods. © 2021 American Automatic Control Council
On Norm-Based Estimations for Domains of Attraction in Nonlinear Time-Delay Systems
For nonlinear time-delay systems, domains of attraction are rarely studied
despite their importance for technological applications. The present paper
provides methodological hints for the determination of an upper bound on the
radius of attraction by numerical means. Thereby, the respective Banach space
for initial functions has to be selected and primary initial functions have to
be chosen. The latter are used in time-forward simulations to determine a first
upper bound on the radius of attraction. Thereafter, this upper bound is
refined by secondary initial functions, which result a posteriori from the
preceding simulations. Additionally, a bifurcation analysis should be
undertaken. This analysis results in a possible improvement of the previous
estimation. An example of a time-delayed swing equation demonstrates the
various aspects.Comment: 33 pages, 8 figures, "This is a pre-print of an article published in
'Nonlinear Dynamics'. The final authenticated version is available online at
https://doi.org/10.1007/s11071-020-05620-8
A Review of Traffic Signal Control.
The aim of this paper is to provide a starting point for the future research within the SERC sponsored project "Gating and Traffic Control: The Application of State Space Control Theory". It will provide an introduction to State Space Control Theory, State Space applications in transportation in general, an in-depth review of congestion control (specifically traffic signal control in congested situations), a review of theoretical works, a review of existing systems and will conclude with recommendations for the research to be undertaken within this project
Control optimization, stabilization and computer algorithms for space applications
Research of control optimization, stochastic stability, and air traffic control problem
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