12,120 research outputs found
Regional controllability and minimum energy control of delayed caputo fractional-order linear systems
We study the regional controllability problem for delayed fractional control systems through the use of the standard Caputo derivative. First, we recall several fundamental results and introduce the family of fractional-order systems under consideration. Afterward, we formulate the notion of regional controllability for fractional systems with control delays and give some of their important properties. Our main method consists of defining an attainable set, which allows us to prove exact and weak controllability. Moreover, the main results include not only those of controllability but also a powerful Hilbert uniqueness method, which allows us to solve the minimum energy optimal control problem. More precisely, an explicit control is obtained that drives the system from an initial given state to a desired regional state with minimum energy. Two examples are given to illustrate the obtained theoretical results.This research was funded by The Portuguese Foundation for Science and Technology
(FCT—Fundação para a Ciência e a Tecnologia), grant number UIDB/04106/2020 (CIDMA).publishe
Relative controllability of linear difference equations
In this paper, we study the relative controllability of linear difference
equations with multiple delays in the state by using a suitable formula for the
solutions of such systems in terms of their initial conditions, their control
inputs, and some matrix-valued coefficients obtained recursively from the
matrices defining the system. Thanks to such formula, we characterize relative
controllability in time in terms of an algebraic property of the
matrix-valued coefficients, which reduces to the usual Kalman controllability
criterion in the case of a single delay. Relative controllability is studied
for solutions in the set of all functions and in the function spaces and
. We also compare the relative controllability of the system for
different delays in terms of their rational dependence structure, proving that
relative controllability for some delays implies relative controllability for
all delays that are "less rationally dependent" than the original ones, in a
sense that we make precise. Finally, we provide an upper bound on the minimal
controllability time for a system depending only on its dimension and on its
largest delay
Approximate Controllability of Delayed Fractional Stochastic Differential Systems with Mixed Noise and Impulsive Effects
We herein report a new class of impulsive fractional stochastic differential
systems driven by mixed fractional Brownian motions with infinite delay and
Hurst parameter . Using fixed point techniques, a
-resolvent family, and fractional calculus, we discuss the existence of a
piecewise continuous mild solution for the proposed system. Moreover, under
appropriate conditions, we investigate the approximate controllability of the
considered system. Finally, the main results are demonstrated with an
illustrative example.Comment: Please cite this paper as follows: Hakkar, N.; Dhayal, R.; Debbouche,
A.; Torres, D.F.M. Approximate Controllability of Delayed Fractional
Stochastic Differential Systems with Mixed Noise and Impulsive Effects.
Fractal Fract. 2023, 7, 104. https://doi.org/10.3390/fractalfract702010
OUTPUT CONTROLLABILITY OF DELAYED CONTROL SYSTEMS IN A LONG TIME HORIZON
In this paper, we consider the output controllability of finite-dimensional control systems governed by a distributed delayed control. For systems with ordinary controls, this problem was investigated earlier. Nevertheless, in many practical and technical problems the control acts with some delay. We give the necessary and sufficient condition for the output controllability. The main goal of our control is to govern the output of the system to some position on a subspace in a given instant, and then keep this output fixed for the remaining times. This property is called the long-time output controllability. For this, sufficient conditions are given. The introduced notions are applied for the investigation of averaged controllability of systems with delayed controls. The general approach for that is to approximate the system by the ordinary ones. Some examples are considered
Global Well-Posedness and Exponential Stability for Heterogeneous Anisotropic Maxwell's Equations under a Nonlinear Boundary Feedback with Delay
We consider an initial-boundary value problem for the Maxwell's system in a
bounded domain with a linear inhomogeneous anisotropic instantaneous material
law subject to a nonlinear Silver-Muller-type boundary feedback mechanism
incorporating both an instantaneous damping and a time-localized delay effect.
By proving the maximal monotonicity property of the underlying nonlinear
generator, we establish the global well-posedness in an appropriate Hilbert
space. Further, under suitable assumptions and geometric conditions, we show
the system is exponentially stable.Comment: updated and improved versio
Hierarchical agent supervision
Agent supervision is a form of control/customization where a supervisor restricts the behavior of an agent to enforce certain requirements, while leaving the agent as much autonomy as possible. To facilitate supervision, it is often of interest to consider hierarchical models where a high level abstracts over low-level behavior details. We study hierarchical agent supervision in the context of the situation calculus and the ConGolog agent programming language, where we have a rich first-order representation of the agent state. We define the constraints that ensure that the controllability of in-dividual actions at the high level in fact captures the controllability of their implementation at the low level. On the basis of this, we show that we can obtain the maximally permissive supervisor by first considering only the high-level model and obtaining a high- level supervisor and then refining its actions locally, thus greatly simplifying the supervisor synthesis task
Control of unstable steady states in neutral time-delayed systems
We present an analysis of time-delayed feedback control used to stabilize an
unstable steady state of a neutral delay differential equation. Stability of
the controlled system is addressed by studying the eigenvalue spectrum of a
corresponding characteristic equation with two time delays. An analytic
expression for the stabilizing control strength is derived in terms of original
system parameters and the time delay of the control. Theoretical and numerical
results show that the interplay between the control strength and two time
delays provides a number of regions in the parameter space where the
time-delayed feedback control can successfully stabilize an otherwise unstable
steady state.Comment: 11 pages, 8 figure
On controllability of neuronal networks with constraints on the average of control gains
Control gains play an important role in the control of a natural or a technical system since they reflect how much resource is required to optimize a certain control objective. This paper is concerned with the controllability of neuronal networks with constraints on the average value of the control gains injected in driver nodes, which are in accordance with engineering and biological backgrounds. In order to deal with the constraints on control gains, the controllability problem is transformed into a constrained optimization problem (COP). The introduction of the constraints on the control gains unavoidably leads to substantial difficulty in finding feasible as well as refining solutions. As such, a modified dynamic hybrid framework (MDyHF) is developed to solve this COP, based on an adaptive differential evolution and the concept of Pareto dominance. By comparing with statistical methods and several recently reported constrained optimization evolutionary algorithms (COEAs), we show that our proposed MDyHF is competitive and promising in studying the controllability of neuronal networks. Based on the MDyHF, we proceed to show the controlling regions under different levels of constraints. It is revealed that we should allocate the control gains economically when strong constraints are considered. In addition, it is found that as the constraints become more restrictive, the driver nodes are more likely to be selected from the nodes with a large degree. The results and methods presented in this paper will provide useful insights into developing new techniques to control a realistic complex network efficiently
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