Hybrid systems with time scales and impulses

Lakshmikantham, V.; Devi, J. Vasundhara

doi:10.1016/j.na.2005.12.043

Cited by 35 publications

(39 citation statements)

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“…As future work a time scale representation for hybrid systems can be considered [25]. Experimental data of the disturbances were used in the simulation, each subfield with a different irradiation profile in order to validate the controller.…”

Section: Discussionmentioning

confidence: 99%

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Mixed Logical Dynamical Nonlinear Model Predictive Controller for Large‐Scale Solar Fields

Elias

Mendes

Normey-Rico

2019

Asian Journal of Control

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This paper presents a control algorithm for reducing heat losses caused by clouds in large solar fields. The formulation is based on a Mixed Logical Dynamical (MLD) representation of the solar field plus the application of a Practical Nonlinear Model Predictive Controller (PNMPC) for calculating the optimal control action. The main purpose of the controller is to deactivate fields with inlet temperature greater than outlet temperature and to manipulate the oil flow rate of the activated fields for tracking the reference of the outlet temperature. A simplified lumped parameters model is used for prediction and simulation of the solar fields.

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Section: Discussionmentioning

confidence: 99%

“…Considering that, the constraints (23) and (24) are approximated as (25) and (26), respectively. The constraints need to be convex as pointed out before.…”

Section: Operational Constraintsmentioning

confidence: 99%

Mixed Logical Dynamical Nonlinear Model Predictive Controller for Large‐Scale Solar Fields

Elias

Mendes

Normey-Rico

2019

Asian Journal of Control

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“…Problem (1), (2) is a generalization of a series of boundary-value problems [1,2,[4][5][6][7][8] for impulsive systems with switchings. On the other hand, problem (1), (2) is a special case of hybrid systems [9,10].…”

Section: Linear Unperturbed Problemmentioning

confidence: 99%

“…Suppose that the boundary-value problem (9), (10) corresponds to the critical case P Q * = 0 and, moreover, the solvability condition (6) for the unperturbed problem (1), (2) is not satisfied for arbitrary inhomogeneities f (t) and α. Then, under the condition P B * 0 = 0, problem (9), (10) has at least one solution…”

Section: Statement Of the Problemmentioning

confidence: 99%

Bifurcation of solutions of an impulsive boundary-value problem

Бойчук¹,

Чуйко²

2008

Nonlinear Oscill

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We establish constructive conditions for the bifurcation of solutions and construct an iteration procedure for finding solutions of a linear Noether boundary-value problem for a system of ordinary differential equations with pulse action in the critical case. We obtain an estimate for the range of values of a small parameter for which the iteration procedure converges. Linear Unperturbed ProblemConsider the problem of finding a solution z 0satisfying the boundary condition [1-3]Lz 0 (·) = α, i = 1, 2, . . . , p,where A i (t) are n×n matrices continuous on the segments [a; τ 1 ], [τ 1 ; τ 2 ], . . . , [τ p ; b], Lz(·) is a linear bounded vector functional of the formare linear bounded functionals, the vector function f (t) is continuous (except for the points τ i , at which the function f (t) may have discontinuities of the first kind), and α ∈ R m . Problem (1), (2) is a generalization of a series of boundary-value problems [1, 2, 4-8] for impulsive systems with switchings. On the other hand, problem (1), (2) is a special case of hybrid systems [9, 10].

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“…In 2002, Zhang and Saker investigated the oscillation of the discrete analogue of Equation , namely,

P_{n + 1} - P_{n} = - δ P_{n} + q e^{- a p_{n - σ}},

. In order to unify continuous and discrete analysis, the theory of calculus on time scales was initiated by Stefan Hilger in 1988 , and it is useful in studying differential and difference equations and provides an effective and feasible way to unify and on time scales. However, from a timescale angle, everyone knows

double-struckR

and

double-struckZ

are classical periodic time scales that can be unified well with the following periodic time scale:

double-struckT = ⋃_{k = - \infty}^{+ \infty} [k (a + b), k (a + b) + a], a, b \in double-struckR, k \in double-struckZ .

…”

Section: Introductionmentioning

confidence: 99%

Matrix measure on time scales and almost periodic analysis of the impulsive Lasota–Wazewska model with patch structure and forced perturbations

Wang

Agarwal

O’Regan

2016

Math Methods in App Sciences

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In this paper, a new impulsive Lasota–Wazewska model with patch structure and forced perturbed terms is proposed and analyzed on almost periodic time scales. For this, we introduce the concept of matrix measure on time scales and obtain some of its properties. Then, sufficient conditions are established which ensure the existence and exponential stability of positive almost periodic solutions of the proposed biological model. Our results are new even when the time scale is almost periodic, in particular, for periodic time scales on double-struckT=double-struckR or double-struckT=double-struckZ. An example is given to illustrate the theory. Finally, we present some phenomena which are triggered by almost periodic time scales. Copyright © 2016 John Wiley & Sons, Ltd.

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Hybrid systems with time scales and impulses

Cited by 35 publications

References 1 publication

Mixed Logical Dynamical Nonlinear Model Predictive Controller for Large‐Scale Solar Fields

Mixed Logical Dynamical Nonlinear Model Predictive Controller for Large‐Scale Solar Fields

Bifurcation of solutions of an impulsive boundary-value problem

Matrix measure on time scales and almost periodic analysis of the impulsive Lasota–Wazewska model with patch structure and forced perturbations

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