The Solvability and Optimal Controls for Some Fractional Impulsive Equation with Finite Delay

2014 ◽  
Vol 3 (2) ◽  
pp. 133-145
Author(s):  
Xianghu Liu ◽  
Yanfang Li
Keyword(s):  
Optimal Controls ◽  
Impulsive Equation ◽  
Finite Delay

scholarly journals The Solvability and Optimal Controls for Some Fractional Impulsive Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xianghu Liu ◽  
Zhenhai Liu ◽  
Jiangfeng Han
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Calculus ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Sufficient Condition ◽  
Optimal Controls ◽  
Uniqueness Of Solutions ◽  
Impulsive Equations ◽  
Impulsive Equation

This paper is concerned with the existence and uniqueness of mild solution of some fractional impulsive equations. Firstly, we introduce the fractional calculus, Gronwall inequality, and Leray-Schauder’s fixed point theorem. Secondly with the help of them, the sufficient condition for the existence and uniqueness of solutions is presented. Finally we give an example to illustrate our main results.

scholarly journals Existence and optimal controls for nonlocal fractional evolution equations of order (1,2) in Banach spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Denghao Pang ◽  
Wei Jiang ◽  
Azmat Ullah Khan Niazi ◽  
Jiale Sheng
Keyword(s):  
Banach Spaces ◽  
Mild Solution ◽  
Measure Of Noncompactness ◽  
Evolution Equations ◽  
Well Posedness ◽  
Optimal Controls ◽  
Lagrange Problem ◽  
Fractional Differential ◽  
Fractional Evolution Systems ◽  
Definition Of

AbstractIn this paper, we mainly investigate the existence, continuous dependence, and the optimal control for nonlocal fractional differential evolution equations of order (1,2) in Banach spaces. We define a competent definition of a mild solution. On this basis, we verify the well-posedness of the mild solution. Meanwhile, with a construction of Lagrange problem, we elaborate the existence of optimal pairs of the fractional evolution systems. The main tools are the fractional calculus, cosine family, multivalued analysis, measure of noncompactness method, and fixed point theorem. Finally, an example is propounded to illustrate the validity of our main results.

scholarly journals Optimal Control Strategies for Switchable Transparent Insulation Systems Applied to Smart Windows for US Residential Buildings

Energies ◽  
2021 ◽  
Vol 14 (10) ◽  
pp. 2917
Author(s):  
Mohammad Dabbagh ◽  
Moncef Krarti
Keyword(s):  
Energy Use ◽  
Control Strategies ◽  
Residential Buildings ◽  
Residential Building ◽  
Optimization Approach ◽  
Optimal Controls ◽  
Peak Demand ◽  
Smart Windows ◽  
Insulation Systems ◽  
Rule Set

This paper evaluates the potential energy use and peak demand savings associated with optimal controls of switchable transparent insulation systems (STIS) applied to smart windows for US residential buildings. The optimal controls are developed based on Genetic Algorithm (GA) to identify the automatic settings of the dynamic shades. First, switchable insulation systems and their operation mechanisms are briefly described when combined with smart windows. Then, the GA-based optimization approach is outlined to operate switchable insulation systems applied to windows for a prototypical US residential building. The optimized controls are implemented to reduce heating and cooling energy end-uses for a house located four US locations, during three representative days of swing, summer, and winter seasons. The performance of optimal controller is compared to that obtained using simplified rule-based control sets to operate the dynamic insulation systems. The analysis results indicate that optimized controls of STISs can save up to 81.8% in daily thermal loads compared to the simplified rule-set especially when dwellings are located in hot climates such as that of Phoenix, AZ. Moreover, optimally controlled STISs can reduce electrical peak demand by up to 49.8% compared to the simplified rule-set, indicating significant energy efficiency and demand response potentials of the SIS technology when applied to US residential buildings.

scholarly journals Data-driven control of complex networks

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Giacomo Baggio ◽  
Danielle S. Bassett ◽  
Fabio Pasqualetti
Keyword(s):  
Complex Networks ◽  
Network Dynamics ◽  
Noisy Data ◽  
Data Driven ◽  
Control Algorithms ◽  
Optimal Controls ◽  
Network Systems ◽  
The Past ◽  
Efficient Control ◽  
Finite Set

AbstractOur ability to manipulate the behavior of complex networks depends on the design of efficient control algorithms and, critically, on the availability of an accurate and tractable model of the network dynamics. While the design of control algorithms for network systems has seen notable advances in the past few years, knowledge of the network dynamics is a ubiquitous assumption that is difficult to satisfy in practice. In this paper we overcome this limitation, and develop a data-driven framework to control a complex network optimally and without any knowledge of the network dynamics. Our optimal controls are constructed using a finite set of data, where the unknown network is stimulated with arbitrary and possibly random inputs. Although our controls are provably correct for networks with linear dynamics, we also characterize their performance against noisy data and in the presence of nonlinear dynamics, as they arise in power grid and brain networks.

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