scholarly journals Minimal time control of exact synchronization for parabolic systems

2021 ◽  
Author(s):  
Lijuan Wang ◽  
Qishu Yan
Keyword(s):  
Parabolic Systems ◽  
Optimal Time ◽  
Optimal Controls ◽  
Initial State ◽  
Solution Vector ◽  
Minimal Time ◽  
Time Control ◽  
System Of Parabolic Equations ◽  
Two Parameters ◽  
Necessary And Sufficient

This paper studies a kind of minimal time control problems related to the exact synchronization for a controlled linear system of parabolic equations. Each problem depends on two parameters: the bound of controls and the initial state. The purpose of such a problem is to find a control (from a constraint set) synchronizing components of the corresponding solution vector for the controlled system in the shortest time. In this paper, we build up a necessary and sufficient condition for the optimal time and the optimal control; we also obtain how the existence of optimal controls depends on the above mentioned two parameters.

scholarly journals Distributed Finite-Time Bipartite Consensus for Multiagent System with Event-Triggered Control

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Haibo Xie ◽  
Zhengjiang Liu ◽  
Chengyong Yan ◽  
Shibo Zhou
Keyword(s):  
Finite Time ◽  
Control Method ◽  
Initial State ◽  
Consensus Control ◽  
Whole Process ◽  
Time Control ◽  
Consensus Values ◽  
Bipartite Consensus ◽  
Necessary And Sufficient ◽  
Event Triggered

This paper investigates the distributed finite-time event-triggered bipartite consensus control for multiagent systems over antagonistic networks. Under the constraint of energy conservation, a distributed nonlinear finite-time control protocol only depending upon local information is proposed coupled with event-triggered strategies, where controllers of agents at triggered instants are only updated to reduce the computation. It is proved that when the antagonistic network is structurally balanced with a spanning tree, a necessary and sufficient condition is established to guarantee all agents to reach consensus values with identical magnitude but opposite signs. More interestingly, the settling time depending on the initial state is obtained over the whole process. Comparing to asymptotic control algorithms, the proposed control method has better disturbance rejection properties and convergence rate. Simulations are given to demonstrate the effectiveness of the theoretical results.

scholarly journals First and second order optimality conditions for the control of Fokker-Planck equations

2021 ◽  
Vol 27 ◽  
pp. 15
Author(s):  
M. Soledad Aronna ◽  
Fredi Tröltzsch
Keyword(s):  
Control Variable ◽  
Sufficient Conditions ◽  
Planck Equation ◽  
Second Order ◽  
Optimal Controls ◽  
Main Emphasis ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Fokker Planck Equations ◽  
Fokker Planck

In this article we study an optimal control problem subject to the Fokker-Planck equation ∂tρ − ν∆ρ − div(ρB[u]) = 0 The control variable u is time-dependent and possibly multidimensional, and the function B depends on the space variable and the control. The cost functional is of tracking type and includes a quadratic regularization term on the control. For this problem, we prove existence of optimal controls and first order necessary conditions. Main emphasis is placed on second order necessary and sufficient conditions.

Minimum Time Control of Second Order Pulse-Width-Modulated Sampled-Data Systems

1962 ◽  
Vol 84 (1) ◽  
pp. 101-109 ◽  
Author(s):  
E. Polak
Keyword(s):  
Pulse Width ◽  
Phase Plane ◽  
Sampling Period ◽  
Second Order ◽  
Data Systems ◽  
Sampled Data ◽  
Relay System ◽  
Pulse Width Modulated ◽  
Minimal Time ◽  
Time Control

This paper treats the minimal time control problem for two second order pulse-width-modulated sampled-data systems, one with a double integrator type plant and one with a plant described by an integral and a time constant. Such plants are encountered in systems with hydraulic components. It is shown rigorously that for minimal time control the phase plane can be divided into two regions: a striplike region around the optimal switching trajectory for a continuous relay system with the same plants, in which the pulse width must be adjusted for optimal action; and the rest of the phase plane in which an optimal p.w.m. system of the type described behaves like a continuous optimal relay system, the pulse duration being equal to the sampling period. A brief description of an electromechanical computer capable of implementing minimal time control for these systems is also given.

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