scholarly journals Asymptotic expansion of a solution of a singularly perturbed optimal control problem with a convex integral quality index, whose terminal part additively depends on slow and fast variables

2020 ◽  
Vol 55 ◽  
pp. 33-41
Author(s):  
A.R. Danilin ◽  
A.A. Shaburov
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Steady State ◽  
Quality Index ◽  
Control Variable ◽  
Small Mass ◽  
Time Interval ◽  
Terminal Part ◽  
Time Optimal ◽  
Integral Quality

The paper deals with the problem of optimal control with a Boltz-type quality index over a finite time interval for a linear steady-state control system in the class of piecewise continuous controls with smooth control constraints. In particular, we study the problem of controlling the motion of a system of small mass points under the action of a bounded force. The terminal part of the convex integral quality index additively depends on slow and fast variables, and the integral term is a strictly convex function of control variable. If the system is completely controllable, then the Pontryagin maximum principle is a necessary and sufficient condition for optimality. The main difference between this study and previous works is that the equation contains the zero matrix of fast variables and, thus, the results of A.B. Vasilieva on the asymptotic of the fundamental matrix of a control system are not valid. However, the linear steady-state system satisfies the condition of complete controllability. The article shows that problems of optimal control with a convex integral quality index are more regular than time-optimal problems.

The Bus Dispatching Optimal Control System Based on Real-Time Data Acquisition

2012 ◽  
Vol 195-196 ◽  
pp. 1008-1016 ◽  
Author(s):  
Jian Li
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Data Acquisition ◽  
Real Time ◽  
Time Interval ◽  
Time Data ◽  
Software Module ◽  
Optimal Control System ◽  
Departure Time ◽  
Real Time Data

In this paper, main software module in the subject The Bus Dispatching Optimal Control System Based on Real-time Data Acquisition has been designed. By gradually changing the departure time interval, the system uses SCM to simulate the system running status in various time periods so as to determine the optimal departure time interval, and has established the integrated and optimal scheduling model through the research and development of four functions i.e. data acquisition, remote network monitoring, C/S/S architecture, network access. This article will focus on the design of the main module of software part in the system.

scholarly journals Two-channel time-optimal control of nonstationary heat conductive process with account for response time of boundary control actions

2021 ◽  
Vol 29 (2) ◽  
pp. 47-60
Author(s):  
Natalya A. Il’ina
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Parabolic Type ◽  
Time Optimal Control ◽  
Optimal Time ◽  
Time Control ◽  
Distributed Parameters ◽  
Control Actions ◽  
Optimal Controllers ◽  
Time Optimal

The task of organization a closed time-optimal control system of linear object with distributed parameters of parabolic type is considered. The object has two lumped internal controls for the power of heat sources excited in the electromagnetic field of an inductor. The proposed method for the synthesis of optimal controllers uses an alternance method for calculating the optimal program controls for each of the control actions. An example of the construction of a quasi-optimal time control system for the process of periodic induction heating of a metal workpiece with constant values of the feedback coefficients calculated for the most characteristic initial spatial distribution is given.

scholarly journals Maximum Principle for Forward-Backward Control System Driven by Itô-Lévy Processes under Initial-Terminal Constraints

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Meijuan Liu ◽  
Xiangrong Wang ◽  
Hong Huang
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Control Variable ◽  
Terminal State ◽  
Necessary Condition ◽  
Utility Optimization ◽  
Terminal Constraints ◽  
Stochastic Optimal Control Problem ◽  
Backward Control ◽  
Existence Of Optimal Control

This paper investigates a stochastic optimal control problem where the control system is driven by Itô-Lévy process. We prove the necessary condition about existence of optimal control for stochastic system by using traditional variational technique under the assumption that control domain is convex. We require that forward-backward stochastic differential equations (FBSDE) be fully coupled, and the control variable is allowed to enter both diffusion and jump coefficient. Moreover, we also require that the initial-terminal state be constrained. Finally, as an application to finance, we show an example of recursive consumption utility optimization problem to illustrate the practicability of our result.

Optimisation of an Amplidyne Speed Control System

1976 ◽  
Vol 9 (12) ◽  
pp. 463-466
Author(s):  
A. Rashwan ◽  
H. Attia
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Steady State ◽  
Feedforward Control ◽  
Speed Control ◽  
The State ◽  
Time Integral ◽  
Load Disturbance ◽  
Speed Error ◽  
Integral Feedback

The optimal-linear-regulator theory is used to optimise an amplidyne speed control system subjected to a constant load disturbance. As such a regulatory system tends to a steady state in response to a step disturbance. To be able to use a quadratic performance index as an optimisation criterion, three different techniques of variable transformation which moved the steady state to the origin of co-ordinates were employed. The first modification technique yielded an optimal control proportional to the state and to the load disturbance, ie, Feedforward Control. The second method led to an optimal control proportional to the state and the time-integral of the speed error, ie, Integral Feedback Control, while the third resulted in an optimal control proportional to the state and to both the load disturbance and to the time-integral of the speed error. This third control may be described as Integral Feedback/Feedforward Control. The transient responses of the system in the three cases to a step load disturbance were calculated, and the Integral Feedback/Feedforward Control gave the best results.

scholarly journals Cone separation, quadratic control systems and control of spin dynamics in the presence of decoherence

2017 ◽  
Vol 375 (2088) ◽  
pp. 20160214
Author(s):  
Navin Khaneja
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Spin Dynamics ◽  
Resonance Spectroscopy ◽  
Control Problems ◽  
State Variables ◽  
Systems And Control ◽  
Time Optimal ◽  
Optimal Efficiency ◽  
And Control

In this paper, we study some control problems related to the control of coupled spin dynamics in the presence of relaxation and decoherence in nuclear magnetic resonance spectroscopy. The decoherence is modelled through a master equation. We study some model problems, whereby, through an appropriate choice of state variables, the system is reduced to a control system, where the state enters linearly and controls quadratically. We study this quadratic control system. Study of this system gives us explicit bounds on how close a coupled spin system can be driven to its target state and how much coherence and polarization can be transferred between coupled spins. Optimal control for the quadratic control system can be understood as the separation of closed cones, and we show how the derived results on optimal efficiency can be interpreted in this formulation. Finally, we study some finite-time optimal control problems for the quadratic control system. This article is part of the themed issue ‘Horizons of cybernetical physics’.

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