Optimal control and the maximum principle for operator equations of the first kind in Banach spaces

2018 ◽  
Author(s):  
Aleksei Ivanovich Prilepko
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Banach Spaces ◽  
Operator Equations ◽  
The Maximum Principle

Optimal Control of a General Environmental Space

1986 ◽  
Vol 108 (4) ◽  
pp. 330-339 ◽  
Author(s):  
M. A. Townsend ◽  
D. B. Cherchas ◽  
A. Abdelmessih
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Moisture Content ◽  
Control Strategies ◽  
Switching Control ◽  
The Maximum Principle ◽  
Environmental Space ◽  
And Performance

This study considers the optimal control of dry bulb temperature and moisture content in a single zone, to be accomplished in such a way as to be implementable in any zone of a multi-zone system. Optimality is determined in terms of appropriate cost and performance functions and subject to practical limits using the maximum principle. Several candidate optimal control strategies are investigated. It is shown that a bang-bang switching control which is theoretically periodic is a least cost practical control. In addition, specific attributes of this class of problem are explored.

scholarly journals Adaptation of the control synthesized by the ACAR method to the control based on the implementation of the maximum principle

2018 ◽  
Vol 226 ◽  
pp. 02012 ◽  
Author(s):  
Viktor P. Lapshin ◽  
Ilya A. Turkin ◽  
Alexey A. Zakalyuzhnyy ◽  
Viktor F. Khlystunov ◽  
Gennadiy A. Kuzin
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Maximum Principle ◽  
Synthesis Method ◽  
The Maximum Principle ◽  
Analytical Construction ◽  
Optimal Linear ◽  
The Moment ◽  
Moment Of Resistance ◽  
Maximum Method

A special case of synthesizing the electromechanical control system by the maximum method and using the Analytical Construction method of Aggregate Regulators (ACAR) is considered in the article. For the basis the task of synthesizing the optimal for speed electromechanical positioning system was chosen, while the moment of resistance to movement linearly depended on the output coordinate of the system, that is, on the angle of the engine rotor rotation. Synthesis of the optimal system for speed makes it possible to increase the efficiency of the entire production process in many production tasks, and the synthesis of the optimal linear control system based on the maximum principle is a fairly well-formalized problem. Here it should be noted that the procedure for synergistic synthesis of the optimal control system has no such formalization. An approach that brings together the solutions obtained by these two methods, which makes it possible to increase the efficiency of the ACAR method by adding some features of the methodology for synthesizing optimal systems by introducing nonlinearity of the “saturation” type is proposed in the article. The results obtained made it possible to formulate the following basic scientific proposition: the synthesis of a control system based on the synergetic approach makes it possible to obtain a system close to optimal (quasi-optimal, but after the modification of the synergetic synthesis method itself.) Here we also formulate the hypothesis of a connection between the time constants, using the ACAR method, with the optimal control switching time determined in the maximum method.

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