Real Ternary Integrator Problem Analysis
Keywords:
Optimal Control, Complete Analysis of the Optimal Control, Real Ternary Integrator Problem, Synthesizing VariablesAbstract
Purpose: Developing mathematical support for energy saving control, able to solve problems of real-time synthesis of optimal control
over energy-intensive objects, on a number of performance conditions. Methods: With the use of maximum principle and synthesizing
variables, we propose an approach to implement a comprehensive analysis of optimal control over objects whose dynamics is described by linear differential equation of the third order. Results: New results were obtained on the problem of the optimal control over objects whose dynamics is described by a real ternary integrator model. The functional (energy or fuel consumption) is minimized, the control actions are constrained, the ends of the phase coordinate change trajectory vector are fixed, the control time interval is also fixed. The obtained results include the analysis of possible types of power-saving control functions, the suggested vector of the synthesizing variables whose dimension is much less than that of the initial data array necessary for a numeral solution of the problem, the conditions of solution existence, etc. The functioning of the object can involve certain variations in its parameters, in the boundaries of the control impact changes, in the initial and final values of the phase coordinate vector components, or in the initial and final moments of the time interval. The title of the problem was shortened to “real ternary integrator problem”. Practical relevance: The obtained results can be used by developers of CAD/CAM and SCADA systems to create software modules for automatic design of algorithms for energy-saving control systems. It can also be used by designers of intellectual controllers able to synthesize controlling impact on thermal devices, electric engines and other energy-intensive objects, and by inventors of special circuit topology for intellectual controllers. Besides, the obtained results can be used to study more sophisticated problems like those involving hybrid and other MIMO-objects.