Abstract
A quasi-optimal control law is developed based on the condition for the maxi-mum of the generalized power function taking into account the stationarity of the Hamiltonian on the switching line for control objects that can be represented by the Lagrange equations of the second kind. The comparative analysis is carried out based on the mathematical simulation using the optimal nonlinear control laws with respect to several criteria. We found that the modes of the proposed control law provide high accuracy of approximation to the optimal performance laws and the Fuller laws, reducing energy costs for control by eliminating more frequent switching. The choice of the parameters of the developed control law makes it possible to implement a wide range of both nonlinear and linear operating modes, which allows to classify the obtained control law as multimode law.
Highlights
The synthesis of control laws that are used in the construction of multi-mode systems can be based on the use of the Lyapunov methods, the methods of optimal synthesis using the principles of L
We can assert that the set of solutions that ensure the stability of the synthesized system is infinite, while there are significantly fewer optimal solutions to the synthesis problem satisfying a given criterion
This paper formulates the problem to construct a multi-mode control for the system (1), (2) subject to condition (3), (6) on the set of the quasi-optimal control laws obtained from the condition for the maximum of the generalized power function [10,11,12,13,14,15]
Summary
The synthesis of control laws that are used in the construction of multi-mode systems can be based on the use of the Lyapunov methods, the methods of optimal synthesis using the principles of L. The empirical solutions using and generalizing the control experience that require methods of intellectualization [1,2,3,4,5] The latter are not effective enough in the case when it is possible to build an accurate mathematical model [6,7,8]. We can assert that the set of solutions that ensure the stability of the synthesized system is infinite, while there are significantly fewer optimal solutions to the synthesis problem satisfying a given criterion. Their set is limited, it is not always possible to use them to construct multi-mode systems. The aim of this work is to construct a multi-mode control based on the proposed approach and to compare the obtained solutions with classical optimal solutions
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