Synthesis control of a nonlinear dynamic object with limited perturbations and using the SDC-method
- Authors: Brahim L.1
-
Affiliations:
- National Research University Higher School of Economics
- Issue: Vol 73, No 2 (2023)
- Pages: 90-99
- Section: Mathematical Modeling
- URL: https://journals.rcsi.science/2079-0279/article/view/286997
- DOI: https://doi.org/10.14357/20790279230209
- ID: 286997
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Abstract
The optimal control problem in the differential game problem with restrictions on the control.
The problem of optimal control under the action of bounded perturbations is formulated for a class of dynamical systems whose nonlinear objects are representable as objects with a linear structure and state-dependent parameters. The introduced quadratic functional allows us to consider the problem with the use of methods of differential games with zero sum. The linearity of the structure of the transformed nonlinear system and the quadratic quality functional allow for the synthesis of optimal controls, i.e. parameters of regulators, go from the need to search for solutions to the Bellman-Isaacs equation to an equation of the Riccati type with state-dependent parameters. The synthesized controls provide the SDC-model with the property of asymptotic stability and make it possible to determine the ratio of the constraints imposed on the controls, under which the condition for the existence of a differential game with zero sum is ensured. The main problem of implementing optimal control is related to the problem of finding a solution to the Riccati equation with state-dependent parameters at the rate of operation of the object. To solve this equation, a suboptimal control method with quasi-stationary values of the parameters is proposed. An estimate of the discrepancy between optimal and suboptimal solutions is given. Example will be provided to illustrate the effectiveness and of FRE technique for design of nonlinear systems based feedback controllers.
About the authors
Ladjal Brahim
National Research University Higher School of Economics
Author for correspondence.
Email: thehay89@gmail.com
Graduate student, Moscow Institute of Electricians and Mathematics
Russian Federation, MoscowReferences
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