Limitations of the pseudoinverse method for the control over linear connected memoryless plants: guaranteed results

1Gritsenko, VI
1Zhiteckii, LS
1Solovchuk, KYu.
1International Research and Training Center for Information Technologies and Systems of the NAS of Ukraine and Ministry of Education and Science of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2019, 8:16-24
https://doi.org/10.15407/dopovidi2019.08.016
Section: Information Science and Cybernetics
Language: Russian
Abstract: 

The paper deals with the discretetime control of the linear INTER connected memoryless plant using the pseudoinverse modelbased approach. It answers the questions related to applicability areas for this approach. The objective of the paper is to derive some asymptotic features of the closedloop control systems containing the pseudoinverse models in their feedback loops. To this end, the memoryless plants having any nonzero gain matrices are considered. Namely, the classes of square nonsingular and singular matrices and nonsquare matrices with arbitrary rank are analyzed. The case where these matrices are known and the case where there is no full information on their elements are separately studied. The assumption that there are the unmeasurable arbitrary, but bounded external disturbances whose bounds may be unknown, in general, is introduced. Three important results about the asymptotic behavior of the control systems with the pseudoinverse models are obtained. First, it is shown that, in the absence of uncertainties, the equilibrium state of these systems always exists, and their stability and optimality are guaranteed. Second, a new effective control law for the stabilization of the illconditioned plants with the known gain matrices is proposed. Third, the several conditions guaranteeing the existence of the equilibrium state and the dissipativeness of the control system in the presence of uncertainties are established. Asymptotic estimates of upper bounds on the norms of the control input and output vectors are given.

Keywords: closedloop control system, dissipativeness, equilibrium state, interconnected memoryless plants, optimality, pseudoinverse model, stability
References: 

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