Symbolic Regulator Sets for a Weakly Nonlinear Discrete Control System with a Small Step

Yulia Danik and Mikhail Dmitriev
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Yulia Danik: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Mocow, Russia
Mikhail Dmitriev: Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 119333 Mocow, Russia

Mathematics, 2022, vol. 10, issue 3, 1-14

Abstract: For a class of discrete weakly nonlinear state-dependent coefficient (SDC) control systems, a suboptimal synthesis is constructed over a finite interval with a large number of steps. A one-point matrix Padé approximation ( PA ) of the solution of the initial problem for the discrete matrix Riccati equation is constructed based on the state-dependent Riccati equation (SDRE) approach and the asymptotics by the small-step of the boundary layer functions method. The symmetric gain coefficients matrix for Padé control synthesis is constructed based on the one-point PA . As a result, the parametric closed-loop control is obtained. The results of numerical experiments illustrate, in particular, the improved extrapolation properties of the constructed regulator, which makes the algorithm applicable in control systems for a wider range of parameter variation.

Keywords: discrete control systems; weakly nonlinear systems; small step; the SDRE approach; matrix discrete Riccati equation; the boundary layer functions method; Padé approximation; finite time interval (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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