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Application of the Hirsch Generic Convergence Statement to the Set‐Point Regulation of Excitable‐Transparent‐Monotone Systems
Author(s) -
Agahi Hamed
Publication year - 2019
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1839
Subject(s) - monotone polygon , set (abstract data type) , convergence (economics) , controller (irrigation) , dynamical systems theory , point (geometry) , statement (logic) , control theory (sociology) , mathematics , set point , computer science , mathematical optimization , control (management) , control engineering , engineering , artificial intelligence , physics , geometry , quantum mechanics , law , political science , agronomy , economics , biology , programming language , economic growth
Monotone systems are dynamical systems whose solutions preserve an ordering, relative to the initial data. This paper focuses on the set‐point regulation problem for excitable‐transparent‐monotone single‐input single‐output systems with well‐defined static characteristics. The suggested technique for designing a static feedback controller is inspired from the Hirsch Theorem for monotone autonomous systems. It is shown that the closed‐loop system is strongly monotone and its generic solution converges to the desired set‐point. A remark is given on the application of the suggested design methodology to delay systems, as well as to systems with reaction‐diffusion equations. A simulation example from the biological world demonstrates the effectiveness of the proposed control strategy in real applications.