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Unifying adaptive control with the nonlinear PI methodology: Designs for unknown strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities
Author(s) -
Psillakis H.E.,
Lagos A.R.
Publication year - 2018
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2846
Subject(s) - backstepping , control theory (sociology) , nonlinear system , parametric statistics , actuator , nonlinear control , controller (irrigation) , adaptive control , trajectory , strict feedback form , mathematics , computer science , control (management) , artificial intelligence , physics , statistics , quantum mechanics , astronomy , agronomy , biology
Summary In this paper, we extend the nonlinear PI control methodology within an adaptive control framework. An adaptive nonlinear PI controller is proposed for output tracking of strict‐feedback nonlinear systems with nonsmooth actuator nonlinearities and unknown control directions. The current approach relaxes the standard assumption of known bounds for the associated system nonlinearities made in earlier nonlinear PI schemes. New theoretical boundedness results have been proved that enable the successful combination of backstepping and linear parametric approximators with the nonlinear PI approach and ensure semiglobal approximate tracking of the output to some reference trajectory. Following recent extensions of the nonlinear PI method to strict‐feedback systems, the intermediate virtual control laws are derived through suitable integral equations. Simulation results are also presented in this paper that verify our theoretical analysis.