Global Tracking Control for High-Order Odd-Rational-Powers Systems with Unknown Nonlinearities and Powers

Zongcheng Liu, Chongchong Han, Hongbo Li (), Jun Guo (), Yong Chen and Qiuni Li
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Zongcheng Liu: Aviation Engineering School, Air Force Engineering University, Xi’an 710038, China
Chongchong Han: Aviation Engineering School, Air Force Engineering University, Xi’an 710038, China
Hongbo Li: Aviation Engineering School, Air Force Engineering University, Xi’an 710038, China
Jun Guo: Unit 93716 of the PLA, Tianjin 301716, China
Yong Chen: Aviation Engineering School, Air Force Engineering University, Xi’an 710038, China
Qiuni Li: Aviation Engineering School, Air Force Engineering University, Xi’an 710038, China

Mathematics, 2023, vol. 11, issue 17, 1-13

Abstract: The global control problem of high-order nonlinear systems with unknown odd rational powers and nonlinearities has been solved in this paper for the first time. Barrier functions were introduced into the controller to set the controller free from rational powers, which solved the problem caused by unknown odd rational powers. In utilizing barrier functions and their inverse functions, two transformations were constructed for the state and tracking errors, which resulted in the global tracking controller for the high-order odd-rational-powers nonlinear systems with unknown system nonlinearities. No knowledge of system nonlinearities and odd rational powers is required to construct the controller in this paper, and only control gains are assumed to be positive to guarantee the controllability of the system, which implies that the proposed method is model-free and has much more relaxed conditions than all the existing methods for high-order nonlinear systems. The global boundedness of all closed-loop signals was proved based on the Lyapunov stability theorem. Finally, simulation results were given to demonstrate the effectiveness of the proposed method.

Keywords: nonlinear systems; uncertain powers; global tracking control; high-order nonlinear systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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