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Multivariable extension of global finite‐time HOSM based differentiator for output‐feedback unit vector and smooth binary control
Author(s) -
Oliveira Tiago Roux,
Rodrigues Victor Hugo Pereira,
Battistel Andrei,
Fridman Leonid
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.2030
Subject(s) - control theory (sociology) , multivariable calculus , differentiator , mathematics , adaptive control , state vector , exponential stability , nonlinear system , computer science , engineering , filter (signal processing) , physics , control (management) , control engineering , artificial intelligence , quantum mechanics , computer vision , classical mechanics
Abstract In this paper, we propose a unit vector control law by output feedback to solve the problem of global exact output tracking for a class of multivariable uncertain plants with nonlinear disturbances. In order to face the nonuniform arbitrary relative degree obstacle, we extend our earlier estimation scheme based on global finite‐time differentiators using dynamic gains to a multivariable architecture. A diagonally stable condition over the system high‐frequency gain (HFG) matrix has to be assumed. Preserving the simplicity of its mono variable framework, variable gain super‐twisting algorithm (STA) is employed to obtain the robust and exact multivariable differentiator. Moreover, state‐norm observers for the unmeasured state variables are constructed to upper bound the disturbances as well as to update the differentiator gains, being both state dependent. Uniform global exponential stability and ultimate exact tracking are proved. As an alternative to chattering alleviation, we appeal to the Emelyanov's concept of binary control in order to obtain a continuous control signal replacing the unit vector function in the controller by a high‐gain gradient adaptive law with parameter projection. As shown in the existing literature for mono variable systems, the proposed multiparameter binary‐adaptive formulation tends to the unit vector control as the adaptation gain increases to infinity, also smoothing the transition from adaptive to sliding mode control. A numerical example is portrayed to illustrate the potentialities of the developed multivariable techniques.