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Adaptive tracking control of high-order nonlinear systems under asymmetric output constraint. (English) Zbl 1457.93050

The authors consider continuous-time high-order nonlinear single input - single output systems with unknown parameters and measurable state vector. The output is constrained asymmetrically by time-dependent smooth functions and a control objective is to track a desired trajectory which satisfies the same constraints as the output of the system. To overcome difficulties with asymmetric constraints the authors propose a nonlinear time-varying transformation of the output and the desired trajectory similar to the ones used by other authors (see e.g. [K. Zhao and Y. Song, IEEE Trans. Autom. Control 64, No. 3, 1265–1272 (2019; Zbl 1482.93260)]). To solve the problem a modified dynamic surface control technique (see e.g. [D. Swaroop et al., IEEE Trans. Autom. Control 45, No. 10, 1893–1899 (2000; Zbl 0991.93041)]) is studied. More precisely, a backstepping based design scheme is proposed which integrates the technique of adding a power integrator and the dynamic surface control implemented for the transformed system. To deal with gain uncertainty the control strategy estimates only one adaptive parameter. The proposed algorithm ensures asymptotic tracking of the output signal along the desired trajectory. The theoretical results are illustrated be two simulation examples. The first example is a second order model of a single-link robotic manipulator and the second one is a model of an unstable two degrees of freedom mechanical system.

MSC:

93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
93C85 Automated systems (robots, etc.) in control theory
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