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Approximate finite-time control for a class of uncertain nonlinear systems with dynamic compensation. (English) Zbl 1379.93054

Summary: In this work, a new robust nonlinear feedback control method with dynamic active compensation is proposed; the active control method has been applied to an integral series of finite-time single-input single-output nonlinear system with uncertainty. In further tracking the closed-loop stability and nonlinear uncertainty, an extended state observer has been employed to solve the immeasurability and nonlinear uncertainty within a nonlinear system. A singular perturbation theory has been used to ensure the finite-time stability of the closed-loop system. Furthermore, numerical simulations show that the robust nonlinear feedback controller tracks the uncertainty in a nonlinear Duffing-type oscillator and proves the effectiveness of the approximate finite-time control strategy proposed. By using an approximate finite-time control approach with active compensation, the uncertainty in a nonlinear system could be accurately estimated and controlled.

MSC:

93B52 Feedback control
93B35 Sensitivity (robustness)
93C41 Control/observation systems with incomplete information
93C10 Nonlinear systems in control theory
93C70 Time-scale analysis and singular perturbations in control/observation systems
93C15 Control/observation systems governed by ordinary differential equations
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