Multivariable variable-gain super-twisting control via output feedback for systems with arbitrary relative degrees. (English) Zbl 1543.93038
Summary: An output-feedback super-twisting algorithm (STA) with variable gains is developed for multiple-input and multiple-output plants with arbitrary relative degrees. Global or semi-global finite-time exact tracking can be guaranteed for a class of uncertain systems with matched nonlinear time-varying disturbances, possibly dependent on the unmeasured states. This represents a significant generalization of recently introduced versions of the STAs to a multivariable setup with arbitrary relative degrees, output-feedback, and variable gains. The construction of such controller is based on a higher-order sliding-mode multivariable differentiator with dynamic gains. The gain adaptation for the controller and differentiator employs state-norm observers to overcome the lack of the full-state measurement. The stability properties of the proposed control system are demonstrated by means of input-to-state stability tools and a Lyapunov function-based analysis. The theoretical results are verified through numerical and academic examples.
{© 2022 John Wiley & Sons Ltd.}
{© 2022 John Wiley & Sons Ltd.}
MSC:
| 93B12 | Variable structure systems |
| 93C40 | Adaptive control/observation systems |
| 93B52 | Feedback control |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 93C10 | Nonlinear systems in control theory |
Keywords:
exact differentiators; global/semi-global stability; higher-order sliding mode; MIMO uncertain plants; output feedback; variable structure systemsReferences:
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