Adaptive Dynamic Surface Control for a Class of Dead-Zone Nonlinear Systems via Output Feedback

Abstract

The paper aims to address output feedback problem for a class of nonlinear systems subjected to unknown dead-zone. High-gain K-filters is firstly designed such that unavailable states of system can be reconstructed. Then, with the help of dynamic surface control (DSC) method, an adaptive output feedback controller design is established, which can alleviate undesired influence of the dead-zone and guarantee the semi-global stability of the system. Furthermore, the L ∞ performance of tracking error is achieved by means of initialization technique. Ultimately, numerical and practical examples clarify the efficiency of the proposed solution.INDEX TERMS Dynamic surface control; Adaptive control; High-gain observer; Dead-zone; Nonlinear systems.

Adaptive neural network observer‐based filtered backstepping control for nonlinear systems with fuzzy dead‐zone and uncertainty

“…Here, we consider two practical examples for investigating the applicability and effectiveness of the proposed algorithm.Example Consider a single‐link robot manipulator with fuzzy dead‐zone input which has the following form 55 : $$$$ M\ddot{q}+\frac{1}{2}m\mathrm{lgsin}(q)=D(u), $$$$ where $$$ q $$$ is the angular position, $$$ M $$$ is the moment of inertia, $$$ m $$$ and $$$ l $$$ are the mass and length of the link respectively, $$$ g $$$ is the gravity acceleration, $$$ u $$$ is the input torque and $$$ D(u) $$$ is the dead‐zone output.…”

“…Remark This example was also considered in Reference [55] which describes dead‐zone by a conventional deterministic model and uses CDSC approach for controller design. The first‐order filters are used to extract derivative of the virtual inputs; also, filtering error is not compensated.…”

“…The first‐order filters are used to extract derivative of the virtual inputs; also, filtering error is not compensated. Compared with Reference [55], in this work, NTD is used instead of the first‐order filters to eliminate the explosion of terms problem, unwanted oscillations and even stability problem that arises because of using first‐order filters in the CDSC approach. Furthermore, filtering errors are compensated by using the proposed error compensation mechanism. Example This example considers the following one‐link manipulator actuated with a DC motor with dead‐zone input 56 : $$$$ {\displaystyle \begin{array}{ll}& J\ddot{q}+B\dot{q}+N\sin (q)=I+{d}_I,\\ {}& M\dot{I}=- HI-{K}_m\dot{q}+D(u),\end{array}} $$$$ where $$$ q $$$, $$$ \dot{q} $$$ and $$$ \ddot{q} $$$ represent the angular position, velocity, and acceleration of the link, respectively.…”

“…Example 1. Consider a single-link robot manipulator with fuzzy dead-zone input which has the following form 55 :…”

“…where 𝛾 i1 , and 𝛾 i2 are learning rates and 𝜎 i1 , and 𝜎 i2 are positive design parameters. Substituting ( 56) in (55), gives:…”