Robust Adaptive Control of MIMO Pure-Feedback Nonlinear Systems via Improved Dynamic Surface Control Technique

This paper presents a global dynamic surface control (DSC) method for a class of uncertain multi-input/multi-output (MIMO) pure-feedback nonlinear systems with non-affine functions possibly being in-differentiable. It is well known that the traditional DSC method is commonly used for reducing the design complexity of the backstepping control method; however, the regulation results of the DSC method are semi-global uniformly ultimately bounded (SGUUB). An improved DSC (IDSC) method is first designed in this paper so that the results are global uniformly ultimately bounded (GUUB). Comparing with the traditional DSC method, the parameters of first-order filters in IDSC are time varying rather than constants. The control design for MIMO pure-feedback nonlinear systems researched is much more complex than the SISO cases, and the presence of in-differentiable non-affine functions considered in this paper makes the control design even more difficult. Therefore, we proposed the IDSC method, which can significantly reduce the complexity of the control design for the MIMO pure-feedback nonlinear systems in cooperation with the backstepping method, and it is proved that IDSC can guarantee the GUUB of all the signals of the system. Finally, the simulation results are provided to demonstrate the effectiveness of the designed method.