Adaptive Fuzzy Asymptotic Control of MIMO Systems With Unknown Input Coefficients Via a Robust Nussbaum Gain-Based Approach

This paper proposes an adaptive fuzzy asymptotic control method for multiple input multiple output (MIMO) nonlinear systems with unknown input coefficients, with a focus on handling unknown input nonlinearities and control directions. For all the existing Nussbaum gain-based approaches, it is difficult to investigate unknown input coefficients problem since multiple time-varying coefficients and disturbances coexist and should be simultaneously tackled in the stability analysis. To overcome the above difficulty, we propose a robust Nussbaum gain-based approach for the adaptive fuzzy asymptotic control of MIMO nonlinear systems. Benefiting from the proposed Nussbaum gain-based approach, bounded disturbances including unmodeled system dynamics and universal approximation errors are handled. Furthermore, the proposed approach helps extend the bounded fuzzy control result to the asymptotic convergence. Hence, both the control robustness and control accuracy are prompted within the frame of the developed Nussbaum gain approach. Finally, a simulation example is carried out to illustrate the effectiveness of the proposed control method.