Direct Adaptive Fuzzy Control of Nonlinear Systems with Unknown Control Directions

For the Adaptive Fuzzy Control (AFC) of uncertain nonlinear systems, the unknown control direction brings about great difficulty in control design. This study presents a novel direct AFC approach for a class of perturbed uncertain affine nonlinear systems with unknown control directions. The overall control input contains a basic direct AFC term and an additional robust control term. A Lyapunov-based ideal control law is proposed to solve the control singularity problem and the Nussbaum gain technique is applied to solve the control direction problem. Using an e super( 2)-modification in adaptive laws, it not only obtains bounded adaptive parameters, but also achieves asymptotic convergence of tracking errors. Moreover, the proposed controller has more compact structure compared with the previous indirect approaches. Simulated studies have demonstrated the effectiveness of the proposed approach.