Self-structuring fuzzy-neural backstepping control with a B-spline-based compensator

To relieve the burdens of network controller design and approximation error bound determination, a self-structuring fuzzy-neural backstepping control system (SSFNBS) with a B-spline-based compensator is proposed. In this paper, a network-identification-based control is represented where the self-structuring fuzzy neural network-based (SSFNN) is used as the observer to approximate the controlled system dynamics. To balance the tradeoff between the structure efficiency and the identification accuracy, a structure learning mechanism of the node-adding process and the node-pruning process is introduced. On the other hand, the B-spline-based compensator is introduced to dispel the effect of approximation error. With the adoption of B-spline functions, the compensation controller can be given in a recurrent way based on the introduction of knot vector and the drawbacks of the conventional compensation controllers can be freed. With the introduction of the B-spline function, the proposed SSFNBS features the following advantages: (1) the capability of network-based controller is improved, (2) the design of the compensation controller can be easily established based on the characteristics of the B-spline function, (3) the stability of closed-loop control system is guaranteed by the means of Lyapunov function with the tuning law of the B-spline-based compensator. To investigate the capabilities of the proposed approach, the SSFNBS is applied to the nonlinear system, chaotic system, and wing rock motion control problems. Through the simulation results the advantages of the proposed SSFNBS can be observed.