RCMAC-Based Adaptive Control for Uncertain Nonlinear Systems

An adaptive control system, using a recurrent cerebellar model articulation controller (RCMAC) and based on a sliding mode technique, is developed for uncertain nonlinear systems. The proposed dynamic structure of RCMAC has superior capability to the conventional static cerebellar model articulation controller in an efficient learning mechanism and dynamic response. Temporal relations are embedded in RCMAC by adding feedback connections in the association memory space so that the RCMAC provides a dynamical structure. The proposed control system consists of an adaptive RCMAC and a compensated controller. The adaptive RCMAC is used to mimic an ideal sliding mode controller, and the compensated controller is designed to compensate for the approximation error between the ideal sliding mode controller and the adaptive RCMAC. The online adaptive laws of the control system are derived based on the Lyapunov stability theorem, so that the stability of the system can be guaranteed. In addition, in order to relax the requirement of the approximation error bound, an estimation law is derived to estimate the error bound. Finally, the simulation and experimental studies demonstrate the effectiveness of the proposed control scheme for the nonlinear systems with unknown dynamic functions

Nomenclature

Unknown but bounded real continuous functions.

Control input.

System output.

External bounded disturbance.

State vector of the system.

Reference trajectory.

Output tracking error.

Tracking error vector.

Sliding hyperplane.

Laplace operator.

Small positive constants.

Sliding mode controller.

Sign function.

Adaptive RCMAC.

Compensated controller.

Input state vector of RCMAC.

Number of elements.

Number of blocks.

Number of receptive fields.

Receptive-field basis function.

Mean of receptive-field basis function.

Variance of receptive-field basis function.

Input of block.

Value of through delay time .

Recurrent weight.

Number of elements in a complete block.

Multidimensional receptive-field function.

Weight value of RCMAC.

Output of RCMAC.

Optimal RCMAC.

Minimum approximation error.

Optimal parameter vector of .

Estimated vector of .

Approximation error bound.

Positive constants.

Constrain set for .

Induced norm of vector.

Upper bound of .