A T-S fuzzy based adaptive critic for continuous-time input affine nonlinear systems

This paper proposes a novel scheme of a Takagi-Sugeno (T-S) fuzzy based adaptive critic for the optimal control of the continuous-time input affine nonlinear system. A novel learning strategy is proposed to update the weights of critic network which resolves the issue of under-determined weight update equations discussed in previous paper. The T-S fuzzy based critic network approximates the global optimal cost as fuzzy average of local costs associated with local linear subsystems. This work clearly demonstrates that the optimal cost of a nonlinear system can be represented as the fuzzy cluster of optimal costs of locally valid linear models in a T-S framework. The proposed scheme has been simulated for four different dynamic systems. Simulation results clearly demonstrate that the T-S fuzzy approximates the optimal cost, with subsystems in each fuzzy zone represents the optimal cost of locally valid linear model.