Composite Adaptive Critic Design

In this paper, we present a novel adaptive critic design with a finite excitation (FE) condition for adaptive optimal control of continuous-time nonlinear systems. The online recorded data is combined with instantaneous data via a hierarchical design scheme to replace the persistence of excitation condition with a FE condition. The online data is recorded in the preprocessing step and verified online, whereas the novel critic is implemented in the assembling step through appropriate algebraic calculations. On this basis, the composite adaptive critic design is developed with satisfactory convergence. The adaptive critic design can be implemented in an online fashion with the hierarchical design scheme, and the FE condition can also be online verifiable. It is shown that the composite adaptive critic design guarantees the closed-loop stability of the equilibrium point and convergence to the optimal solution. Simulations are conducted to show the efficacy of the composite adaptive critic design.