Direct Adaptive Optimal Control for Uncertain Continuous-Time LTI Systems Without Persistence of Excitation

This brief presents a novel direct adaptive optimal controller design for uncertain continuous-time linear time-invariant systems. The optimal gain parameter, obtained from the Riccati equation, is continuously estimated without using knowledge of the system dynamics, rather information rich past, and current data along the system trajectory is used for parameter estimation. This approach guarantees parameter convergence to the close neighborhood of the optimal controller by relaxing the restrictive persistence of excitation condition, typically required for achieving parameter convergence in approximate/adaptive optimal control methods. A Lyapunov-based analysis establishes the uniformly ultimately bounded stability of the designed controller. Further a simulation example demonstrates the efficacy of the proposed result.