Optimal Output Feedback Tracking Control for Takagi–Sugeno Fuzzy Systems

In this study, an optimal output feedback tracking control approach with a Q-learning algorithm is presented for Takagi–Sugeno (T–S) fuzzy discrete-time systems with immeasurable states. First, a state reconstruction method based on the measured output data and input data is applied to handle immeasurable states problem. Then, the optimal output feedback tracking control input policy is designed and boiled down to the algebraic Riccati equations (AREs). To obtain the solution to AREs, a Q-learning value iteration (VI) algorithm is formulated, which directly learns each state-action value. Consequently, the sufficient conditions for the convergence of the proposed optimal algorithm are derived by constructing an approximate Q-function. It is proved that the presented optimal output feedback tracking control method can guarantee the controlled systems to be stable and output track the given reference signal. Finally, we take the truck-trailer system as the simulation example, the simulation results validate feasibility of the presented optimal control methodology.