Model-Free Adaptive State Feedback Control for General Nonlinear Systems With Time-Delay

This article proposes a model-free adaptive state feedback control algorithm based on linear matrix inequalities (LMIs) for general unknown multiple input multiple output (MIMO) nonlinear systems that experience known time-delay. The algorithm first establishes an equivalent dynamic linear state-space model for the nonlinear system using the dynamic linearization method. A Luenberger observer is incorporated to estimate the unmeasurable states. Subsequently, the objective function of the pseudo partial derivative (PPD) is redesigned to ensure that the estimation error of the PPD matrix is bounded. Based on the dynamic model, the corresponding estimates, and the system time-delay, a Lyapunov–Krasovskii function is defined. An LMI, including the time-delay, is then obtained as a sufficient condition to guarantee the stability of both the system and the state observer. By solving the LMI, a state feedback gain is derived, which in turn mitigates the effect of time-delay on the system stability. The theoretical analysis demonstrates the asymptotic stability of the closed-loop control system. Finally, the proposed algorithm is validated by simulation testing and experimental results.