Adaptive Control for Complex Systems with Dynamics and Time-Varying Powers

This work focuses on presenting a control algorithm to investigate nonlinear systems, which contain time-varying powers, inverse dynamics, and uncertainties. First, some appropriate transformations are introduced to obtain a new system. Then, a Lyapunov function, which covers quadratic and high-order components, is recursively constructed for control design. Subsequently, by introducing the neural networks, the uncertain functions encountered during the design are approximated. Based on the inequality techniques, the nonlinear terms are skillfully estimated. By defining the bounds of some unknown parameters and using the adaptive technique, some virtual controllers are selected in each step to dominate the nonlinear functions and guarantee that the derivative of the Lyapunov function satisfies the required form. Finally, a new adaptive controller is constructed and semiglobal practical finite time stability (SGPFS) is guaranteed. The proposed approach is verified with a numerical example.