Adaptive guaranteed cost control for nonlinear systems with unknown parameters and time delays based on fully actuated system approaches

This paper investigates the adaptive guaranteed cost stabilization (AGCS) problems for two classes of high-order nonlinear systems with unknown parameters (vector) and time delays. Firstly, based on the high-order fully actuated (HOFA) system approaches, the Lyapunov–Krasovskii functional (LKF) and the guaranteed cost control (GCC), a new AGCS strategy is proposed for HOFA nonlinear system with unknown parameter vector and time delays. Then, based on the above result, another AGCS controller for a class of strict-feedback systems (SFSs) with unknown parameters and time delays is obtained. Two designed controllers ensure that all of the states of two closed-loop systems are global boundedness, and preset arbitrarily the upper bound of cost functions (UBCFs) characterizing the output performance. More importantly, the UBCFs are independent of system initial values, unknown parameters (vector), and even time delays, which is difficult to achieve by using existing control methods. To do this, this paper introduces a local smooth nonlinear function (LSNF), and gives its corresponding lemma, which provide an important mathematical tool. Finally, three simulation examples, including an application in the electromechanical system, are given to prove the effectiveness and the practicability of our proposed control method.