CONTROL METHODS FOR PRACTICAL TRACKING OF NONLINEAR SYSTEMS UNDER NON-STRICT CONDITIONS

Abstract

For high-order nonlinear systems, especially in the presence of uncertainties and time-varying delays, achieving practical output tracking is a challenging scientific problem. This paper proposes control methods operating under non-strict conditions. During the study, state- and output-feedback controllers were synthesized based on the homogeneous domination approach, the power integrator technique, and Lyapunov-Krasovskii functionals. The proposed approach enables the construction of control laws while taking into account parameter uncertainties and time delays in the system. The obtained results theoretically prove that all states of the closed-loop system are uniformly bounded and that the tracking error converges to a predefined accuracy region after a finite time. Compared with existing results, the proposed method is characterized by relaxed assumptions on the system and applicability to high-order nonlinearities. In particular, it is highly effective in ensuring stability and achieving accurate tracking under parametric uncertainties and time-varying delays. Moreover, the theoretical results demonstrate that the proposed approach can be applied to various engineering systems, including robotics, automated control systems, and energy processes.