Synthesis of Invariant Immersion and Dynamic Surface Control Methods for Nonlinear Uncertain Objects

The paper discusses a modern method for synthesizing adaptive controllers for nonlinear objects with uncertain parameters, presented in lower triangular form. The adaptive control system is developed based on a combination of the backstepping method using first-order low-pass filters (or the dynamic surface control method) and the invariant immersion method based on the attractiveness of invariant manifolds. Estimation of unknown parameters using the invariant immersion method allows the control system to avoid undesirable transient processes that arise due to the unpredictable dynamic behavior of traditional parameter tuning laws in adaptive control synthesis. The stability (robustness) of the closed-loop system is proven using Lyapunov functions. Simulation results in the MATLAB/Simulink software environment of a numerical example of an adaptive control system for a third-order uncertain nonlinear object demonstrate the effectiveness of the proposed control scheme.