Dynamic Observer-Based Fast Fixed-Time Filtered Backstepping Controller Design for a Constrained Uncertain Nonlinear System

In this article, a fast fixed-time filter (FFTF)-based-backstepping control system is proposed for a class of uncertain high-order nonlinear systems with full-state constraints. To effectively tackle the lumped uncertainty, a dynamic gain fixed-time disturbance observer (DGFDO) is constructed to estimate the uncertainty, where the observer parameters are dynamically tuned and the estimation error converges to zero in fixed time. In order to solve the full-state constraints problem, the state transformation technique is employed with avoiding “feasibility conditions.” For overcoming the “explosion of complexity” problem of the backstepping method, an FFTF is constructed, where the filter error can be ensured to achieve fixed-time stability. In the light of Lyapunov theory, it is proved that all signals of the closed-loop system are bounded, all states are kept in their constraints, and output error converges to an arbitrarily small neighborhood around zero in fixed time. Finally, simulation results are demonstrated to verify the effectiveness of the theoretical results.