Prescribed-Time Adaptive Tracking for Nonlinear Systems via Nonvanishing Disturbance Observer and Command Filtering
This paper addresses the prescribed-time (PT) tracking control problem for a class of nonlinear systems subjected to nonvanishing uncertain disturbances. To address the issue of discontinuous observation error derivatives caused by parameter constraints in conventional prescribed-time observer (PTO) designs, an improved PTO with a novel time-varying gain structure is proposed. The proposed observer removes the need for additional parameter conditions, ensures global continuity of the observation error derivatives, and enables smooth disturbance estimation and control input switching. To handle the inherent complexity explosion issue in backstepping design, a finite-time command filter (FTCF) is subsequently employed to approximate the virtual control signals. The continuity properties of the signals provided by the aforementioned observer naturally satisfy the requirement of the command filter that the input signal be continuous and possess a first-order derivative over the domain of definition. An adaptive compensation mechanism is further developed to correct the approximation errors introduced by the command filter in an online manner. Simulation results demonstrate that the proposed control scheme effectively achieves PT tracking control with prescribed performance for nonlinear systems under nonvanishing disturbances, while ensuring the continuity and boundedness of all closed-loop signals. Note to Practitioners—The practical control of nonlinear systems, such as robotic manipulators and uncrewed vehicles, is significantly complicated by the presence of persistent nonvanishing disturbances. These disturbances, which do not decay to zero over time, can severely degrade tracking performance and even lead to instability. This work proposes a practical PT control framework for nonlinear systems subject to persistent nonvanishing disturbances, enabling error convergence to zero within a user-defined timeframe regardless of initial conditions. The core innovation integrates an improved PTO, a FTCF, and an adaptive event-triggered mechanism (ETM). The improved PTO ensures the global continuity of disturbance estimation error and its derivatives via a novel time-varying gain structure, eliminating the control signal jumps typical at switching instants in traditional PT designs. The FTCF completely circumvents the complexity explosion problem inherent in standard backstepping. The scheme allows engineers to directly and independently prescribe the convergence times for both disturbance observation and final tracking, independent of initial conditions. A prescribed performance function, based on a barrier Lyapunov function, guarantees that the system output adheres to predefined transient and steady-state performance bounds throughout operation. This work provides practitioners with a robust, high-performance, and implementable PT control solution for a wide class of disturbed nonlinear systems.