A Fully Actuated System Approach to Prescribed Performance Control of n-DOF Interconnected Nonlinear Systems via Cascaded Extended State Observers

This paper studies prescribed performance control for uncertain generalized n-degree-of-freedom (n-DOF) interconnected nonlinear systems (INSs) under the fully actuated system (FAS) approach. The considered systems contain nonlinear couplings, modeling and input-gain uncertainties, actuator nonlinearities, and external disturbances, while only position measurements are available. Cascaded first-order extended state observers (ESOs) are introduced to estimate the unmeasured velocities and lumped uncertainties. Then, a prescribed-time performance function is designed to impose predefined tracking constraints with a user-specified convergence time and terminal bound. By using an error transformation, the constrained tracking problem is converted into a transformed error system. Based on the resulting FAS model, a compact control law is developed, yielding assignable closed-loop eigenstructure. It is proved that all transformed tracking errors are uniformly ultimately bounded and that the prescribed performance constraints are satisfied.