The adaptive practical prescribed-time (PPT) neural control is studied for multi-input multi-output (MIMO) nonlinear systems with unknown nonlinear functions and unknown input gain matrices. Unlike existing PPT design schemes based on backstepping, this study proposes a novel PPT control framework using the dynamic surface control (DSC) approach. Firstly, a novel nonlinear filter (NLF) with an adaptive parameter estimator and a piece-wise function is constructed to effectively compensate for filter errors and facilitate prescribed-time convergence. Based on this, a unified DSC-based adaptive PPT control algorithm, augmented with a neural networks (NNs) approximator, is developed, where NNs are used to approximate unknown nonlinear system functions. This algorithm not only addresses the inherent computational complexity explosion associated with traditional backstepping methods but also reduces the constraints on filter design parameters compared to the DSC algorithm that relies on linear filters. The simulation showcases the effectiveness and superiority of the devised scheme by employing a two-degree-of-freedom robot manipulator.

The identification of affinely parameterized state–space system models is quite popular to model practical physical systems or networked systems, and the traditional identification methods require the measurements of both the input and output data. However, in the presence of partial unknown input, the corresponding system identification problem turns out to be challenging and sometimes unidentifiable. This paper provides the identifiability conditions in terms of the structural properties of the state–space model and presents an identification method which successively estimates the system states and the affinely parameterized system matrices. The estimation of the system matrices boils down to solving a bilinear optimization problem, which is reformulated as a difference-of-convex (DC) optimization problem and handled by the sequential convex programming method. The effectiveness of the proposed identification method is demonstrated numerically by comparing with the Gauss–Newton method and the sequential quadratic programming method.