Model Predictive Control With Predefined Performance Boundaries and Its Application to Gyroscopes

Presetting the transient and steady-state performance of the dynamic system holds significant engineering value. This article introduces a model predictive controller with predefined performance boundaries, distinguished by its ability to control the morphology of transient processes. The core feature reflects the construction of state boundary constraints guided by the damping ratio. The construction process of constraints relies on solving a class of second-order Lyapunov inequalities, which can preset the system's damping ratio, thereby influencing the shape of the transient process. In addition, a function-adaptive law is developed to account for the nonlinear dynamics of the system. This function-adaptive law integrates optimization-based command-filtering technology, which extracts differential information from unknown signals. The stability of the controller and function-adaptive law is established using the Lyapunov criterion. Finally, the effectiveness of the proposed model predictive controller and its predefined boundary constraints are validated through experiments conducted on a gyroscope platform.