Stability Guaranteed Approximation of Model Predictive Control Using Unsupervised Learning

This work presents an unsupervised learning-based approach to approximate the controller of the Lyapunov-based Model Predictive Control (MPC) for a class of continuous-time nonlinear systems. The proposed design aims to produce an optimal control input by aligning the objectives and constraints of the learning problem with those of the MPC. The MPC is approximated by a deep feedforward neural network (DFNN) whose output can strictly satisfy the system constraints. A sufficient condition is provided under which the stability of the closed-loop system with the approximation DFNN control implemented in a sampling-and-hold fashion can be guaranteed. Additionally, we define a polyhedral Lyapunov function to shape the domain of attraction, allowing it to approach the shape of the state boundary defined by polyhedral state constraints, thereby providing potential for enlarging the domain of attraction. The implementation of the proposed method on a permanent magnet synchronous generator wind turbine and a continuous stirred tank reactor illustrates the effectiveness and performance of the designed approximation controller.