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Stability Guaranteed Approximation of Model Predictive Control Using Unsupervised Learning
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DOI：10.1109/TASE.2025.3616115.png)
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Abstract
En 中文
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. Note to Practitioners—The approximation controller design proposed in this paper aims to reduce the computational time of Model Predictive Control (MPC) in complex, large-scale systems while meeting real-time performance requirements. The proposed method can compute control signals effectively, ensuring the satisfaction of the system’s constraints. The implementation of the proposed approximation MPC involves the following steps: first, determine the input and output constraints of the dynamic system, along with the stability constraint of the Lyapunov-based MPC, to access the feasible region; second, based on the desired approximation accuracy and the feasible region of the state, specify the sampling scale for each state dimension and construct the training dataset, construct the loss function of the neural network model as the sum of the Laypunov-based MPC performance index evaluated at all states in the training set, and optimize the network parameters with gradient ascent; finally, integrate the approximation Lyapunov-based MPC controller with the control platform. At every time step, the control signal is generated by the trained deep feedforward neural network (DFNN) with optimized network parameters. Preliminary experiments suggest that this approach is feasible.
Keywords:
Model predictive control
controller approximation
Lyapunov technique
stability
machine learning
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