Constraints-Informed Neural-Laguerre Approximation of Nonlinear MPC with Application in Power Electronics

This paper considers learning online (implicit) nonlinear model predictive control (MPC) laws using neural networks and Laguerre functions. Firstly, we parameterize the control sequence of nonlinear MPC using Laguerre functions, which typically yields a smoother control law compared to the original nonlinear MPC law. Secondly, we employ neural networks to learn the coefficients of the Laguerre nonlinear MPC solution, which comes with several benefits, namely the dimension of the learning space is dictated by the number of Laguerre functions and the complete predicted input sequence can be used to learn the coefficients. To mitigate constraints violation for neural approximations of nonlinear MPC, we develop a constraints-informed loss function that penalizes the violation of polytopic state constraints during learning. Box input constraints are handled by using a clamp function in the output layer of the neural network. We demonstrate the effectiveness of the developed framework on a nonlinear buck-boost converter model with sampling rates in the sub-millisecond range, where online nonlinear MPC would not be able to run in real time. The developed constraints-informed neural-Laguerre approximation yields similar performance with long-horizon online nonlinear MPC, but with execution times of a few microseconds, as validated on a field-programmable gate array (FPGA) platform.