[1910.10835] Large Scale Model Predictive Control with Neural Networks and Primal Active Sets
We show how the concepts of warm starting and early termination can be used to combine the primal active set solver with the neural network to accelerate inference times

Abstract: This work presents an explicit-implicit procedure that combines an offline
trained neural network with an online primal active set solver to compute a
model predictive control (MPC) law with guarantees on recursive feasibility and
asymptotic stability. The neural network improves the suboptimality of the
controller performance and accelerates online inference speed for large
systems, while the primal active set method provides corrective steps to ensure
feasibility and stability. We highlight the connections between MPC and neural
networks and introduce a primal-dual loss function to train a neural network to
initialize the online controller. We then demonstrate online computation of the
primal feasibility and suboptimality criteria to provide the desired
guarantees. Next, we use these neural network and criteria measures to
accelerate an online primal active set method through warm starts and early
termination. Finally, we present a data set generation algorithm that is
critical for successfully applying our approach to high dimensional systems.
The primary motivation is developing an algorithm that scales to systems that
are challenging for current approaches, involving state and input dimensions as
well as planning horizons in the order of tens to hundreds.

Fig. 1. Space Filling Generator: Illustration of the data generation procedure with varying number of goal (Sobol) states. Fig. 2. Train and Test Distribution Illustraton of the different distributions for the train and test set. With enough goal (Sobol) states, both fill the entire feasible polyhedra. Fig. 3. Proposed efficient data set generation algorithm for the double integrator system (2 state dimensions). (Scaling to Large Systems)Fig. 4. Overview of the data set sizes and time statistics. (Data Set Generation Algorithm)Fig. 5. Neural network architectures. Each layer is fully connected and followed by the ReLu nonlinearity. Bolded are the input and output sizes of the network. (System Descriptions)Fig. 6. Training metrics: The Lagrangian Loss is defined in Eqn. (??), and the Lagrangian Estimate is defined in Eqn. (??). (System Descriptions)Fig. 7. (Sys. 4) Histogram of iterations for both NN and cold start initialization methods and p.f. + sub. and optimal termination methods. (Test Metrics)Fig. 8. (Sys. 4) Average time required to solve high dimensional oscillating masses using cold start in testing, our method in testing, and hot start in data generation (Test Metrics)Fig. 9. Test Set Metrics: These metrics report the number of iterations and suboptimality of the the various intialization and temrmination methods on the 4 systems. Our method is displayed in magenta, and the baseline method is displayed in olive. (Test Metrics)Fig. 10. Rejection sampling does not scale to large systems. (Scaling Metrics)