Approximating Explicit Model Predictive Control Using Constrained Neural Networks

This paper presents a method to compute an approximate explicit model predictive control (MPC) law using neural networks. The optimal MPC control law for constrained linear quadratic regulator (LQR) systems is piecewise affine on polytopes. However, computing this optimal control law becomes computationally intractable for large problems, and motivates the application of reinforcement learning techniques using neural networks with rectified linear units. We introduce a modified reinforcement learning policy gradient algorithm that utilizes knowledge of the system model to efficiently train the neural network. We guarantee that the network generates feasible control inputs by projecting onto polytope regions derived from the maximal control invariant set of the system. Finally, we present numerical examples that demonstrate the characteristics and performance of our algorithm.