Efficient model predictive control for nonlinear systems modelled by deep neural networks
This work addresses real-time control problems for engineers dealing with constrained nonlinear systems, but it is incremental as it builds on existing MPC and neural network modeling techniques.
The paper tackled the challenge of real-time model predictive control for nonlinear systems modeled by deep neural networks by proposing exact mixed integer programming and approximate linear relaxation methods, achieving computational efficiency with simulation results on an inverted pendulum system.
This paper presents a model predictive control (MPC) for dynamic systems whose nonlinearity and uncertainty are modelled by deep neural networks (NNs), under input and state constraints. Since the NN output contains a high-order complex nonlinearity of the system state and control input, the MPC problem is nonlinear and challenging to solve for real-time control. This paper proposes two types of methods for solving the MPC problem: the mixed integer programming (MIP) method which produces an exact solution to the nonlinear MPC, and linear relaxation (LR) methods which generally give suboptimal solutions but are much computationally cheaper. Extensive numerical simulation for an inverted pendulum system modelled by ReLU NNs of various sizes is used to demonstrate and compare performance of the MIP and LR methods.