Approximating Nonlinear Model Predictive Controllers using Support Vector Machines

Abstract

Typically, Model Predictive Control (MPC) for highly dynamic systems poses challenges to the computation power needed to optimize the control in real-time. In this paper, we present an explainable methodology to approximate MPCs with low input penalization as a closed form expression, using learning by demonstration. Classical approaches, e.g. using neural networks, result in over-complicated controllers and require huge datasets. In this paper, the prior knowledge on the typical bang-bang behavior of low-input penalized MPC will be exploited to approximate the MPC-law by only sparsely sampling the state space. This is achieved by identifying the switching surface of the sampled MPC-solution using Support Vector Machines (SVMs). The result is a light-weight, interpretable, easy to tune, explicit control law suitable for real-time applications. The methodology is validated in simulation on a benchmark problem from the field of process control (stirred tank reactor), and on a physical set-up of a highly dynamic motion control problem (parallel SCARA). The results, both in simulation and experimentally, show that strong approximation can already be obtained by using very light-weight controllers which, for the SCARA, were able to run on a frequency of at least 2kHz on the experimental setup.