Stability of neural net based model predictive control

This paper illustrates the stability problems associated with the use of finite horizon model predictive controllers by using a recurrent neural network to predict accurately the input-output response of a simple linear system that exhibits nonminimum-phase behavior. The stability of the resulting closed-loop system depends on the particular tuning parameters of the controller (horizon length, penalty weights, etc.) even in the absence of process-model mismatch. Although these problems are not unique to neural net models, or even finite-horizon model predictive controllers, most modern control theories have addressed the nominal stability problems encountered with controllers based on other forms of input-output models. Similarly, it is desirable to establish a framework for model predictive control using neural network models that does not suffer from nominal stability problems. In this paper, the authors propose a state-space description of a class of externally recurrent neural network model. This state-space description allows the application of theoretical results for nonlinear systems to ensure nominal stability for the resulting closed-loop system.