On Satisfaction of the Persistent Excitation Condition for the Zone MPC: Numerical Approach

Abstract

In recent years, advanced control techniques such as Model Predictive Control based on optimization and making use of a model providing the predictions of the future behavior of the controlled system have been massively developed. These model-based controllers rely heavily on the accuracy of the available model (predictor of the controlled system behavior) which is crucial for their proper functioning. However, as the current operating conditions can be shifted away from those under which the model has been identified, the model sometimes happens to lose its prediction properties and needs to be re-identified. Unlike the theoretical assumptions, the data from the real operation suffer from undesired phenomena accompanying the closed-loop data. In the current paper, we focus on developing an algorithm which would serve as an alternative to the (often costly or even unrealizable) open loop excitation experiment. The requirements such an algorithm should meet are: low computational complexity, low level of original MPC performance degradation and ability to provide sufficiently informative data when necessary. Unlike to the currently available approaches which solve this problem for the classical MPC formulation (tracking error penalization), in this paper we propose an algorithm which works well also for the zone MPC formulation (penalization of output zone violation), however, it is versatile enough and can be extended considering wider variety of the optimization formulations.