Unifying Input-Output and State-Space Perspectives of Predictive Control

Predictive control refers to the concept where the current control decision is based on a prediction of the system controlled response a number of times into the future. Originally derived from input-output models, recent years have seen efforts to interpret and develop predictive control from the state-space domain. This paper presents a formulation that unifies the two perspectives. Although a general state-space model is used as the starting point of the derivation, the predictive controller gains are ultimately synthesized from input-output data. There is no need for explicit model identification, and no observer is required in the implementation. Central to this development is a special interaction matrix which can be explained in the context of a “generalized” Cayley-Hamilton theorem. Experimental results are provided to illustrate this unified perspective of predictive control, including a comparison between data-based and modelbased predictive controller designs.