A method includes obtaining data identifying values of one or more process variables associated with an industrial process controller and identifying one or more constraint violations using the data. The method also includes, for each identified constraint violation, analyzing a behavior of the controller, a behavior of an industrial process being controlled, and how the controller was being used by at least one operator for a period of time. At least part of the period of time is prior to the identified constraint violation. The method further includes generating a graphical display based on the analysis, where the graphical display identifies one or more probable causes for at least one of the one or more constraint violations.

Provided is an analysis apparatus comprising: a variation model storage unit configured to store a plurality of variation models indicating variation in characteristics of a plant corresponding to an operating condition of the plant; a model extraction unit configured to acquire structure information indicating a structure model of an analysis target plant and to extract the variation model corresponding to the structure model; and an analysis unit configured to analyze the analysis target plant, based on the structure model of the analysis target plant and the variation model extracted by the model extraction unit.

An adaptive engine and a method of adaptive control are disclosed. The method comprises receiving an input regressor, where the input regressor comprises a reference signal, a system output measurement, and a control output. The method includes applying one or more estimation laws to the input regressor to estimate two or more sets of estimated model parameter tensors, ; receiving two or more possible control signals; generating two or more estimated system outputs; and selecting a control signal from a set comprising at least the first possible control signal and the second possible control signal, or a combination of possible control signals blended from two or more of the sets.

An adaptive engine and a method of adaptive control are disclosed. The method comprises receiving an input regressor, where the input regressor comprises a reference signal, a system output measurement, and a control output. The method includes applying one or more estimation laws to the input regressor to estimate two or more sets of estimated model parameter tensors, ; receiving two or more possible control signals; generating two or more estimated system outputs; and selecting a control signal from a set comprising at least the first possible control signal and the second possible control signal, or a combination of possible control signals blended from two or more of the sets.