Training a model of a non-linear process

A computer accessible memory medium that stores program instructions for training a parametric universal nonlinear dynamic approximator of a nonlinear process, wherein the program instructions are executable by a processor to perform:

• identifying process inputs and outputs (I/O);
• determining an order for a parameterized dynamic model comprised in the parametric universal nonlinear dynamic approximator, wherein the order specifies the number of parameters for the parameterized dynamic model, and wherein the parameters of the parameterized dynamic model are not inputs or outputs of the nonlinear process;
• determining a structure for a nonlinear approximator comprised in the parametric universal nonlinear dynamic approximator for modeling dependencies of the parameters of the parameterized dynamic model upon operating conditions of the nonlinear process;
• collecting data for the identified process I/O;
• determining constraints on behavior of the parametric universal nonlinear dynamic approximator from prior knowledge, including one or more constraints for the nonlinear approximator for modeling dependencies of the one or more parameters of the parameterized dynamic model;
• formulating an optimization problem for training the nonlinear approximator;
• executing an optimization algorithm to train the nonlinear approximator subject to the determined constrains by solving the optimization problem, thereby determining the dependencies of the parameters of the parameterized dynamic model upon operating conditions of the process, wherein outputs of the nonlinear approximator are not outputs of the nonlinear process;
• verifying compliance of the parametric universal nonlinear dynamic approximator with the specified constraints;
• and
• storing the trained nonlinear approximator and the parameterized dynamic model, wherein the stored nonlinear approximator and the parameterized dynamic model compose a trained parametric universal nonlinear dynamic approximator;
• wherein the trained parametric universal nonlinear dynamic approximator is usable to optimize and control the nonlinear process.

A system for training a parametric universal nonlinear dynamic approximator of a nonlinear process, the system comprising:

• means for identifying process inputs and outputs (I/O);
• means for determining an order for a parameterized dynamic model comprised in the parametric universal nonlinear dynamic approximator, wherein the order specifies the number of parameters for the parameterized dynamic model, and wherein the parameters of the parameterized dynamic model are not inputs or outputs of the nonlinear process;
• means for determining a structure for a nonlinear approximator comprised in the parametric universal nonlinear dynamic model upon operating conditions of the nonlinear process;
• means for collecting data for the identified process I/O;
• means for determining constraints on behavior of the parametric universal nonlinear dynamic approximator from prior knowledge, including one or more constraints for the nonlinear approximator for modeling dependencies of the one or more parameters of the parameterized dynamic model;
• means for formulating an optimization problem for training the nonlinear approximator;
• means for executing an optimization algorithm to train the nonlinear approximator subject to the determined constraints by solving the optimization problem, thereby determining the dependencies of the parameters of the parameterized dynamic model upon operating conditions of the process, wherein outputs of the nonlinear approximator are not outputs of the nonlinear process;
• means for verifying compliance of the parametric universal nonlinear dynamic approximator with the specified constraints;
• and
• means for storing the trained nonlinear approximator and the parameterized dynamic model, wherein the stored nonlinear approximator and the parameterized dynamic model compose a trained parametric universal nonlinear dynamic approximator;
• wherein the parametric universal nonlinear dynamic approximator is usable to optimize and control the nonlinear process.