Method and apparatus for optimizing a system model with gain constraints using a non-linear programming optimizer

• US 20060184477A1
• Filed: 04/03/2006
• Published: 08/17/2006
• Est. Priority Date: 05/06/1996
• Status: Active Grant

• Current Assignee: Rockwell Automation Technologies Incorporated (Allen-Bradley Co., Inc.)
• Original Assignee: Rockwell Automation, Inc.
• Inventors: Piche, Stephen, Hartman, Eric Jon, Gerules, Mark
• Granted Patent: US 7,315,846 B2
• Time in Patent Office: Days
• US Class Current: 706/21
• CPC Class Codes: G05B 13/027 using neural networks only
• CPC Class Codes: G05B 13/042 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G05B 13/048 using a predictor
• CPC Class Codes: G05B 17/02 electric
• CPC Class Codes: G06N 3/02 Neural networks

Abstract

Method and apparatus for training a system model with gain constraints. A method is disclosed for training a steady-state model, the model having an input and an output and a mapping layer for mapping the input to the output through a stored representation of a system. A training data set is provided having a set of input data u(t) and target output data y(t) representative of the operation of a system. The model is trained with a predetermined training algorithm which is constrained to maintain the sensitivity of the output with respect to the input substantially within user defined constraint bounds by iteratively minimizing an objective function as a function of a data objective and a constraint objective. The data objective has a data fitting learning rate and the constraint objective has constraint learning rate that are varied as a function of the values of the data objective and the constraint objective after selective iterative steps.

Claims

1. A method, comprising:

providing a trained model, wherein the trained model comprises a representation of a plant or process, wherein the trained model comprises one or more inputs and one or more outputs, wherein the model comprises one or more gains, and wherein each gain comprises a respective partial derivative of an output with respect to a respective input;

specifying one or more gain constraints, wherein each of the one or more gain constraints corresponds to a respective gain;

specifying a desired behavior of the plant or process;

optimizing the trained model with a non-linear programming optimizer subject to the one or more gain constraints to determine one or more input values that result in the desired behavior subject to the one or more gain constraints; and

wherein the one or more input values are usable to operate the plant or process to produce the desired behavior.

2. The method of claim 1, wherein said optimizing the trained model further comprises optimizing a specified objective function.

3. The method of claim 1, wherein the one or more gain constraints comprise one or more of:

at least one hard constraint, comprising a strict limitation on a corresponding at least one gain used in said optimizing the trained model;

or

at least one soft constraint, comprising a weighted penalty with respect to a corresponding at least one gain used in said optimizing the trained model.

4. The method of claim 1, wherein at least one of the gain constraints comprises one or more of:

a lower bound on the corresponding gain;

or

an upper bound on the corresponding gain.

5. The method of claim 1, wherein the trained model comprises a neural network.

6. The method of claim 1, the method further comprising:

providing the plant or process input data to the model;

executing the trained model to generate one or more predicted plant or process outputs based on the plant or process input data; and

wherein the one or more predicted plant or process outputs are useable to manage the plant or process.

7. The method of claim 6, the method further comprising:

managing the plant or process according to the predicted output.

8. The method of claim 6, the method further comprising:

comparing the one or more predicted plant or process outputs to one or more actual outputs of the plant or process; and

if the one or more predicted plant or process outputs are different from the one or more actual outputs of the plant or process, introducing bias onto the trained model to correct for the difference, thereby producing one or more biased predicted plant or process outputs.

9. The method of claim 8, the method further comprising:

managing the plant or process according to the one or more biased predicted plant or process outputs.

10. The method of claim 1, wherein the trained model comprises a steady state model.

11. The method of claim 1, wherein the trained model comprises a dynamic model.

12. The method of claim 1, wherein the trained model comprises one or more of:

a linear portion;

or

a non-linear portion.

13. The method of claim 1, wherein said optimizing comprises:

optimizing the trained model using one or more of;

one or more other constraints;

or

one or more other optimizers.

14. The method of claim 1, the method further comprising:

providing the one or more input values as input to the plant or process;

operating the plant or process in accordance with the one or more input values to produce the desired behavior.

15. The method of claim 14, the method further comprising:

comparing one or more actual outputs of the plant or process to one or more desired outputs of the plant or process; and

if the actual outputs of the plant or process are different from the one or more desired outputs, introducing bias onto the trained model to-correct for the difference.

16. The method of claim 1,

wherein the desired behavior comprises one or more desired outputs for the plant or process.

17. The method of claim 1,

wherein the desired behavior comprises maximizing profit for the plant or process.

18. A computer-accessible memory medium, wherein the memory medium comprises program instructions executable to:

implement a trained model, wherein the trained model comprises one or more inputs and one or more outputs, wherein the trained model comprises a representation of a plant or process, wherein the model comprises one or more gains, and wherein each gain comprises a respective partial derivative of an output with respect to a respective input;

specify one or more gain constraints, wherein each of the one or more gain constraints corresponds to a respective gain;

specify a desired behavior of the plant or process;

optimize the trained model with a non-linear programming optimizer subject to the one or more gain constraints to determine one or more input values that result in the desired behavior subject to the one or more gain constraints; and

wherein the one or more input values are usable to operate the plant or process to produce the desired behavior.

19. A system, comprising:

means for providing a trained model, wherein the trained model comprises one or more inputs and one or more outputs, wherein the trained model comprises a representation of a plant or process, wherein the model comprises one or more gains, and wherein each gain comprises a respective partial derivative of an output with respect to a respective input;

means for specifying one or more gain constraints, wherein each of the one or more gain constraints corresponds to a respective gain;

means for specifying a desired behavior of the plant or process;

means for optimizing the trained model with a non-linear programming optimizer subject to the one or more gain constraints to determine one or more input values that result in the desired behavior subject to the one or more gain constraints; and

wherein the one or more input values are usable to operate the plant or process to produce the desired behavior.

20. A system, comprising:

a trained model, representing a plant or process, wherein the trained model comprises;

one or more inputs;

one or more outputs; and

one or more gains, wherein each gain comprises a respective partial derivative of an output with respect to a respective input; and

a non-linear programming optimizer, coupled to the trained model;

wherein the trained model is constrained by one or more gain constraints, wherein each of the one or more gain constraints corresponds to a respective gain;

wherein the trained model is operable to receive a desired behavior of the plant or process;

wherein the non-linear programming optimizer is operable to optimize the trained model subject to the one or more gain constraints, wherein the non-linear programming optimizer is operable to optimize the trained model to determine one or more input values that result in the desired behavior of the plant or process subject to the one or more gain constraints; and

wherein the one or more input values are usable to operate the plant or process to produce the desired behavior.