Control system with dimension reduction for multivariable optimization
A control system is configured to operate a multiple-input system to achieve an optimal value for a performance variable of the multiple-input system. The control system includes a mapper configured to generate a mapping from a first number of manipulated variables to a second number of latent variables. The second number is smaller than the first number and each of the latent variables includes a linear combination of the manipulated variables. The control system also includes an extremum-seeking controller configured to receive the performance variable from the multiple-input system as a feedback and modulate values of the second number of latent variables to drive the performance variable to the optimal value. The mapper is further configured to use the mapping to translate modulated values of the second number of latent variables to modulated values of the first number of manipulated variables and provide the modulated values of the first number of manipulated variables to the multiple-input system.
1. A control system for operating a multiple-input system to achieve an optimal value for a performance variable of the multiple-input system, the control system comprising:
one or more processors; and
one or more computer-readable storage media having instructions stored thereon that, when executed by the one or more processors, cause the one or more processors to implement operations comprising:
generating a mapping from a first number of manipulated variables to a second number of latent variables, wherein the second number is smaller than the first number and each of the latent variables includes a linear combination of the manipulated variables;
receiving the performance variable as a feedback signal;
modulating values of the second number of latent variables to drive the performance variable to the optimal value;
translating modulated values of the second number of latent variables to modulated values of the first number of manipulated variables using the mapping; and
providing the modulated values of the first number of manipulated variables to the multiple-input system.
2. The control system of claim 1 , wherein generating the mapping from the first number of manipulated variables to the second number of latent variables includes using a principle component analysis (PCA) process.
3. The control system of claim 1 , wherein generating the mapping from the first number of manipulated variables to the second number of latent variables includes using a partial least squares (PLS) process.
4. The control system of claim 1 , wherein generating the mapping from the first number of manipulated variables to the second number of latent variables includes using a canonical correlation analysis (CCA) process.
5. The control system of claim 1 , the operations further comprising determining optimal values for all the latent variables using a multivariable extremum-seeking controller.
6. The control system of claim 1 , the operations further comprising determining an optimal value for each latent variable using a plurality of single-variable extremum-seeking controllers each assigned to a different latent variable.
7. The control system of claim 1 , the operations further comprising determining optimal values for the latent variables using a hybrid extremum seeking controller that operates in multiple different modes.
8. The control system of claim 1 , wherein modulating values of the second number of latent variables to drive the performance variable to the optimal value comprises modulating values of the second number of latent variables to drive a gradient of the performance variable to zero.
9. The control system of claim 1 , wherein modulating values of the second number of latent variables to drive the performance variable to the optimal value comprises perturbing the second number of latent variables with a periodic dither signal.
10. The control system of claim 1 , wherein modulating values of the second number of latent variables to drive the performance variable to the optimal value comprises perturbing the second number of latent variables with a stochastic excitation signal.
11. A method for operating a multiple-input system to achieve an optimal value for a performance variable of the multiple-input system, the method comprising:
generating a mapping from a first number of manipulated variables to a second number of latent variables, wherein the second number is smaller than the first number and each of the latent variables includes a linear combination of the manipulated variables;
receiving the performance variable from the multiple-input system as a feedback signal and modulating values of the second number of latent variables to drive the performance variable to the optimal value; and
using the mapping to translate modulated values of the second number of latent variables to modulated values of the first number of manipulated variables and providing the modulated values of the first number of manipulated variables to the multiple-input system.
12. The method of claim 11 , wherein generating the mapping from the first number of manipulated variables to the second number of latent variables includes using a principle component analysis (PCA) process to generate the mapping.
13. The method of claim 11 , wherein generating the mapping from the first number of manipulated variables to the second number of latent variables includes using a partial least squares (PLS) process to generate the mapping.
14. The method of claim 11 , wherein generating the mapping from the first number of manipulated variables to the second number of latent variables includes using a canonical correlation analysis (CCA) process to generate the mapping.
15. The method of claim 11 , wherein modulating values of the second number of latent variables to drive the performance variable to the optimal value includes using a multivariable extremum-seeking controller to determine optimal values for all the latent variables.
16. The method of claim 11 , wherein modulating values of the second number of latent variables to drive the performance variable to the optimal value includes using a plurality of single-variable extremum-seeking controllers each assigned to a different latent variable to determine an optimal value for each latent variable.
17. The method of claim 11 , wherein modulating values of the second number of latent variables to drive the performance variable to the optimal value includes using a hybrid extremum-seeking controller to operate in multiple different operating modes for determining optimal values for the latent variables.
18. The method of claim 11 , wherein modulating values of the second number of latent variables to drive the performance variable to the optimal value comprises modulating values of the second number of latent variables to drive a gradient of the performance variable to zero.
19. The method of claim 11 , wherein modulating values of the second number of latent variables to drive the performance variable to the optimal value comprises perturbing the second number of latent variables with a periodic dither signal.
20. The method of claim 11 , wherein modulating values of the second number of latent variables to drive the performance variable to the optimal value comprises perturbing the second number of latent variables with a stochastic excitation signal.