Control system with dimension reduction for multivariable optimization
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Solution Overview
Problem
Conventional approaches for selecting a subset of variables in multivariable extremum-seeking optimization face challenges due to exponential complexity and computational load, making it difficult to determine optimal variable inclusion thresholds.
Innovation Solution
A control system that uses dimension reduction techniques like PCA, PLS, and CCA to map a large number of manipulated variables to a smaller set of latent variables, allowing for optimal control of performance variables through extremum-seeking controllers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a subset of variables is chosen from the total possible number of variables to reduce complexity, then device complexity and computational load are reduced, but measurement precision and control accuracy deteriorate due to loss of information from excluded variables
Solution Approach 1:
The patent introduces latent variables as intermediary representations that capture the essential information from multiple manipulated variables through linear combinations. These latent variables serve as a compressed intermediary space that preserves performance-relevant information while reducing the dimensionality that the extremum-seeking controller must directly handle, thus maintaining accuracy while reducing complexity.
Solution Approach 2:
The patent extracts and separates the performance-critical information from the full set of manipulated variables by projecting them into a smaller set of latent variables. This extraction process isolates the essential degrees of freedom that influence performance, removing redundant or less important variable dimensions while preserving the core optimization capability.
2Productivity
If dimension reduction is applied to reduce computational load, then productivity and processing efficiency are improved, but loss of information occurs when mapping from manipulated variables to latent variables
Solution Approach 1:
The patent transforms the parameter representation from the original manipulated variable space to a latent variable space through linear transformation. This parameter change allows the system to operate in a reduced-dimensional space with fewer computational requirements while the transformation matrices preserve the ability to recover or approximate the original variable relationships when needed.
Data Source
AI summary
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.