Canonical Transformations for Complex System Collective Control
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Solution Overview
Problem
Existing systems and methods for controlling complex systems fail to account for the collective behavior of many individual systems, leading to ineffective characterization, simulation, and control of such systems.
Innovation Solution
A complex transformer is introduced to calculate singularity spectrums, enabling improved control of complex systems by transforming input functionals into output functionals through a series of canonical and inverse canonical transformations, based on generating functionals and Hamilton-Jacobi equations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If existing control systems are used for complex systems, then individual system control is achieved, but collective behavior and emergent properties are not captured
Solution Approach 1:
The patent segments the complex system into individual subsystems while introducing a hierarchical control architecture. The control system operates at multiple levels: individual system level and collective system level. This segmentation allows precise control of individual components while capturing emergent collective behaviors through the hierarchical structure, resolving the contradiction between measurement precision and adaptability.
Solution Approach 2:
The patent introduces an intermediary layer (the hierarchical control architecture) that bridges individual system control and collective system behavior. This intermediary captures emergent properties and coordinates between individual subsystems and the overall collective system, enabling both precise individual characterization and accurate collective behavior modeling simultaneously.
2Reliability
If traditional control methods are applied, then simple systems are effectively controlled, but complex systems with discontinuous behavior and emergent properties cannot be properly characterized
Solution Approach 1:
The patent implements a dynamic control architecture that adapts to the complexity of the system being controlled. The hierarchical structure allows the control system to dynamically adjust between managing individual subsystems and coordinating collective behavior, providing reliable control for both simple and complex systems without requiring overly complex fixed-structure control devices.
3Adaptability or versatility
If functional approximators are constrained away from conservative structure, then flexibility is increased, but the canonical structure of complex systems is not captured
Solution Approach 1:
The patent applies local quality by allowing different parts of the functional approximator to have different structural properties. The hierarchical control architecture enables conservative structures to be maintained where canonical properties are critical, while allowing flexibility in other regions where adaptability is more important, thus capturing both canonical structure and system diversity.
Data Source
AI summary
Controlling a complex system including: obtaining an input of a functional of field and co-field functions; determining, based on the input functional and using a canonical functional transformation, an input function; determining, based on the input function and using a function transformation, the input basic state and co-state variables; determining, based on the input basic state and co-state variables and using a canonical transformation, input fundamental state and co-state variables; determining, based on the input fundamental state and co-state variables and using a control function transformation, output fundamental state and co-state variables; determining, based on the output fundamental state and co-state variables and using an inverse canonical transformation, output basic state and co-state variables; determining, based on the output basic state and co-state variables and using a function transformation, the output function; and determining, based on the output function and using an inverse canonical functional transformation, an output functional of the field and co-field functions.