Rule-Based Control Patches for Complex Dynamical Systems
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Solution Overview
Problem
Existing control methods for complex dynamical systems, such as electric grids and factory robots, face challenges due to high computational demands and lack of interpretability, particularly with model predictive control (MPC) and neural networks, which become intractable for large systems and lack transparency.
Innovation Solution
A method to generate an explicit rule-based control algorithm by identifying patches on a control data manifold, classifying control points, and training regression models for each patch, allowing for efficient and interpretable control actions without extensive online computation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If model predictive control (MPC) is used to control complex dynamical systems, then optimal control solutions are achieved, but computational complexity and hardware requirements increase significantly
Solution Approach 1:
The patent segments the control problem by dividing the state space into multiple regions and creating separate explicit control laws for each region. This segmentation transforms a single complex optimization problem into multiple simpler, pre-computed control laws that can be easily implemented on hardware controllers without requiring extensive online computation.
Solution Approach 2:
The patent applies preliminary action by pre-computing explicit control laws offline for different regions of the state space. These pre-computed control laws are stored and ready for immediate application during online operation, eliminating the need to solve complex optimization problems in real-time and reducing hardware requirements.
2Productivity
If explicit model predictive control is used to compute optimal control actions offline, then online computational burden is reduced, but the size of explicit functions increases rapidly with system complexity
Solution Approach 1:
The patent divides the state space into multiple regions and creates separate explicit control laws for each region. This segmentation prevents the explicit functions from becoming intractably large by localizing the complexity to smaller, manageable regions rather than attempting to create a single global explicit function for the entire state space.
Solution Approach 2:
The patent applies local quality by creating region-specific control laws that are optimized for local dynamics rather than attempting a uniform global solution. Each local control law is simpler and more tailored to its specific region, reducing the overall complexity while maintaining global optimality.
3Productivity
If data-driven machine learning models are used to replace online MPC computation, then computational efficiency is improved, but interpretability and analytical comprehensibility are lost
Solution Approach 1:
The patent creates explicit control laws that copy the essential structure and behavior of MPC solutions in a simplified, interpretable form. Rather than using opaque neural networks, the patent generates explicit mathematical functions that replicate MPC's optimal control characteristics while maintaining analytical comprehensibility and ease of verification.
4Measurement precision
If neural networks with large numbers of hidden nodes are used to accurately mimic MPC solutions, then control accuracy is improved, but computational resource requirements increase
Solution Approach 1:
The patent generates explicit control laws that accurately replicate MPC solutions without requiring complex neural network architectures. By directly computing explicit functions from MPC formulations, the patent achieves high control accuracy while avoiding the computational resource demands of large-scale neural networks.
Data Source
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AI summary
A method for configuring a controller of a dynamical system includes obtaining a control data manifold formed by a plurality of stored control points, each representative of a state signal specifying a state of the dynamical system and an assigned control signal. Each state signal is mapped to a multi-dimensional state space. The assigned control signal is generated by a first control algorithm as a function of the state signal. The method includes detecting patches on the control data manifold by identifying control points on the control data manifold that belong to a common local approximation function, and training a classifier to classify control points into different patches. The method further includes training a respective regression model for each detected patch for approximating a relationship between state signals and the control signals in that patch, to create an explicit rule-based control algorithm.