Explicit Rule-Based Control Using State-Space Patch Regression
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Solution Overview
Problem
Existing control methods for complex dynamical systems, such as electric grids and automotive vehicles, face challenges due to high computational demands and non-linear optimization issues, particularly with explicit model predictive control (MPC) and neural networks, which can be intractable for large systems and lack interpretability.
Innovation Solution
A method is developed to generate an explicit rule-based control algorithm by mapping state signals to a control data manifold, detecting patches, training classifiers and regression models, and creating a simple indicator function to identify active patches for determining control actions, allowing for efficient online control without stringent computational requirements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If explicit model predictive control (MPC) is used to control complex dynamical systems, then optimal control solutions are achieved, but computational efforts and mathematical challenges increase significantly
Solution Approach 1:
The patent segments the complex control problem into multiple simpler local approximation functions defined over different patches in the state space. Each patch has its own simplified control law, avoiding the need to solve complex optimization problems online while maintaining overall optimality through the partitioning strategy.
Solution Approach 2:
The patent performs preliminary computation offline by pre-computing the local approximation functions and their valid regions (patches) for each operating condition. This preliminary action transfers the computational burden from online operation to offline setup, enabling simple evaluation during real-time control.
2Measurement precision
If the number of system states and constraints increases in explicit MPC, then control accuracy is maintained, but the size of explicit functions increases rapidly becoming intractable
Solution Approach 1:
The patent divides the high-dimensional state space into multiple lower-dimensional patches, each governed by a simple local approximation function. This segmentation maintains control accuracy within each patch while avoiding the exponential growth of function size that would occur if a single global function were used for the entire high-dimensional space.
Solution Approach 2:
The patent introduces a new dimension by partitioning the state space into discrete patches, transforming the continuous high-dimensional control problem into a piecewise structure. This dimensional transformation allows simple linear functions to approximate complex non-linear behavior in each local region without requiring large global functions.
3Productivity
If neural networks are used to replace online MPC computation, then computational speed improves, but interpretability and analytical comprehensibility are lost
Solution Approach 1:
The patent creates a simplified copy of the MPC control law in the form of piecewise linear approximation functions that replicate the optimal control behavior without requiring complex neural network structures. This copying approach maintains interpretability while achieving fast online evaluation similar to neural networks.
Solution Approach 2:
The patent changes the parameter representation from complex neural network weights and activations to simple linear function parameters (coefficients and valid regions). This parameter transformation enables analytical comprehensibility while maintaining computational efficiency through the piecewise structure.
4Measurement precision
If a large number of hidden nodes are used in neural networks to accurately mimic MPC solutions, then control accuracy improves, but computational resources and device complexity increase
Solution Approach 1:
The patent achieves high control accuracy by segmenting the state space into multiple patches, each with its own simple approximation function. This segmentation strategy provides the necessary complexity to capture non-linear behavior without requiring large numbers of hidden nodes, as each local function only needs to approximate behavior in its specific region.
Solution Approach 2:
The patent uses simple, computationally inexpensive local approximation functions that can be rapidly evaluated and discarded after use, replacing the need for expensive, resource-intensive neural network structures. Each local function is a simple mathematical expression that requires minimal computational resources to evaluate.
Data Source
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.