Nonlinear State Model Learning for Convex Predictive Control
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Solution Overview
Problem
Existing model learning techniques face challenges in determining a unique input that stabilizes system control and improves output correlation to a target value, due to nonconvex optimization problems and irregular fluctuations caused by high non-linearity in machine learning models.
Innovation Solution
A model learning apparatus that uses bijective mappings ψ and ϕ to linearize the equation of state, ensuring a unique solution for input determination, and incorporates exogenous inputs to predict system states with high accuracy, employing multilayer neural networks to adjust weights and biases for precise output prediction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If a machine learning model with high non-linearity is used to learn the system model, then the model can capture complex nonlinear relationships, but the optimal control problem becomes nonconvex leading to multiple solutions and irregular input fluctuations
Solution Approach 1:
The patent transforms the nonlinear system model parameters by introducing a bijective mapping function that converts the original nonlinear state-space model into an equivalent linear model in transformed coordinates. This parameter transformation allows the system to maintain the ability to represent nonlinear relationships while enabling convex optimization for reliable control solutions.
Solution Approach 2:
The patent introduces a bijective mapping function as an intermediary transformation that bridges the nonlinear original system and the linear control framework. This intermediary coordinate transformation allows control inputs to be determined in the transformed linear space and then mapped back to the original nonlinear system, ensuring uniqueness and stability.
2Productivity
If model predictive control is applied to a nonlinear system, then future state prediction and optimization are enabled, but the control stability cannot be guaranteed due to nonconvex optimization
Solution Approach 1:
The patent changes the parameter representation of the system by applying a bijective mapping to transform the nonlinear state-space equations into a linear form. This allows model predictive control to be applied in the transformed coordinate system where convex optimization guarantees stability, while the bijective nature ensures equivalence to the original nonlinear system behavior.
Solution Approach 2:
The patent effectively changes the dimensional space by applying a coordinate transformation through the bijective mapping function. The system is controlled in this transformed dimensional space where linear control theory applies, and the results are mapped back to the original space, enabling stable control of nonlinear systems.
3Ease of manufacture
If conventional model learning is used without bijective mapping, then learning simplicity is maintained, but the control apparatus cannot determine a unique optimum input value
Solution Approach 1:
The patent applies parameter transformation through bijective mapping functions that convert the learned nonlinear model into an equivalent linear representation. This transformation is integrated into the learning process itself, allowing the system to learn in the transformed space where unique optimal solutions are guaranteed, thereby improving input determination precision without significantly complicating the learning procedure.
Data Source
AI summary
A model learning apparatus is configured to learn a model that shows a relationship between an input variable v input into a system and an output variable y output from the system. The model learning apparatus includes a storage that stores a model used to learn a nonlinear equation of state for predicting the output variable y by using the input variable v, and a processor programmed to learn the equation of state by using the model and an input-output data set including multiple sets of input variable data and output variable data with respect to the model. The model is an equation of state including a bijective mapping ψ that uses the input variable v as an input thereof and a bijective mapping ϕ that uses the output variable y as an input thereof.