Lifted-Space Motion Control Under Constraints With Error Bounds
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Indirect data-driven control methods for constrained systems require large amounts of data for model-building, and existing direct methods struggle with constraint handling, leading to potential inaccuracies and safety issues.
Innovation Solution
A controller that transforms states and control inputs into a lifted space to determine a linear model of dynamics, accounts for modeling errors using a Koopman operator, and uses convex optimization to optimize motion under constraints, reducing data requirements and computational resources.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If indirect data-driven control methods are used to build accurate physics-based models, then model accuracy is improved, but data requirements increase significantly
Solution Approach 1:
The patent extracts only the essential control-relevant dynamics from the full physics-based model, rather than attempting to capture complete physical behavior. This selective extraction reduces data requirements while maintaining sufficient accuracy for control purposes.
Solution Approach 2:
The patent transforms the modeling approach by changing parameters from continuous physics-based descriptions to discrete, data-driven representations that capture essential dynamics with fewer data points. This includes using simplified state-space models with reduced order.
2Quantity of substance
If direct data-driven control methods are used to reduce data requirements, then data requirements are reduced, but constraint handling capability deteriorates
Solution Approach 1:
The patent segments the control problem into two parts: using direct data-driven methods for the controller structure while applying separate constraint handling mechanisms. This allows reduced data requirements while maintaining reliability through dedicated constraint satisfaction algorithms.
Solution Approach 2:
The patent introduces intermediary computational layers that bridge the data-driven controller and constraint satisfaction requirements. These intermediaries process the raw controller outputs and enforce constraints, allowing the use of simple data-driven methods while ensuring reliable constraint handling.
3Measurement precision
If full physics-based models (PDE/ODE) are used to capture system dynamics, then model accuracy is improved, but computational complexity increases
Solution Approach 1:
The patent transforms static, complex physics models into dynamic, adaptive representations that adjust their complexity based on operating conditions. This allows accurate dynamics capture when needed while reducing computational burden during normal operation through model order reduction and adaptive simplification.
Data Source
AI summary
To control a motion of a device subject to constraints, a sequence of states and corresponding control inputs are transformed into a lifted space to determine a linear model of the dynamics of the device in the lifted space by minimizing fitting errors between the lifted states and approximation of the lifted states according to the linear control law. The fitting errors define an error model as a function bounding a data-driven envelope of a Lipschitz continuity on the fitting errors allowing to solve an optimal control problem in the lifted space according to the linear model subject to the constraints reformulated based on an evolution of the error model. The control input in the lifted space is transformed back to the original space for control.