Model Predictive Control With Uncertainty Sets
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Solution Overview
Problem
Current model predictive control (MPC) methods face challenges in handling uncertainty in machine parameters, leading to potential constraint violations, reduced control performance, and high computational requirements, which result in suboptimal machine operation and slow response times.
Innovation Solution
The method updates the machine model and cost function iteratively, incorporating parameter uncertainty into the cost function to ensure constraint satisfaction and proportional error handling, using a prediction horizon-based approach to adjust parameters and maintain control inputs within defined ranges.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If adaptive or learning-based MPC is used to estimate unknown parameters, then control performance is improved, but constraints may be violated or control performance is excessively reduced to conservatively enforce constraints
Solution Approach 1:
The patent transforms the adaptive MPC problem into a robust MPC problem by changing the parameter representation from single-point estimates to uncertainty sets. The cost function is modified to include uncertainty parameters, and the optimization is performed over worst-case scenarios within uncertainty bounds, ensuring constraints are satisfied for all possible parameter values rather than just the estimated value.
Solution Approach 2:
The patent applies prior cushioning by incorporating uncertainty margins into the cost function and constraints before optimization. The cost function includes terms that penalize deviations considering parameter uncertainty, and constraints are formulated to hold for all parameters within uncertainty sets, providing a safety buffer against constraint violations.
2Reliability
If model parameters are updated to improve accuracy, then control performance improves, but computational complexity increases
Solution Approach 1:
The patent changes the parameter representation from continuous adaptive estimates to bounded uncertainty sets with finite vertices. This transformation allows the use of efficient convex optimization algorithms and quadratic programming techniques, reducing computational complexity while maintaining robustness to parameter variations.
Solution Approach 2:
The patent segments the continuous parameter space into discrete uncertainty sets with finite vertices. By optimizing against the worst-case vertices of these segmented sets rather than continuous parameter variations, the computational burden is significantly reduced while maintaining robust performance guarantees.
3Reliability
If constraints are strictly enforced during parameter estimation, then safety is improved, but response speed decreases
Solution Approach 1:
The patent changes the constraint formulation from time-varying adaptive constraints to static robust constraints based on uncertainty sets. The constraints are designed to hold for all parameters within the uncertainty sets, allowing faster computation without sacrificing safety, as the same constraint satisfaction guarantees are achieved through the robust formulation.
Data Source
AI summary
An operation of the machine is iteratively controlled with control inputs determined from an optimization of a cost function along a prediction horizon subject to constraints on the control inputs. The optimization is performed according to the model and the cost function includes at least one parameter of the model. During at least some iterations of the control, the parameter of the model is updated resulting in updating the cost function.