Control Contraction Metric Tuning for Robust Nonlinear Control
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Solution Overview
Problem
Current adaptive control systems, particularly in aerospace applications, face challenges in efficiently synthesizing controllers that balance robustness and performance while handling nonlinear dynamics and uncertainties.
Innovation Solution
The proposed method employs a 'double loop' optimisation procedure using Control Contraction Metrics (CCMs) within a Linear Matrix Inequality (LMI) framework to determine optimised parameters for system control, addressing the trade-off between robustness and performance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a single optimisation procedure is used for controller synthesis, then the computational complexity is reduced, but the ability to balance robustness and performance deteriorates
Solution Approach 1:
The controller synthesis optimisation is divided into two separate procedures: a first optimisation procedure that prioritises robustness (using a first CCM with smaller weight on performance), and a second optimisation procedure that prioritises performance (using a second CCM with larger weight on performance). This segmentation allows each procedure to focus on one aspect without compromising the other, resolving the contradiction between computational simplicity and balanced performance-robustness optimization.
2Productivity
If aggressive optimisation is performed to improve performance, then system performance is enhanced, but system stability deteriorates
Solution Approach 1:
The first optimisation procedure is performed beforehand to establish robust controller parameters that ensure system stability. This preliminary action creates a stable foundation upon which the second optimisation procedure can then enhance performance without compromising stability. The sequential execution ensures that performance enhancement does not come at the cost of system stability.
3Adaptability or versatility
If multiple parameters are optimised simultaneously, then the control solution is more comprehensive, but the computational cost increases
Solution Approach 1:
The simultaneous optimisation of multiple parameters (robustness parameters and performance parameters) is segmented into two sequential optimisation procedures. The first procedure optimises robustness parameters, and the second procedure optimises performance parameters. This segmentation reduces the computational burden of each individual optimisation while maintaining the comprehensiveness of the overall control solution.
Data Source
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AI summary
There is herein disclosed a method for controlling a system. The method comprises obtaining a set of parameters for the system. The set of parameters comprise at least a first parameter, a second parameter and a third parameter and the set of parameters relate to features of the system suitable for controlling. The method further comprises performing a first optimisation procedure using the first parameter and second parameter to determine an optimised first parameter and optimised second parameter. The first optimisation procedure comprises defining a first control contraction metric (CCM) for the system. The method further comprises performing a second optimisation procedure using the first parameter, second parameter and third parameter, to determine an optimised third parameter. The second optimisation procedure comprises defining a second CCM metric for the system. The method further comprises combining the optimised first parameter, optimised second parameter and optimised third parameter to produce a final solution for controlling the system.