Machine Control Policy Tuning for Robust LQR Under Uncertainty
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Solution Overview
Problem
Controllers for machines like robots and autonomous vehicles face challenges in handling uncertainty and perturbations from environments, such as changing lighting or sensor noise, which are not explicitly modeled during training, necessitating a robust control mechanism.
Innovation Solution
A method involving a computer-implemented control system that determines a policy using a cone program with parameters for a linear quadratic regulator, optimizing a cost function while considering constraints and perturbations, and using partial derivatives to adjust parameters for minimizing loss, incorporating elements that model perturbations and their variance.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If a linear quadratic regulator is used for controlling the machine, then the control optimality is improved, but the robustness against uncertainty and perturbations deteriorates
Solution Approach 1:
The patent transforms the LQR control parameters into a cone program formulation with adjustable parameters that can be optimized to satisfy both optimality and robustness requirements simultaneously, resolving the contradiction between control performance and uncertainty handling
Solution Approach 2:
The patent introduces dynamic adjustment of control parameters through the cone program solution, allowing the controller to adapt to varying uncertainty levels and perturbations while maintaining optimality, thus achieving both reliability and adaptability
2Reliability
If safety constraints are explicitly modeled during training, then the safety is improved, but the representability of uncertainty deteriorates
Solution Approach 1:
The patent introduces an intermediary cone program formulation that bridges safety constraints and uncertainty representation, allowing both to be satisfied simultaneously through the parameter optimization process rather than choosing one over the other
3Reliability
If the controller is made robust against perturbations, then the reliability is improved, but the device complexity increases
Solution Approach 1:
The patent replaces the traditional complex robust control structure with a cone program optimization framework that achieves robustness through mathematical optimization rather than complex system architecture, reducing controller complexity while maintaining reliability
Data Source
AI summary
A device and computer implemented method of controlling a machine. The method includes determining a state of the machine, determining a policy comprising parameters in particular a gain, for mapping the state of the machine to an input for the machine, mapping the state to the input according to the policy, an controlling the machine according to the input. A cone program is defined by a plurality of parameters of a linear quadratic regulator for the machine. A cost function is defined depending on the plurality of parameters and the policy. A constraint is defined for the parameters and for a solution of the cone program. The determining of the policy comprises determining the solution to the cone program so that the cost function meets a criterion subject to the constraint.