The paper presents a method to synthesize neural network controllers for a class of uncertain linear time-invariant (LTI) plants such that the closed-loop system is dissipative. The class of plants considered consists of LTI systems interconnected with an uncertainty, which can represent unmodeled dynamics, nonlinearities, and other uncertainties.
The key steps are:
Derive a dissipativity condition for uncertain LTI systems where the uncertainty satisfies an integral quadratic constraint (IQC).
Use this dissipativity condition to construct a linear matrix inequality (LMI) that can be used to synthesize neural network controllers with dissipativity guarantees. The neural network controller is modeled as an uncertain LTI system where the uncertainty represents the nonlinearities of the neural network.
Present a projection-based reinforcement learning algorithm to train the neural network controller to maximize a reward function while satisfying the dissipativity LMI constraint.
The paper demonstrates the effectiveness of the proposed approach through simulation examples on an inverted pendulum and a flexible rod on a cart.
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by Neelay Junna... alle arxiv.org 04-12-2024
https://arxiv.org/pdf/2404.07373.pdfDomande più approfondite