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Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees
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abstract
This paper presents a method to synthesize neural network controllers to maximize reward subject to the hard constraint that the feedback system of plant and controller be dissipative, certifying requirements such as stability and $L_2$ gain bounds. It considers nonlinear and uncertain plants, modeled as the interconnection of a linear time-invariant (LTI) system and an uncertainty block, which incorporates nonlinearities. The uncertainty of the plant and the activation functions of the neural network are both described using integral quadratic constraints (IQCs). First, a dissipativity condition is derived for uncertain LTI systems. Second, this condition is used to construct a linear matrix inequality (LMI) which can be used to synthesize neural network controllers. Finally, this convex condition is used in a projection-based training method to synthesize neural network controllers with dissipativity guarantees. Numerical examples on an inverted pendulum and a flexible rod on a cart are provided to demonstrate the effectiveness of this approach.
Forward citations
Cited by 4 Pith papers
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Implicit Neural Networks as Static Controllers: Certificates and Performance Separation
Implicit neural static controllers admit LMI/IQC certificates on LTI plants, and a saturated ReLU law strictly beats all admissible finite-order dynamic linear controllers on a scalar constrained plant.
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Polynomial Constraints for Robustness Analysis of Nonlinear Systems
Polynomial constraints abstract non-polynomial or uncertain system components so sum-of-squares programming can compute region-of-attraction estimates, with explicit links to integral quadratic constraints.
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Controller Design for Bilinear Neural Feedback Loops
The paper gives LMI-based controller synthesis guaranteeing local exponential stability for bilinear systems with neural networks in the loop.
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Learning Neural Controllers with Optimality and Stability Guarantees Using Input-Output Dissipativity
Neural controllers trained to satisfy a learned dissipativity inequality are shown to stabilize the closed loop and to solve a constructed infinite-horizon optimal control problem.
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