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We study the optimal control of multiple-input and multiple-output dynamicalsystems via the design of neural network-based controllers with stability andoutput tracking guarantees. While neural network-based nonlinear controllershave shown superior performance in various applications, their lack of provableguarantees has restricted their adoption in high-stake real-world applications.This paper bridges the gap between neural network-based controllers and theneed for stabilization guarantees. Using equilibrium-independent passivity, aproperty present in a wide range of physical systems, we propose neuralProportional-Integral (PI) controllers that have provable guarantees ofstability and zero steady-state output tracking error. The key structure is thestrict monotonicity on proportional and integral terms, which is parameterizedas gradients of strictly convex neural networks (SCNN). We construct SCNN withtunable softplus-$\beta$ activations, which yields universal approximationcapability and is also useful in incorporating communication constraints. Inaddition, the SCNNs serve as Lyapunov functions, giving us end-to-endperformance guarantees. Experiments on traffic and power networks demonstratethat the proposed approach improves both transient and steady-stateperformances, while unstructured neural networks lead to unstable behaviors.

Structured Neural-PI Control with End-to-End Stability and Output Tracking Guarantees