We study the optimal control of multiple-input and multiple-output dynamical
systems via the design of neural network-based controllers with stability and
output tracking guarantees. While neural network-based nonlinear controllers
have shown superior performance in various applications, their lack of provable
guarantees has restricted their adoption in high-stake real-world applications.
This paper bridges the gap between neural network-based controllers and the
need for stabilization guarantees. Using equilibrium-independent passivity, a
property present in a wide range of physical systems, we propose neural
Proportional-Integral (PI) controllers that have provable guarantees of
stability and zero steady-state output tracking error. The key structure is the
strict monotonicity on proportional and integral terms, which is parameterized
as gradients of strictly convex neural networks (SCNN). We construct SCNN with
tunable softplus-β activations, which yields universal approximation
capability and is also useful in incorporating communication constraints. In
addition, the SCNNs serve as Lyapunov functions, giving us end-to-end
performance guarantees. Experiments on traffic and power networks demonstrate
that the proposed approach improves both transient and steady-state
performances, while unstructured neural networks lead to unstable behaviors.Comment: arXiv admin note: text overlap with arXiv:2206.0026