Title: Synthesizing Neural Network Controllers with Closed-Loop Dissipativity Guarantees

Abstract:

This study introduces a methodology for generating neural network controllers that maximize reward while strictly adhering to the hard constraint that the feedback loop comprising the plant and controller remains dissipative. This approach ensures the certification of critical performance metrics, including stability and $L_2$ gain bounds. The framework addresses nonlinear and uncertain plants, which are represented as an interconnection between a linear time-invariant (LTI) system and an uncertainty block that accounts for nonlinear behaviors. Both the plant’s uncertainty and the neural network’s activation functions are characterized through integral quadratic constraints (IQCs). The process begins by deriving a dissipativity condition for uncertain LTI systems. Subsequently, this condition facilitates the construction of a linear matrix inequality (LMI) designed for synthesizing neural network controllers. Finally, the proposed convex condition is integrated into a projection-based training algorithm to produce neural network controllers with guaranteed dissipativity properties. The efficacy of this method is validated through numerical case studies involving an inverted pendulum and a flexible rod mounted on a cart.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC