Adaptive filtered feedback-driven Nash equilibrium seeking for structurally uncertain nonaffine multiagent systems

This paper addresses two challenging issues in distributed Nash equilibrium seeking for a class of nonaffine, high-order nonlinear systems. The first lies in the complexity explosion that arises in adaptive feedback control when dealing with intricate system nonlinearities. The second concerns the oscillations caused by uncertain high-order nonaffine dynamics with unknown control directions. To overcome these challenges, a modified finite-time nonlinear tracking differentiator with linear damping components is established, settling down the high sensitivity of traditional filters. A unified framework is developed to handle input nonlinearities, including backlash-like hysteresis and dead zones, by integrating neural network approximation mechanisms with advanced Nussbaum functions, enabling effective compensation for such nonlinear effects. Building on leader-following consensus protocols and gradient-based game theory, distributed adaptive filtered feedback Nash equilibrium seeking strategies are constructed, with both centralized and decentralized control gains designed accordingly. Finally, a simulation example under different input nonlinearity scenarios is presented to demonstrate the validity of the proposed strategy. © 2026 IEEE.