Discrete-Time Extremum-Seeking Control for Non-Convex MISO Hammerstein Systems Using Stochastic Dithers

This paper presents a discrete-time extremum seeking control (ESC) scheme for multi-input single-output (MISO) Hammerstein systems with unknown linear dynamics and a multi-input multi-output (MIMO) cost function. The steady-state cost function may have multiple extrema and, combined with the linear dynamics, exhibits complex behaviour; it is assumed to be differentiable, non-convex, and accessible only via noisy, dynamically filtered sensor measurements. The proposed algorithm integrates stochastic dithers with a stochastic approximation approach incorporating expanding truncation (SAAWET), ensuring bounded iterates and closed-loop stability under unmodelled sensor dynamics. Convergence to the set of stationary points of the composite cost function is established from arbitrary initial conditions. The framework extends discrete-time ESC theory to non-convex, high-dimensional settings with measurement noise and dynamic sensing, providing a rigorous foundation for real-time optimisation of nonlinear dynamic systems.