Adaptive Momentum Zonotopic Filter With Self-Evolving Noise Bounds for Linear Discrete Systems With Time Delay and Its Application

To address the problem of state estimation for a linear time-invariant discrete system with time delay, an adaptive momentum zonotopic filter with self-evolving noise bounds (AMZF-SENBs) is proposed based on the Frobenius radius. First, a parameterized zonotope is used to wrap the system state. Subsequently, a scalar cost function and its first-order gradient are introduced to measure the distance between the real and predicted measurements. Then, an adaptive momentum (Adm) gradient descent algorithm is studied to optimize the cost function. By adjusting the momentum terms, an effective optimization process is achieved by adjusting the number and step sizes of the iterations. Furthermore, with the aim of being more accurate in modeling measurement noise, a forgetting factor is added to the iterations. The current and estimated noise bounds are combined to form a new zonotope, which is then optimized using the Frobenius radius to be more conservative. Finally, the performance of the proposed AMZF-SENB algorithm is validated using an experimental buck-boost circuit platform. Experimental results demonstrate that, compared to the traditional P -radius method, the interval observer (IO), and the robust zonotopic Kalman filter (R-ZKF), AMZF-SENB achieves faster convergence, wider adaptability, and reduces the average interval width of the state feasible region, thereby enabling faster and more accurate state estimation while maintaining robustness.