Adaptive Gradient Descent Control of Stable, First Order, Time-delay Dynamic Systems According to Time-Varying FIR Filter Model Assumption

This study investigates robust control performance of adaptive gradient descent control in case of parametric perturbation of first order stable LTI systems. The proposed adaptive gradient descent control method is a variant of direct gradient descent control. The study aims to implement an adaptive control scheme for modeling-free control of stable, first-order, time delay plant models. The method implements two gradient descent optimizers. The first one performs only for synthesis of control signal, and the second optimizer works for a short-time model prediction based on instant input-output relation of a plant. We use a time-varying finite impulse response (TV-FIR) form to approximate short-term input-output relations of a first order stable plant dynamics and this work is an extended version of adaptive gradient descent control schemes that were presented in [6] and [7]. Adaptation and control laws are derived for this FIR model premise according to gradient descent method. The robust control performance of the proposed control method is investigated according to simulation results and compared with performance of optimal PI controller designs.