Gradient descent dynamics is an optimization techniques that is widely used in machine learning applications. This technique updates model parameter in the direction of descending of learning error. In this study, Lyapunov stability of continuous time gradient descent dynamics is investigated and robust stability condition, which is needed for implementation of gradient descent dynamics in intelligent control system applications, is evaluated. In a illustrative example, for a De Jong‘s function type error function, solutions of continuous gradient descent dynamics and Euler method based numerical solutions are compared and stability concerns is discussed.
Lyapunov methods , Optimization , Nonlinear dynamical systems , Stochastic processes , Adaptive cont
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  and . 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.
Gradient descent method, control, nonlinear systems, TRMS