Performance improvement of direct gradient descent control for general nonlinear systems

This paper is concerned with direct gradient descent control (DGDC) of general nonlinear systems. DGDC manipulates control inputs directly so as to decrease a performance function like the squared error, based on the gradients of the performance function and the steepest descent method. We propose several methods to improve performances of DGDC. Convergence speed and asymptotical stability of DGDC are improved by two approaches. The first one is to consider time derivative of the performance function. Namely, to improve the convergence, we modify the DGDC by decreasing both the performance function and its time derivative. The second one is to introduce a new artificial control vector and to consider the extended controller for DGDC such that two kinds of performance function are decreased. Our simulation results with the modified DGDC showed very good performances for various plants.