Direct gradient descent control of general nonlinear systems

This paper is concerned with the direct gradient descent control (DGDC), which produces a dynamic state feedback control for stabilizing general nonlinear systems. DGDC manipulates control inputs directly so as to decrease the performance functions like squared errors, based on the gradient of the performance function and the steepest descent method. The stability of DGDC is proved by using the comparison function method. We also prove that if the linearized system of DGDC has a minimum phase property, then a proportional coefficient for the steepest descent method exists such that DGDC achieves asymptotic stability. Based on this results a design method of asymptotically stable DGDC is proposed.