Lyapunov steepest descent control of constrained linear systems

A steepest descent algorithm for the optimal control of a cascaded hydropower system

“…If a suitable method of solution is unknown, steepest descent is guaranteed to iterate towards the minimum point but characterised by slow convergence. Numerous researches on this method have been on the determination of appropriate step size and means of speeding it up [26].…”

Trajectory following method on output tracking of non-linear non-minimum phase systems

“…Like controller which is designed based on input-output linearized technique, the stability of gradient descent control algorithm depends on the stability of internal dynamics of the system. In [2], it has been shown that for minimum phase systems, output tracking is achieved by gradient descent control algorithm. If performance index for minimum phase systems is generated only by error of output system from the desired output (external state), then for non-minimum phase system performance index is generated by the external state and the internal state.…”

Trajectory Following Method on Output Regulation of Affine Nonlinear Control Systems with Relative Degree not Well Defined

“…The steepest descent control corresponds to specifying a preferred direction of motion, opposite to the gradient of a specified scalar-valued "descent function". The steepest descent control is effective at yielding global asymptotic stability [6]. The related research is found in [7][8][9] which has proposed the direct gradient descent control.…”

“…Based on Grantham's idea [5][6] we study the output regulation of affine nonlinear systems (SISO) by using modified steepest descent control. First we define the descent function as a squared form.…”