Parametric synthesis of a nonlinear control law based on the optimal damping principle

Abstract

The paper is devoted to the development of an algorithm for the control law synthesis of a moving object using the optimal damping approach, which was first proposed by V.I. Zubov in the early 1960s. The purpose of control is to move the control object from the initial position to a given final equilibrium position, that is, the boundary value control problem is solved. In the general case, the mathematical model of object is specified using nonlinear ordinary differential equations. For such systems there is no universal approach to the synthesis of the control law in the boundary value problem. The choice of control algorithm depends on many factors. In this work, to synthesize the control law, the optimal damping method is used, which allows to reduce the original optimal control problem to a parametric optimization problem. However, this approach allows us to obtain only an approximate solution to the problem. The paper considers the solution to the boundary value problem of optimal control of the sea vessel motion. A mathematical model of the vessel dynamics is formed in the form of a equation system that is used to solve the problem of dynamic positioning, which is a special case of a boundary value problem in control theory. A synthesis of optimal control is carried out to ensure the movement of a sea vessel from an initial position to a given final equilibrium position. Conditions are given under which the found control guarantees the asymptotic stability of the final equilibrium position.