Discrete control of nonlinear system with uncertain information under disturbance conditions

The problem of stabilization around zero under disturbance and uncertain data in terms of differential pursuit game is considered. The dynamics are described by a nonlinear autonomous system of differential equations. The set of control values of the pursuer is finite, and that of the evader (interference) is compact. The goal of the control, that is, the goal of the pursuer, is to bring, within a finite time, the trajectory to any predetermined neighborhood of some ball centered at zero and a non-zero radius, regardless of the actions of the interference. The pursuer’s control is determined at discrete moments of time on the basis of the partition moment and the value from the state space, which is equal to the sum of state coordinates at the partition moment and the value of some auxiliary function. The value of the auxiliary function is restricted by the norm by a predetermined value, which is considered to be known to the pursuer. In this paper, we obtain conditions for the relationship between the parameters of the problem and the number that limits the norm of the auxiliary function, allowing for capture in the specified sense. The winning control is constructed constructively and uses a fixed step of dividing the time interval. In addition, an estimate of the capture time is obtained.