A New Approximate Method for Construction of the Normal Control

Abstract

The problem of construction of the normal control (namely, the control with the least norm in L2 space) that generates a given trajectory of a control system is considered. A new method for constructing approximations of the normal control is suggested for a class of control systems with dynamics linear in controls and non-linear in state coordinates where the dimension of the control parameter is greater than or equal to the dimension of the state variables. This method relies on necessary optimality conditions in auxiliary variational problems. An illustrating example is exposed. The results of numerical simulation are compared with the results obtained with another approach. © 2018