Necessary conditions for optimality of a singular surface in the form of synthesis for a nonlinear controlled system (Q1899724)

A unified approach for the definition of the singular surface and of the singular equations of motion is presented. It is applicable to optimal control as well as differential games problems. The main point consists in the statement of necessary conditions for optimality on the singular surface in the form of a collection of equality constraints. A singular Hamiltonian has been constructed from these constraints and its characteristic system of equations represents the singular motion. Two types of singular surfaces are investigated corresponding to the so- called universal and chattering regimes. For the time optimal control of affine nonlinear systems a generalized condition for singular control is given.