Minimization of a degenerate linear-quadratic functional on the trajectories of a quasilinear system

This paper considers the problem of minimizing a degenerate quadratic functional on the trajectories of a quasilinear control system. A distinctive feature of the problem is that its solution exists in the space of generalized functions. An auxiliary problem is constructed for the original problem. Its solution exists in the space of absolutely continuous functions. Parameter expansion methods and L.S. Pontryagin’s maximum principle are applied to solve it. A finite number of iterations results in construct- ing a suboptimal control for the auxiliary problem. Using this control, a suboptimal control for the original problem is constructed. This control has impulse components concentrated at the initial and final moments. Be- tween these instants, the control is a continuous function. The constructed control is a program control. It can be used to construct a positional con- trol that, when subject to disturbances, will generate a impulse-sliding mode.