On the optimal impulse control in descriptor systems

We study the optimal impulse control problem with the quadratic performance functional for a descriptor system. The system evolution is described by a linear differential-algebraic equation unsolved with respect to the derivative of the state. The system is controlled by changing the measurable control and the pure impulse control. The pure impulse control is characterized by impulse intensities and moments of impulse applications. The main restriction is that the characteristic matrix pencil corresponding to the state equation is regular. In terms of characteristic matrix pencil we establish the conditions for the existence and uniqueness of the optimal control and the corresponding optimal state. The optimal control and the optimal state are constructed by using the adjoint state which is a solution of the adjoint two-point boundary value problem. The results are illustrated by the example of descriptor system that describes transient states in a radio technical filter. For this system we consider the energetic performance functional with impulse intensities characterizing the energy of inertial elements and input voltage of the filter and also intensities and moments of impulse applications. Transient states under impulsive perturbations of currents and voltages are described by using the formula of constants variation for the impulsive descriptor system. © 2019 by Begell House Inc.