β Scribed by A.M. Shmatkov
No coin nor oath required. For personal study only.
A problem which arises when estimating the attainability domains of linear dynamical systems by ellipsoids is investigated in a short time interval in the case when the initial position of the system in phase space is known precisely for some at least coordinates. A method is proposed which allows one to avoid problems associated with the degeneracy of the right-hand sides of the differential equations of the locally optimal ellipsoidal approximation. The mathematical meaning of these equations is made more precise in the case of the minimization of the phase volume. An example is given.
π SIMILAR VOLUMES
The modification of the algorithms of the calculus of variations and Pontryagin's maximum principle required for them to be applicable to non-linear descriptor control systems is demonstrated. The classical calculus of variations is still applicable in optimization without constraints on the control