Seminar talk, 14 October 2015

From Geometry of Differential Equations
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Speaker: Vladimir Chetverikov

Title: Terminal control via covering method

The point-to-point steering problem is to take the system from a given initial state to a given final state. The suggested method is based on the addition of the initial underdetermined system to a determined system E. Additional equations must be chosen so that all points of a covering from E to a system Y satisfy the final conditions, while the set of points that satisfy the initial condition is transversal to the fibers of this covering. Then solution of the terminal control problem is the solution of two related Cauchy problems for systems E and Y.

This approach generalizes the known method for solving the terminal control problem for flat systems. But unlike the known method, the suggested approach allows to search solutions in a much wide class of functions, thus take into account the constraints on the system.

Furthermore, the talk will discuss other problems from control theory that can be solved by methods of infinite dimensional geometry.

Chetverikov V.N. The covering method for the solution of terminal control problem, Science and education, BMSTU, 2 (2014), 125-143 (in Russian), local copy