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Ellipsoidal Estimates Of Reachable Sets of Impulsive Control Systems with Bilinear Uncertainty

Oxana Matviychuk
The paper deals with the state estimation problem for impulsive control systems under bilinear uncertainty. It is assumed that we know the bounding set for initial system states and any additional statistical information is not available. Also the matrix included in the differential equations of the system dynamics is uncertain and only bounds on admissible values of this matrix coefficients are known. Under such conditions the dynamical system is nonlinear and reachable set
loses convexity property. We use Minkowski function to describe the trajectory tubes and their set-valued estimates. Basing on the techniques of approximation of the generalized trajectory tubes by the solutions of control systems without measure terms and using the techniques of ellipsoidal calculus we present here a state estimation algorithms for the studied impulsive control problem bilinear type. The motivations to consider set-membership approach in state estimation problems for dynamical systems with uncertainty may be found in
many applied areas including engineering problems in physics and cybernetics.
CYBERNETICS AND PHYSICS, Vol. 5, No. 3. 2016, 96–104.
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