Estimates of Reachable Sets of Control Systems with Bilinear–Quadratic Nonlinearities

Abstract

The problem of estimating reachable sets of nonlinear impulsive control systems with quadratic nonlinearity and with uncertainty in initial states and in the matrix of system is studied. The problem is studied under uncertainty conditions with set – membership description of uncertain variables, which are taken to be unknown but bounded with given bounds. We study the case when the system nonlinearity is generated by the combination of two types of functions in related differential equations, one of which is bilinear and the other one is quadratic. The problem may be reformulated as the problem of describing the motion of set-valued states in the state space under nonlinear dynamics with state velocities having bilinear-quadratic kind. 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 nonlinear impulsive control problem bilinear-quadratic type.