Robust Capture Zone Approximation by Interval Integration with Uncertainty

Abstract

The problem of intercepting a maneuverable target (evader) by an interceptor (pursuer) is considered using a linearized kinematical model with first order acceleration dynamics of the interceptor and the target. The robust capture zone of a pursuer’s feedback strategy is the set of all initial positions, from which the capture (zero miss distance) is guaranteed by this strategy against any admissible evader’s control, while the time realizations of this strategy satisfy the prescribed control constraint. Subject to small angles assumption, an original (non-linear) system is linearized and scalarized by using the zero-effort miss distance as a new scalar state variable. For a scalarized system, approximate robust capture zones of linear and saturated linear strategies are constructed. The construction algorithm, based on the viability theory (capture basin algorithm), employs the interval arithmetic and is realized by contractor programming. Numerical examples are presented. Approximate robust capture zones are compared with exact ones, constructed by using a robust controllability approach.