Analysis of a Nonlinear System Using Interval Arithmetic

Computation of an Output Admissible Set

抄録

Interval arithmetic is applied to analysis of a nonlinear system, in particular, to computation of an output admissible set, which plays an important role in constrained control. A discrete-time system whose dynamics is expressed in polynomials is considered first. When the initial state of such a system is known to belong to some multi-dimensional interval, interval arithmetic enables us to compute an interval that includes all possible states after some time steps. This fact together with polynomial optimization is used to compute an output admissible set. Numerical examples show efficacy of the proposed approach. Extensions are considered to non-polynomial systems and continuous-time systems.