Computing capture tubes

Abstract

International audienceA dynamic system can often be described by a state equation ˙x = h(x, u, t)where x ∈ Rn is the state vector, u ∈ Rm is the control vector and h :Rn × Rp × R → Rn is the evolution function. Assume that the control lowu = g (x, t) is known (this can be obtained using control theory), the systembecomes autonomous. If we define f (x, t) = h(x, g (x, t) , t), we get the followingequation.˙x = f (x, t) .The validation of some stability properties of this system is an important anddifficult problem [2] which can be transformed into proving the inconsistency of aconstraint satisfaction problem. For some particular properties and for invariantsystem (i.e., f does not depend on t), it has been shown [1] that the V-stabilityapproach combined interval analysis [3] can solve the problem efficiently. Here,we extend this work to systems where f depends on time