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UubUnunbium (element 112)
UubUniformly Ultimately Bounded
UubUrban Utility Boundary
UubUnion Upper Bound (probability of error)
UubUniversity of Ulster at Belfast (University of Ulster)
UubUniform Upper Bound
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References in periodicals archive ?
Then according to Lyapunov theorem, error [??], NN weight error [??], predictor error e, and filtered error r are all UUB. The control error [delta] is thus bounded based on (24) and Assumption 1.
then the closed-loop system is UUB and the [H.sub.[infinity]] control performance (18) is guaranteed as prescribed [[rho].sup.2].
Following the same procedure as that of Theorem 11, we get that the local tracking errors are cooperatively UUB.
For bounded initial conditions, if there exist a [C.sup.1] continuous and positive definite Lyapunov function V(x) satisfying a([parallel]x[parallel]) [less than or equal to] V(x) [less than or equal to] b([parallel]x[parallel]) such that [??](x) [less than or equal to] -[delta]V(x) + [pi], where a, b : [R.sup.n] [right arrow] R are class K functions and [delta], [pi] are positive constants, then the solution x(t) is uniformly ultimately bounded (UUB).
Considering the identification model (6), the identification error (8) will be uniformly ultimately bounded (UUB) if the weights updating laws are as follows:
where [??] is the estimation of a and is updated by (33a), then the system is ensured to be UUB stable.
The stability analysis demonstrates a Uniformly Ultimately Bounded (UUB) control method.
and [??] is updated by (29a), then the closed-loop system (11) is ensured to UUB stable.
If the state tracking errors (17), the desired states (15), the auxiliary dynamic system (25), the surge control law [[tau].sub.uc] (26), the yaw control law [[tau].sub.rc] (27), and the adaptive laws (28) are applied to the hovercraft system represented by (6) and, for any bounded initial condition, the closed-loop control system signals [s.sub.u], [s.sub.r], [[xi].sub.u], [[xi].sub.r], [e.sub.u], [e.sub.[beta]], [x.sub.e], [y.sub.e] and [[??].sub.iu] and [[??].sub.ir], i = 1,2, ..., n, are uniformly ultimately bounded (UUB).
Then, the estimate error x is uniformly ultimately bounded (UUB).