We take the perfect polytropic gas state equation
p = ([gamma] - 1)[rho][epsilon], [gamma] = const > 1, and exclude the absolute temperature from consideration.
As shown via the example, our results agree with those developed for nonlinear systems, described in terms of the state equations
. However, our results are more general since not all nonlinear i/o equations are realizable in the state space form.
For fixed control u [member of] [L.sup.2]([OMEGA]), the state equation
(3) admits a unique solution y [member of] H.
At this point, according to (2), (3), (4), (5), (6), (7), (8), (9), and (10), the state equations
of the system are deduced as
Indeed, in this case the condensate has a state equation
which coincides with one of the cosmological constants and can contribute to the dark energy of the universe [41, 42].
Since the discrete large-signal state equations
in (A.15), (A.16), and (A.21) have a high nonlinearity, control design technique based on the linear control theory cannot directly be applied.
The periodic signal with phase different from the original signal is as a driving force in the state equations
of the system.
Equation (26) can be used to build state equations
shown in (28).
We observe from these simulations that although the feedback produces a multiplicative uncertainty in the state equation
and greatly enhances the nonlinearity in the update equation, we are able to recover the true values through the EKF formulation.
Normal Use Limit State Equation
. For the bridge with infrequent traffic, the role of environmental factors may be greaterthanthe effectofthe vehicleload.
JC method has many advantages: it can take the distribution of variables in limit state equations
[g.sub.1] and [g.sub.2] into account, and, what is more, the points obtained by linear method based on Taylor expansion locate in the failure hypersurface.
Since the difference between the actual water level at each spatial point and the target one could be defined as [[increment of y].sub.s] = [y.sub.s] - [bar.H], in which [y.sub.s] = [[[h.sub.1], ..., [h.sub.k], ..., [h.sub.m]].sup.T] [member of] [R.sup.m] and [bar.H] = [[[[bar.H].sub.1], ..., [[bar.H].sub.k], ..., [[bar.H].sub.m]].sup.T] [member of] [R.sup.m], the state equations
(4) could be rewritten as