A Gröbner basis for an ideal
To further improve the accuracy, a Chebyshev fuzzy interval method (CFIM) is proposed, in which the Chebyshev polynomials is used to approximate the response functions.
3.2, in which the autoregressive polynomial of the signal contains a unit root.
Probabilistic analysis of underground rock excavations is performed using response surface method and SORM, in which the quadratic polynomial with cross terms is used to approximate the implicit limit state surface at the design point.
In addition, the modified sequential optimization method, in which the nonintrusive polynomial chaos expansion (PCE) method and the most probable point (MPP) searching method are employed, is proposed to solve the reliability-based optimization problem efficiently.
To construct the function ℛ, we consider the characteristic polynomial of A(K) (3) in which the coefficients of the polynomial are functions of the parameter vector K.
with constraints sum^{N}_{j=1}gamma_{j}p_{i}(x_{j})=0,quad i=1,2,ldots,M, (7). in which p i ∈Π m−1, i=1,2,…,M, where Π m represents the polynomial space in which the total degree of all polynomials is then m in N variables [36] left(begin{array}{c} N+m-1 m-1 end{array}right).
However, instead of integrating the equations for the polynomial chaos coefficients directly, they used projective integration [39] to do so, in an 'equation-free' approach [40] in which the equations satisfied by the polynomial chaos coefficients are never actually derived.
Under suitable conditions, we prove that the energy functional decays to zero as the time tends to infinity by the method of perturbation energy, in which the usual exponential and polynomial decay results are only special cases.
In the developed adaptive AQM (ACDM), the output feedback pole placement is implemented in an indirect model reference adaptive control (MRAC) scheme, in which the closed loop characteristic polynomial is determined by CDM and the system parameters are estimated using a modified recursive gradient method.
