Also, to find a second-best payoff vector when the core is empty, we propose a new solution concept called the weak ε-core+, which can utilize the approximate value of the optimal coalition structure.
To utilize the approximate Newton iteration, the weight-updating algorithm is given by w = w − ∇ J w ∇ ∇ J w p = w − E y ^ w H y ^ ∗ g w H y ^ 2 − μ 0 / 2 1 / δ 2 c 1 c 1 T w − κ c 1 − w E y ^ y ^ H E g w H y ^ 2 + w H y ^ 2 g ′ w H y ^ 2 − μ 0 / 2 1 / δ 2 c 1 c 1 T − I. (24).
For the integral of time multiplied by absolute error (ITAE) reference model tracking, a chain observer is designed to establish the virtual estimated states for the decoupled subsystems by utilizing the obtained approximated continuous-time models.
While many recovery algorithms aiming at solving (1) for x have been proposed in literature [18, 19], we utilize the versatile approximate message passing (AMP) framework that was introduced in [21 23].
In the proof of Theorem 6, we utilize the following approximate equation: (mathrm{PD}_{varepsilon})quad left { textstylebegin{array}l@{quad}l} -varDelta _{p} u+lambda_{1} |u|^{p-2}u-mu varDelta _{q}u+mulambda_{2}|u|^{q-2}u =f(x,u,nabla u)+varepsilonpsi&mbox{in } D, u>0&mbox{in } D, u(x)= 0 &mbox{on }partial D, end{array}displaystyle right.
Compared with traditional EKFs, the constant state filter shows good performance when the measurement sampling interval is large or a priori estimation of the state is unavailable, because the dynamic model and observation model are transformed into approximate linear forms by utilizing the constant state vector.
This model approximates effective particle density utilizing the hydrodynamic size-dependent parameter ε agg.
Thus, in the directed evolution of a cytochrome P450, Otey et al. utilized the SCHEMA algorithm to approximate the effect of recombination with different parent P450s on the protein structure.
The radial basis functions neural networks (RBFNN) are utilized to approximate the unknown functions of the systems, the adaptation laws and the controllers are designed based on the transformed systems.
