Analysis and Control of Boolean Networks: A Semi-tensor by Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

  • admin
  • March 23, 2017
  • System Theory
  • Comments Off on Analysis and Control of Boolean Networks: A Semi-tensor by Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

By Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

Research and regulate of Boolean Networks provides a scientific new method of the research of Boolean regulate networks. the elemental software during this strategy is a singular matrix product known as the semi-tensor product (STP). utilizing the STP, a logical functionality will be expressed as a traditional discrete-time linear method. within the mild of this linear expression, yes significant concerns pertaining to Boolean community topology – fastened issues, cycles, temporary instances and basins of attractors – will be simply printed via a collection of formulae. This framework renders the state-space method of dynamic keep an eye on structures acceptable to Boolean regulate networks. The bilinear-systemic illustration of a Boolean keep an eye on community makes it attainable to enquire uncomplicated keep an eye on difficulties together with controllability, observability, stabilization, disturbance decoupling and so on.

Show description

Read Online or Download Analysis and Control of Boolean Networks: A Semi-tensor Product Approach PDF

Best system theory books

Adaptive networks: theory, models and applications

With adaptive, advanced networks, the evolution of the community topology and the dynamical techniques at the community are both very important and sometimes essentially entangled. fresh examine has proven that such networks can convey a plethora of latest phenomena that are eventually required to explain many real-world networks.

Modeling and Identification of Linear Parameter-Varying Systems

In the course of the earlier twenty years, the framework of Linear Parameter-Varying (LPV) platforms has develop into a promising approach theoretical method of h- dle the controlof mildly nonlinear and particularly place established platforms that are universal in mechatronic functions and within the strategy ind- try out. The start of the program type was once initiated by means of the necessity of engineers to accomplish greater functionality for nonlinear and time-varying dynamics, c- mon in lots of business functions, than what the classical framework of Linear Time-Invariant (LTI) regulate supplies.

Mutational Analysis: A Joint Framework for Cauchy Problems in and Beyond Vector Spaces

Usual differential equations play a imperative position in technological know-how and feature been prolonged to evolution equations in Banach areas. for plenty of purposes, notwithstanding, it really is tough to specify an appropriate normed vector area. Shapes and not using a priori regulations, for instance, shouldn't have an seen linear constitution.

Additional resources for Analysis and Control of Boolean Networks: A Semi-tensor Product Approach

Sample text

3 2 ⎡ X ⎤ (21) × (−1) + (−13) × 3 (21) × 2 + (−13) × 2 Y = ⎣ (01) × (−1) + (2 − 1) × 3 (01) × 2 + (2 − 1) × 2 ⎦ (2 − 1) × (−1) + (11) × 3 (2 − 1) × 2 + (11) × 2 ⎤ ⎡ −5 8 2 8 = ⎣ 6 −4 4 0 ⎦ . 2 1. The dimension of the semi-tensor product of two matrices can be determined by deleting the largest common factor of the dimensions of the two factor matrices. For instance, Ap×qr Br×s Cqst×l = (A B)p×qs Cqst×l = (A B C)pt×l . In the first product, r is deleted, and in the second product, qs is deleted.

Obviously, ψ is a tensor of covariant degree 4. Next, we consider a more general case. Let μ : V → R be a linear mapping on V , μ(ei ) = ci , i = 1, . . , n. Then, μ can be expressed as μ = c1 e1∗ + c2 e2∗ + · · · + cn en∗ , where ei∗ : V → R satisfies ei∗ (ej ) = δi,j = 1, 0, i = j, i = j. It can be seen easily that the set of linear mappings on V forms a vector space, called the dual space of V and denoted by V ∗ . Let X = x1 e1 + x2 e2 + · · · + xn en ∈ V and μ = μ1 e1∗ + μ2 e2∗ + · · · + μn en∗ ∈ V ∗ .

Hence the data arrangement is important for the semitensor product of data. 1), the elements of x are labeled by k indices. Moreover, suppose the elements of x are arranged in a row (or a column). It is said that the data are labeled by indices i1 , . . , ik according to an ordered multi-index, denoted by Id or, more precisely, Id(i1 , . . , ik ; n1 , . . , nk ), if the elements are labeled by i1 , . . , ik and arranged as follows: Let it , t = 1, . . , k, run from 1 to nt with the order that t = k first, then t = k − 1, and so on, until t = 1.

Download PDF sample

Rated 4.00 of 5 – based on 9 votes