By Daizhan Cheng, Hongsheng Qi, Zhiqiang Li
Research and keep an eye on of Boolean Networks offers a scientific new method of the research of Boolean keep watch over networks. the basic instrument during this method is a unique matrix product referred to as the semi-tensor product (STP). utilizing the STP, a logical functionality could be expressed as a standard discrete-time linear process. within the mild of this linear expression, sure significant concerns referring to Boolean community topology – fastened issues, cycles, temporary occasions and basins of attractors – might be simply printed via a suite of formulae. This framework renders the state-space method of dynamic keep watch over platforms acceptable to Boolean keep watch over networks. The bilinear-systemic illustration of a Boolean regulate community makes it attainable to enquire uncomplicated keep an eye on difficulties together with controllability, observability, stabilization, disturbance decoupling and so forth.
Read or Download Analysis and Control of Boolean Networks: A Semi-tensor Product Approach PDF
Similar system theory books
Research and regulate of Boolean Networks offers a scientific new method of the research of Boolean keep watch over networks. the elemental instrument during this strategy is a singular matrix product referred to as the semi-tensor product (STP). utilizing the STP, a logical functionality could be expressed as a traditional discrete-time linear approach.
This publication includes the complaints of the Workshop on Networked Embedded Sensing and keep an eye on. This workshop goals at bringing jointly researchers engaged on assorted facets of networked embedded structures in an effort to alternate learn studies and to spot the most medical demanding situations during this fascinating new zone.
Conservation biology is based not just at the basic techniques, yet at the particular tools, of inhabitants ecology to either comprehend and expect the viability of infrequent and endangered species and to figure out how top to regulate those populations. the necessity to behavior quantitative analyses of viability and administration has spawned the sector of "population viability analysis," or PVA, which, in flip, has pushed a lot of the new improvement of beneficial and lifelike inhabitants research and modeling in ecology often.
This monograph provides a unique approach to sliding mode keep watch over for switch-regulated nonlinear platforms. The Delta Sigma modulation method permits one to enforce a continuing keep watch over scheme utilizing one or a number of, self reliant switches, therefore successfully merging the to be had linear and nonlinear controller layout strategies with sliding mode keep an eye on.
- Homology and Systematics: Coding Characters for Phylogenetic Analysis
- Continuous System Modeling
- Elementary symbolic dynamics and chaos in dissipative systems
- Global behavior of nonlinear difference equations of higher order with applications
- Intentional Risk Management through Complex Networks Analysis
Extra info for Analysis and Control of Boolean Networks: A Semi-tensor Product Approach
Tk ; n1 , . . , nt+1 , nt , . . , nk ). W[m,n] can be constructed in an alternative way which is convenient in some applications. Denoting by δni the ith column of the identity matrix In , we have the following. 7 W[m,n] = δn1 1 δm ··· δnn 1 δm ··· δn1 m δm ··· δnn m . δm For convenience, we provide two more forms of swap matrix: ⎡ T⎤ Im ⊗ δn1 ⎢ ⎥ .. W[m,n] = ⎣ ⎦ . 49) Im ⊗ δnn T and, similarly, 1 m , . . , In ⊗ δm . 50) The following factorization properties reflect the blockwise permutation property of the swap matrix.
31) 36 2 Semi-tensor Product of Matrices 2. Let X ∈ Rn , Y ∈ Rq be column vectors and A ∈ Mm×n , B ∈ Mp×q . Then, (AX) (BY ) = (A ⊗ B)(X Y ). 32) Particularly, (AX)k = (A ⊗ · · · ⊗ A)X k . 33) k 3. Let X ∈ Rm , Y ∈ Rp be row vectors and A, B be matrices (as in 2. above). Then (XA) (Y B) = (X Y )(B ⊗ A). 34) Hence, (XA)k = Xk (A ⊗ · · · ⊗ A). 35) k 4. Consider the set of real kth order homogeneous polynomials of x ∈ Rn and denote it by Bnk . Under conventional addition and real number multiplication, Bnk is a vector space.
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.