Get Analysis and Control of Boolean Networks: A Semi-tensor PDF

By Daizhan Cheng, Hongsheng Qi, Zhiqiang Li

ISBN-10: 0857290967

ISBN-13: 9780857290960

ISBN-10: 0857290975

ISBN-13: 9780857290977

Research and keep an eye on of Boolean Networks provides a scientific new method of the research of Boolean regulate networks. the basic device during this method is a singular matrix product referred to as the semi-tensor product (STP). utilizing the STP, a logical functionality might be expressed as a traditional discrete-time linear process. within the mild of this linear expression, sure significant matters bearing on Boolean community topology – mounted issues, cycles, brief instances and basins of attractors – should be simply printed by way of a suite of formulae. This framework renders the state-space method of dynamic keep an eye on structures acceptable to Boolean keep an eye on networks. The bilinear-systemic illustration of a Boolean keep watch over community makes it attainable to enquire easy regulate difficulties together with controllability, observability, stabilization, disturbance decoupling and so on.

Show description

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

Best system theory books

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

Research and regulate of Boolean Networks provides a scientific new method of the research of Boolean keep an eye on networks. the elemental software during this procedure is a unique matrix product referred to as the semi-tensor product (STP). utilizing the STP, a logical functionality may be expressed as a standard discrete-time linear method.

Download e-book for iPad: Active Sensor Planning for Multiview Vision Tasks by Shengyong Chen, Y. F. Li, Jianwei Zhang, Wanliang Wang

This particular publication explores the real matters in learning for energetic visible notion. The book’s 11 chapters draw on contemporary vital paintings in robotic imaginative and prescient over ten years, rather within the use of recent recommendations. Implementation examples are supplied with theoretical tools for trying out in a true robotic procedure.

Get Chaos Theory in Politics PDF

The current paintings investigates worldwide politics and political implications of social technology and administration due to the newest complexity and chaos theories. in the past, deterministic chaos and nonlinear research haven't been a focus during this sector of analysis. This e-book treatments this deficiency by using those tools within the research of the subject material.

Extra info for Analysis and Control of Boolean Networks: A Semi-tensor Product Approach

Example text

18 Suppose we are given a matrix A ∈ Mm×n . 1. Let Z ∈ Rt be a column vector. Then AZ T = Z T W[m,t] AW[t,n] = Z T (It ⊗ A). 73) 2. Let Z ∈ Rt be a column vector. Then ZA = W[m,t] AW[t,n] Z = (It ⊗ A)Z. 74) 3. Let X ∈ Rm be a row vector. Then T XT A = Vr (A) X. 75) 4. Let Y ∈ Rn be a row vector. Then AY = Y T Vc (A). 76) 5. Let X ∈ Rm be a column vector and Y ∈ Rn a row vector. Then XY = Y W[m,n] X. 19 Let A ∈ Mm×n and B ∈ Ms×t . 18 Assume ⎡ a A = 11 a21 a12 , a22 where m = n = 2, s = 3 and t = 2.

Xm S m and take their sum. i Step 2: Multiply m i=1 xi S by Y (which is a standard inner product). It is easy to check that this algorithm produces the same result. Now, in the first step it seems that we have (S 1 · · · S n ) × X. This calculation motivates a new algorithm, which is defined as follows. 5 Let T be an np-dimensional row vector and X a p-dimensional column vector. Split T into p equal blocks, named T 1 , . . , T p , which are 1 × n matrices. Define a left semi-tensor product, denoted by , as p T X= T i xi ∈ R n .

17 1. Let X = (x11 , x12 , x13 , x21 , x22 , x23 ). That is, {xij } is arranged by the ordered multi-index Id(i, j ; 2, 3). A straightforward computation shows ⎡ 1 ⎢0 ⎢ ⎢0 Y = W[23] X = ⎢ ⎢0 ⎢ ⎣0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 1 0 0 ⎤ ⎡ ⎤ ⎤⎡ x11 0 x11 ⎥ ⎢ ⎥ ⎢ 0⎥ ⎥ ⎢ x12 ⎥ ⎢ x21 ⎥ ⎢ x13 ⎥ ⎢ x12 ⎥ 0⎥ ⎥=⎢ ⎥. ⎥⎢ ⎥ ⎢ ⎥ ⎢ 0⎥ ⎥ ⎢ x21 ⎥ ⎢ x22 ⎥ 0 ⎦ ⎣ x22 ⎦ ⎣ x13 ⎦ x23 x23 1 That is, Y is the rearrangement of the elements xij in the order of Id(j, i; 3, 2). 2. Let X = (x1 , x2 , . . , xm )T ∈ Rm , Y = (y1 , y2 , .

Download PDF sample

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


by Mark
4.5

Rated 4.44 of 5 – based on 19 votes