User talk:Mtxu

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Hello,

I'm Maria Calle,

I have a question about CVX and how to work with.

I'm a student from Spain. I'm studying engineering in automatic control. I'm in my last year and I'm making a project of investigacion. It's about LQR and how to synthesize the weighting matrix Q and R by pole assignment.

To make a program about it, I'm reading the article: Linear Quadratic Optimal Output Feedback Control For Systems With Poles In A Specified Region, Lisong Yuan, Luke E. K. Achenie, Weisun Jiang. [1]

To initializate the gain matrix they say that they apply the method described in the article:

Arzelier et al., Pole Assignment of Linear Uncertain Systems in a Sector Via a Lyapunov-Type Approach

they said that it's necessary to solve by convex programm. Until last week I didn't knew anything about convex program.

I have a system, A, B and C. It have to move poles to one region, for it, I make a transform to the original system. (A_alfa, B_alfa, C_alfa).

I have to know the gain matrix, with is:

$LaTeX: K=R*W^{(-1)}$

It's knew that:

$LaTeX: v(x)=x'*P*x=x'*W^{(-1)}*x$ .

$LaTeX: x'*(A'*P+P*A)*x-2*x'P*B*K*x<0$ .

$LaTeX: u(t)=-K*x(t)$ .

$LaTeX: Hij(W,R)=W*A_{/alfa i} '+A{/alfa i}*W-B_{/alfa i}*R-R'*B_{/alfa j} '<0$

and

$LaTeX: W=eye(2,2)*w, w \in{} R^{(2x2)}$

$LaTeX: R=eye(2,2)*w, w \in{} R^{(4x2)}$ .

The ecuation must: $LaTeX: min f(W,R)=min(p1)+min(p2)$

subject to:

$LaTeX: w_{nn} \leq{} p1$

$LaTeX: -p2 \leq{} r_{qn}\leq{} p2$

with

$LaTeX: n=1,....4, q=1...2.$

$LaTeX: W=w*eye(4)$

$LaTeX: R=r*eye(2,4)$

and:

$LaTeX: W \geq{} \epsilon1*eye(4)$

$LaTeX: Hij(W,R) \leq{} -\epsilon2*eye(4)$

Now the article says that aplaing the convex programm, it posible to solve the ecuation.

They present the next algoritm: 1) Initialization

$LaTeX: l=0, W1=W1=eye(4), R1=R2=zeros(2,4)$

2)Calculate

$LaTeX: \lambda(W)=\lambda min(W)$

$LaTeX: \lambda_{Hij}=\lambda max(Hij(Wi,Ri))$

3)if

$LaTeX: \lambda(W) \geq \epsilon1$

$LaTeX: lambda_H(ij) \leq -\epsilon2$

STOP

Else

$LaTeX: l=l+1$

calculate eigenvalues(v_w y v_Hij).

calculate the constraint linear: C1(W,R)

$LaTeX: v_w'*W1*v_w \geq \epsilon1$ if $LaTeX: (\epsilon1-\lambda_w)>(\lambda_Hij+\epsilon2)$

$LaTeX: v_Hij'*Hij*v_Hij \leq -\epsilon2$ if $LaTeX: (\epsilon1-\lambda_w)\leq (\lambda_Hij+\epsilon2)$

4)Solve

$LaTeX: min(p1+p2)$

under

$LaTeX: \epsilon1 \leq w_{nn} \leq p1$

$LaTeX: -p2 \leq r_{qn}\leq p2$

$LaTeX: C_k(W,R)$

$LaTeX: k=1,...z$

Now I have no idea of how to continue, or how to program the algoritm.

They said the method for solving it's mathematical convex program.

Thanks a lot for all, Greetings.

Retrieved from "http://www.convexoptimization.com/wikimization/index.php/User_talk:Mtxu"

@@ Line 1: / Line 1: @@
 Hello,
-I have a question in Control theory:
+I'm Maria Calle,
-I'm Maria Calle, I have an question abot CVX and how to work with. I hope here is the place for answer about.
+I have a question about [http://www.stanford.edu/~boyd/cvx CVX] and how to work with.
-I'm one student from Spain. I'm studing engienering in automatic control. I'm in my last year and I'm making a proyect of investigacion. It's about LQR and how to sintonice it by pole assignment.
+I'm a student from Spain. I'm studying engineering in automatic control.  I'm in my last year and I'm making a project of investigacion.
+It's about LQR and how to synthesize the weighting matrix Q and R by pole assignment.
+To make a program about it, I'm reading the article: Linear Quadratic Optimal Output Feedback Control For Systems With Poles In A Specified Region, Lisong Yuan, Luke E. K. Achenie, Weisun Jiang. [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.68]
+To initializate the gain matrix they say that they apply the method described in the article:
-I have some problems with the initialitation of the gain matrix. I'm reading one article for know how to make it. In the article they said that it's necessary to solve by convex programm. Until last week I didn't knew anything about convex program.
+[http://convexoptimization.com/TOOLS/Arzelier.pdf Arzelier ''et al''., Pole Assignment of Linear Uncertain Systems in a Sector Via a Lyapunov-Type Approach]
+they said that it's necessary to solve by convex programm.
+Until last week I didn't knew anything about convex program.
-So I'm begining whit CVX program and now I'm lost. Could you help me? I don't know how to continue.
+I have a system,  A, B and C. It have to move poles to one region, for it, I make a transform to the original system. (A_alfa, B_alfa, C_alfa).
-----
+I have to know the gain matrix, with is:
+<math>K=R*W^{(-1)}</math>
+It's knew  that:
+<math>v(x)=x'*P*x=x'*W^{(-1)}*x</math>.
+<math>x'*(A'*P+P*A)*x-2*x'P*B*K*x<0</math>.
+<math>u(t)=-K*x(t)</math>.
+<math>Hij(W,R)=W*A_{/alfa i} '+A{/alfa i}*W-B_{/alfa i}*R-R'*B_{/alfa j} '<0</math>
+and
+<math>W=eye(2,2)*w, w \in{} R^{(2x2)}</math>
+<math>R=eye(2,2)*w, w \in{} R^{(4x2)}</math>.
+The ecuation must: <math>min f(W,R)=min(p1)+min(p2)</math>
+subject to:
+<math>w_{nn} \leq{} p1</math>
+<math>-p2 \leq{} r_{qn}\leq{} p2</math>
+with
+<math>n=1,....4, q=1...2.</math>
+<math>W=w*eye(4)</math>
+<math>R=r*eye(2,4)</math>
+and:
+<math>W \geq{} \epsilon1*eye(4)</math>
+<math>Hij(W,R) \leq{} -\epsilon2*eye(4)</math>
+Now the article says that aplaing the convex programm, it posible to solve the ecuation.
+They present the next algoritm:
+) Initialization
+<math>l=0, W1=W1=eye(4), R1=R2=zeros(2,4)</math>
+)Calculate
+<math>\lambda(W)=\lambda min(W)</math>
+<math>\lambda_{Hij}=\lambda max(Hij(Wi,Ri))</math>
+)if
+<math>\lambda(W) \geq \epsilon1</math>
+<math>lambda_H(ij) \leq -\epsilon2</math>
+STOP
+Else
+<math>l=l+1</math>
+calculate eigenvalues(v_w y v_Hij).
+calculate the constraint linear: C1(W,R)
+<math>v_w'*W1*v_w \geq \epsilon1</math>       if    <math>(\epsilon1-\lambda_w)>(\lambda_Hij+\epsilon2)</math>
+<math>v_Hij'*Hij*v_Hij \leq -\epsilon2</math>    if   <math>(\epsilon1-\lambda_w)\leq  (\lambda_Hij+\epsilon2)</math>
+)Solve
+<math>min(p1+p2)</math>
+under
+<math>\epsilon1 \leq w_{nn} \leq p1</math>
+<math>-p2 \leq r_{qn}\leq p2</math>
+<math>C_k(W,R)</math>
+<math>k=1,...z</math>
+Now I have no idea of how to continue, or how to program the algoritm.
+They said the method for solving it's mathematical convex program.
+Thanks a lot for all, Greetings.

User talk:Mtxu

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