Is it possible to stabilize an Infinite-dimensional system by stabilization of the corresponding approximated finite-dimensional system?

More Ali Namadchian's questions See All

Does Fokker-Planck equation give us the exact measure of the statistical ensemble of the trajectories of the stochastic differential equation?

It is known that the FPE gives the time evolution of the probability density function of the stochastic differential equation. I could not see any reference that relates the PDF obtain by the FPE...

09 October 2019 9,834 6 View

Is it necessary for engineers to know the definitions of mathematical spaces?

We know that mathematicians study different mathematical spaces such as Hilbert space, Banach space, Sobolev space, etc... but as engineers, is it necessary for us to understand the definition of...

09 October 2019 4,950 4 View

In stochastic systems(SDEs), Most of the time we assumed that the disturbance and noise vanish at the equilibrium point, is it reasonable assumption?

One of the main stability theories for stochastic systems is stochastic Lyapanuv stability theory, it is the same as Lyapanuv theory for deterministic systems. the main idea is that for the...

31 December 2018 4,292 4 View

Under which condition it is possible to change the dynamics of a nonlinear system to an arbitrary dynamic with feedback control input?

Imagine we have an ODE system x_dot=[f1(x,u), f2(x,u), f3(x,u),....fn(x,u)] where f1,..,fn are nonlinear functions of control input u and states x, x is member of R^n and u is member of...

31 December 2018 7,430 6 View

Is there a general framework to compute the reachability set of nonlinear affine-control systems?

for linear control systems x_dot=Ax+Bu the reachability set can be calculated using the Image of the controllability matrix, i.e R=([B AB A^2B,....,]) and reachability set=Im(R) when rank(R)=n,...

31 December 2018 1,854 3 View

Is it possible to prove the stability of a continuous time system from its corresponding discrete version?

In a simplest case imagine we have a continuous finite-dimensional dynamic system described by and ODE x_dot=f(x) (1) , Is it possible to prove the asymptotic stability of (1) by...

11 December 2018 5,264 30 View

Which one is a stronger stability condition? Lyapunov stochastic stability or detailed balance?

in most cases for continuous time stochastic systems which are modeled by SDE, the Lyapunov stability conditions can guarantee the stochastic stability of the system, another definition In...

11 December 2018 3,911 4 View

Is it possible to establish the stability results based on pseudo-spectra for a linear differential operator?

In the theory of the stability of the differential operators, one could prove the stability results based on spectra of an operator, (all eigenvalues must be negative for example). one problem...

10 November 2018 2,847 7 View

Which neural network structure is better for approximation of dynamical systems?

there are different kinds of neural networks. MLP, RBF, LSTM, recurrent, ... I have to approximate a dynamical system with neural network, which type of NN is more suitable for this task?

08 September 2018 2,186 5 View

What is the best method for generating a data-set for training in high dimensional function approximation with neural network?

Imagine we have an 7-D function f(P_i), i=1,...,7. Fortunately, we can create our own data sets for training, i.e we can choose as many samples from the sample space of each P_i (the sample space...

07 August 2018 6,717 5 View

What is the most Operating System (OS) which can be INSTALL on Tiny hard devices like Raspberry Pi (RPi) hardware ?

I'm targeting to deploy a mesh network and manually configure MANET routing protocols. I'm preparing scenarios, architectures, and hard devices needed to do that. Are there some step-by-step...

03 March 2021 1,931 5 View

Could you recommend any books about Number Theory?

Beginner level books. High level books. Analytical Number Theory. Algebraic Number Theory. Combinatorical Number Theory. Books about partitions. Books about primes.

03 March 2021 7,174 5 View

Can we classify HV and LV lines based on line length?

I have dataset which shows the length of power lines. I need to classify the lines based on the line length. Is there a rule to classify the High voltage (HV) and low voltage (LV) lines based on...

03 March 2021 4,116 4 View

Resistor definition in Piezoelectric bimorph with ANSYS workbench

Hello, good day! I am trying to simulate similar bimorph piezoelectric harvester with below commands. However, the output power doesn't change with resistor value. Please help to find the reason. ET,10,CIRCU94,0 !SET UP RESISTOR R,1,100000 !RESISTANCE VALUE TYPE,10 !SET ELEMENT TYPE E,1,2 !CREATE RESISTOR BETWEEN NODES 1 AND 2 Thanks in advance Regards,

02 March 2021 0 0 View

Is there a classification scheme for rock cavities or caverns with respect to their size and shape?

The range of forms and sizes of cavities in rock is very big. Is there a classification scheme for rock cavities regarding their size and shape?

02 March 2021 4,511 3 View

Arena simulation - how do i model the following model in ARENA (see description) (new to ARENA)?

Hello, I'm fairly new to ARENA and I have the following problem: I have two queues in which, in each queue, a different order type arrives (both having an arrival rate of exponential 10). Order...

02 March 2021 2,431 3 View

Why are the velocities so high in my Boussinesq approximation Fluent simulation?

Hello, I have a mechanism where air rises due to convective flows. In this simulation, nothing is driving the air except this. I understand that the Boussinesq approximation only works for small...

02 March 2021 4,910 3 View

Is there a powerful system for the security of the systems distributed on IoT systems?

02 March 2021 3,858 10 View

Which is suitable for use with Python? MySQL or SQL Server?

Which is suitable for use with Python? MySQL or SQL Server? What is your suggestion?

01 March 2021 3,422 3 View

Isolates of Hymenoscyphus fraxineus?

Dear Dr. Cai, my name is Simone Prospero and I work in the team of Phytopathology at the Swiss Federal Institute for Forest Snow and Landscape Research (WSL;...

01 March 2021 1,133 1 View

Konstantin Petrovich Lovetskiy

May be that artical Article Tikhonov regularization of optimal control problems governed...

could help to solve your problem...

Mohamed-Mourad Lafifi

Dear Ali,

Also i suggest you to see links and attached files may be you can found a solution for your problem .

https://core.ac.uk/download/pdf/82475668.pdf

http://archive.schools.cimpa.info/anciensite/NotesCours/PDF/2006/Zuazua.pdf

https://pdf.sciencedirectassets.com/272578/1-s2.0-S0022247X00X05483/

https://www.rug.nl/research/portal/files/3176978/thesis.pdf

Best regards

Kabir Sadeghi

As in the finite-dimensional case, a state-space based controller for the infinite dimensional H∞ disturbance-attenuation problem may be calculated by solving two Riccati equations. These operator Riccati equations can rarely be solved exactly. It can be approximated the original infinite-dimensional system by a sequence of finite-dimensional systems. The solutions to the corresponding finite-dimensional Riccati equations can be shown to converge to the solution of the infinite-dimensional Riccati equations. Furthermore, the corresponding finite-dimensional controllers yield performance arbitrarily close to that can be obtained with the infinite-dimensional controller.

I hope it is helpful to you.

All the best.

Ali Namadchian

Dear Kabir Sadeghi

Thank you very much

could you please introduce me a reference about what you have said in your answer

Dear Ali Namadchian

You are most welcome.

In my page of ReseachGate, or by googling my name you can find all of them easily. If you do not succeed let me know.

Thanks very much, Dr. Kabir Sadeghi