12 December 2017 1 1K Report

In most of the literature for Generalized MPC, it is assumed that D matrix in state space model of the system is zero, I have a system with non-zero D (not a strictly proper system), what should I do?

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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...

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

we can approximate an infinite-dimensional system with a finite-dimension system, (for example by proper orthogonal decomposition) If we stabilize the approximate finite dimension of an...

09 October 2019 223 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

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