# Questions tagged [dynamic-system]

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### Time-Invariant (non)autonomous Systems

Regarding potential distinctions between autonomous, non-autonomous, time-invariant and time-varying systems, I have found out opinions supporting that: autonomous systems are time-invariant and non-...
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### How to Improve the Kalman Filter for Tracking the Periodic Motion of a Car?

I have a quite typical Kalman filter to design. I really read a lot of articles about the design of this filter but the performances of my filter are still quite bad. Here is my situation. I have a ...
215 views

### How to Reduce Phase Lag Caused by Kalman Filter

Background I have been developing a system using a moving robot with a distance sensor against another robot. I want to control these robots by estimating relative velocity and acceleration derived ...
26 views

I have recently stumbled across a paper about learning arbitrary dynamical systems in a spiking neural network. The paper assumes an underlying dynamical system of the form $\dot{x}=f(x)+c(t)$ where $... 0answers 10 views ### Non-linear system identification with random lag errors I've been researching this topic for a little while and I haven't found anything particularly concrete. I'd very interested to know if there is an accepted solution for this problem, and whether there ... 1answer 85 views ### Time invariance and linearity of recursive system I am confused about the definition of linearity and time invariance of recursive system Given $$y[n] = y[n-1] - y[n-2] - x[n]$$ To test time invariance, we shift the input$x[n]$for shifting and ... 1answer 95 views ### Kalman Filter - Order of Update Step? I have seen some literature where the covariance is updated first, like$(P_k)^{-1} = (P_k^-)^{-1} + H^T R^{-1} H$, where$P^-$is the a priori estimate of the state covariance$P$. Then, the updated ... 3answers 178 views ### Discrete State Space Model - Why Are We Calculating$ x \left[ k + 1 \right] $Instead of$ \dot{\boldsymbol{x}} \left( t \right) \$?

A continuous state space model is defined as follows. $$\dot{\boldsymbol{x}}(t) = A \boldsymbol{x}(t)+ B \boldsymbol{u}(t) \\ \boldsymbol{y}(t)= C \boldsymbol{x}(t)+ D \boldsymbol{u}(t)$$ If we ...