All Questions
Tagged with oc.optimization-and-control stability
7 questions with no upvoted or accepted answers
3
votes
0
answers
107
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Stability of a nonlinear dynamical system with non-elementary dynamics
I am trying to prove stability and get a non-asymptotic upper bound on the convergence rate of a nonlinear discrete-time dynamical system, whose dynamics are stated in terms of the (non-elementary) ...
- 31
2
votes
0
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48
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Characterization of multifunctions with globally asymptotically stable minimal invariant sets
Let $(X, d)$ be a compact connected metric space. Consider a compact-valued upper semicontinuous multifunction $F: X \rightrightarrows X$. The reachable set $R[x]$ of $F$ from $x\in X$ is defined as:
...
- 111
2
votes
0
answers
61
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Strong stability of the wave equation with time depending potential
It is well known that the wave equation with frictional damping
$$\eqalign{
& {y_{tt}} = {y_{xx}} - a(t,x){y_t}{\text{ }}{\text{,(t}}{\text{,x)}} \in {\text{ }}(0,\infty ) \times (0,1) \cr
...
- 617
1
vote
0
answers
52
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On Designing Some Optimal Control Problems
In the context of a dynamical systems, some states may not be attainable with scalar controls from $L^1(0,T)$, but they may be reachable with feedback controls.
If we know that the system is null ...
- 55
1
vote
0
answers
69
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What is a suitable state feedback adaptive law in discrete time?
I am trying to find a discrete adaptive law and prove stability in an analogous way to a well-known case in continuous time. Let me give a rough explanation of the background.
In continuous time, let ...
- 11
1
vote
0
answers
79
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Showing a modified system of quadratic equations is stable
I have and $n$ dimensional dynamical system, given by
$\dot{x} = M D(x) P x - \frac{c}{2}x$
$P$ is a full rank $n \times n$ matrix, with $p_{ij} \in [0,c]$, such that $p_{ij}=c-p_{ji}$ for some ...
- 111
0
votes
0
answers
113
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Reference for matrix Lyapunov function / matrix dynamic system / stability
We usually consider $\dot{x} = f(x)$, where $x$ is a vector.
Now, I want to consider $$\dot{X}=f(X,U),$$ where $X$ is a square matrix $\mathbb{R}^{n\times n}$ state, $U$ is a square matrix variable $\...
- 101