All Questions
Tagged with nonlinear-dynamics optimal-control
8
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Are there any known results on the uniqueness of solution of an optimal control problem? [closed]
In particular, I am looking for a result for the uniqueness of an optimal control problem in which the dynamical system is nonlinear ODE, with pure state constraint. The optimal control problem is to ...
- 77
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Pontryagin Maximum Principle with terminal and initial conditions
Consider a control problem with Lagragian $L(t,x,u)$ (where $u$ is the control, $x \in \mathbb{R}^d$ the state) and dynamics $\dot{x}=f(x,u,t)$. I have mostly seen problems in which the dynamical ...
- 81
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The product of the two positive definite matrices
I met a problem in Lyapunov stability proof:
$\dot{V}\leq -c\delta^T\bigg[\mathbb{T}\bigg((\mathbb{L}+G)\otimes(BR^{-1}B^T)\bigg)\bigg]\delta $
where $\mathbb{T}$ is a symmetric and positive definite ...
- 11
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Maximizing the vertical distance from a repulsive time-varying barrier
Continuing topic: https://mathematica.stackexchange.com/questions/246825/multidimensional-obstacle-avoidance-in-ode-part-ii
Given dynamical system:
$\boldsymbol{x}=f(\boldsymbol{x},u,t)$
where $\vec{\...
- 731
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60
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Multidimensional obstacle avoidance in ODE
Artificial potential barriers are known that allow robots to avoid obstacles. They are constructed as follows. https://authors.library.caltech.edu/106548/1/2010.09819.pdf
Can you please tell me how ...
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110
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Increasing convergence rate using Optimal Control and Pontryagin Maximum Principle
My question is in addition to Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function, but requires help from the mathematical side ...
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Nonlinear system with time-optimal control
Given nonlinear system:
\begin{cases} \dot{x_1}=x_3+u \\ \dot{x_2}=-x_2+\dot{f} \\ \dot{x_3}=-x_3+x_2 \cdot \alpha \sin(\omega t) \\ \dot{x_4}=-x_4+x_2 \cdot (\frac{16}{\alpha^2}(\sin(\omega t)-\frac{...
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Proving a nonlinear system of derivatives is not asymptotically stable to the origin
I'm trying to prove that a system on nonlinear differential equations is not asymptotically stable to the origin.
The overall problem is an inverted pendulum on a cart that can be controlled with an ...
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