# Questions tagged [optimal-control]

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### Is the viscosity solution of Hamilton-Jacobi equation of practical use in optimal control?

My understanding is, given an optimal control problem, one can show that the optimal cost satisfies a Hamilton-Jacobi PDE and use dynamic programming to figure out the optimal control. However, ...
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### LQR vs. Numerical Optimal Control

I'm a little confused by the differences between LQR control and numerical optimal control (such as direct multiple shooting, direct collocation and pseudospectral optimal control). It seems that LQR ...
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### MPC controller unable to control the height of the quadcopter

I am trying to develop a model predictive controller for my quadcopter. As the equations are non-linear in nature, I linearized the quadcopter at a hovering point. After linearizing, I discretized it ...
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### Optimizing error for PID based control of Line Following Robot

I am working to find the optimal PID gains of my line following robot. To do this, I need to optimize any performance index dependent on the error (a typical example is the integral absolute error). ...
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### Issue with LQR Q matrix for a cart-pendulum model

I am currently trying to develop a controller using LQR for a Segway. The model that I am using is an inverted pendulum on a massless cart. I have made animations of the uncontrolled pendulum and of ...
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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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### why do we need state feedback in H-infinity concept instead of output feedback

I have faced control of a flexible manipulator which have a zero dynamic related to flexible parts dynamic. the zero dynamic states (generalized states) are not observable in input-output dynamic and ...
I recently encountered the following optimal control problem. The purpose of the system is to find the parameter $x$ at which the maximum or minimum of the function $f$ a is reached. $x$ is unknown to ...