Questions tagged [optimal-control]
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15
questions with no upvoted or accepted answers
5
votes
0answers
48 views
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, ...
4
votes
1answer
198 views
what's wrong with this robust control scheme?
I'm learning how to control a double integrator with $H_\infty$.
my model is simply
$$\begin{gather}
\dot{r} = v \\
\dot{v} = F/m \\
r(t_0) = 0\text{ m}, $v(t_0) = 0\text{ m/s}, m = 1000\text{ kg}
\...
3
votes
0answers
53 views
LQR Implementation in MATLAB
I am trying to implement a simple LQR controller in MATLAB for a purely deterministic system. The code is shown below:
...
3
votes
0answers
62 views
How to solve LMIs with equality constraints using MATLAB?
I would like to find n by n matrices P and Q that minimize
J = norm(P) + w*norm(Q), where w is a given weight,
subject to
P>=0, Q>=0, and f(P,Q)=0, where f(P,Q)=0 is a given function of P and R.
I ...
2
votes
0answers
37 views
avoidance with LQR
I'm interested in using linear quadratic regulators (LQR) to model prey avoidance behaviors. I want to adapt the LQR algorithm to incorporate dynamics and state costs that maximize the distance from a ...
1
vote
0answers
33 views
LQR control effort / control bandwidth relationship
I'm working with a linear system, having given matrices A and B
$$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$
$$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$
...
1
vote
0answers
18 views
Optimal Control Singular Arcs
This is about linear time-invariant, stationary problems.
According to Donald Kirk's book Optimal Control Theory, for minimum-fuel problems on page 299, I was told that if there exists a singular arc,...
1
vote
1answer
106 views
simulation of an attitude optimal Backstepping controller based quaternion for a UAV in MATLAB
I'am trying to implement this open access research article Attitude Optimal Backstepping Controller Based Quaternion for a UAV
I did not find the same result in this paper Can anyone tell me where my ...
1
vote
0answers
41 views
1
vote
1answer
71 views
Extended Kalman Filter formulation
For a nonlinear system,
$$
\begin{align}
&{\boldsymbol x}(k+1)={\boldsymbol f}({\boldsymbol x}(k),{\boldsymbol u}(k),{\boldsymbol w}(k)) \\
&{\boldsymbol y}(k)={\boldsymbol h}({\boldsymbol x}(...
1
vote
0answers
157 views
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 ...
0
votes
0answers
2 views
Zero overshoot criterion from the initial point $x_0$ to the final $x_*$, $x_*$ unknown in advance
Let's say there is an ODE:
$\dot{x}=f(t,x)+u$
Condition: variable $x$ passes from initial state $x_0$ to final state $x_*$, that do not know in advance.
Is it possible to make a transient in such a ...
0
votes
1answer
18 views
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 ...
0
votes
0answers
36 views
Optimal control of the gradient type PDE
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 ...
0
votes
0answers
29 views
Low accuracy current feedback measurement in motor control
Given a very low accuracy current sensor in a 3 phase inverter (in my case used for motor control) what is the best way to tackle the issue and keep reasonable performance and robustness at the same ...
