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, ...
4
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1answer
203 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
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0answers
54 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
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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
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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
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0answers
37 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
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0answers
20 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
111 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
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0answers
41 views

Does open loop stability guarantee an MPC stability?

In the following publication ...
1
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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
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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
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0answers
38 views

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{...
0
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1answer
21 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
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0answers
37 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
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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 ...