Questions tagged [optimal-control]
The optimal-control tag has no usage guidance.
20
questions with no upvoted or accepted answers
5
votes
0
answers
52
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
1
answer
236
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
$$\begin{gather}
\dot{r} = v \\
\dot{v} = F/m \\
r(t_0) = 0\text{ m}, $v(t_0) = 0\text{ m/s}, m = 1000\text{ kg}
\...
3
votes
0
answers
75
views
LQR Implementation in MATLAB
I am trying to implement a simple LQR controller in MATLAB for a purely deterministic system. The code is shown below:
...
3
votes
0
answers
66
views
How to solve LMIs with equality constraints using MATLAB?
I would like to find n by n matrices P and Q that minimize
J = norm(P) + w*norm(Q), where w is a given weight,
subject to
P>=0, Q>=0, and f(P,Q)=0, where f(P,Q)=0 is a given function of P and R.
I ...
2
votes
0
answers
67
views
LQR control effort / control bandwidth relationship
I'm working with a linear system, having given matrices A and B
$$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$
$$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$
...
2
votes
0
answers
37
views
avoidance with LQR
I'm interested in using linear quadratic regulators (LQR) to model prey avoidance behaviors. I want to adapt the LQR algorithm to incorporate dynamics and state costs that maximize the distance from a ...
2
votes
0
answers
167
views
LQR vs. Numerical Optimal Control
I'm a little confused by the differences between LQR control and numerical optimal control (such as direct multiple shooting, direct collocation and pseudospectral optimal control). It seems that LQR ...
1
vote
0
answers
31
views
Equations of motion in matrix form and energy consumption
I am working on Lagrangian derived high-dimensional motion equations for a robot in matrix form. The structure of such an equation is known:
$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+G(q)=0$
In here, $M(q)$, $...
1
vote
0
answers
43
views
Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x
I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system.
i.e.
$$
\dot{x}(t) = Ax(t)
$$
is stable ...
1
vote
0
answers
25
views
Increasing convergence rate using Optimal Control and Pontryagin Maximum Principle
My question is in addition to Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function, but requires help from the mathematical side ...
1
vote
0
answers
26
views
Optimal Control Singular Arcs
This is about linear time-invariant, stationary problems.
According to Donald Kirk's book Optimal Control Theory, for minimum-fuel problems on page 299, I was told that if there exists a singular arc,...
1
vote
0
answers
53
views
Does open loop stability guarantee an MPC stability?
In the following publication
...
1
vote
1
answer
96
views
Extended Kalman Filter formulation
For a nonlinear system,
$$
\begin{align}
&{\boldsymbol x}(k+1)={\boldsymbol f}({\boldsymbol x}(k),{\boldsymbol u}(k),{\boldsymbol w}(k)) \\
&{\boldsymbol y}(k)={\boldsymbol h}({\boldsymbol x}(...
0
votes
0
answers
27
views
Modelling an S-shaped Second Order Process Response
I am trying to model an S-shaped second order process response as a transfer function in Simulink, as shown in figure 3 in the linked article. Ideally the response should be overdamped. I have tried ...
0
votes
0
answers
33
views
Block-diagram combining two controlled subsystems
I have two subsystems which are shown in the picture below.
One of them is a system of stable and controlled differential equations of a mechanical system.
Second is a block that implements a function ...
0
votes
0
answers
24
views
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). ...
0
votes
0
answers
80
views
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 ...
0
votes
0
answers
52
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
votes
0
answers
39
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
0
answers
34
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 ...