Model Predictive Control (MPC) is a process control method considering the system model and its predicted future optimization while respecting the defined constraints.
Questions tagged [model-predictive-control]
37 questions
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votes
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Discrete time linear quadratic regulator - uniqueness of feedback gain given Riccati solution
Suppose we have a controllable discrete time linear system
\begin{align*}
x_{t+1} = Ax_t + Bu_{t}
\end{align*}
In order to design a stabilizing LQR controller with respect to supply rate $l(x,u)=x^{\top}Qx + u^{\top}Ru$ with positive definite $Q$…
3
votes
0 answers
Invariant set for the heat equation
I have problems proving that a set of temperature distributions is invariant. I've been looking a lot for material related to my problem, but I was unable to find the correct keywords or relate the relevant concepts to my problem.
In essence I'd…
Sven0000
- 81
3
votes
2 answers
Model Predictive Control
I have a few confusions about Model Predictive Control (MPC). Since they are all minor questions related to the same category, I ask them under one topic.
In an article, the cost function is defined as:
$$J(t)=\sum_{j=1}^{N_p}\delta(j) ( y(t+j|t)…
arcsin
- 85
2
votes
0 answers
Mixed integer model predictive control for exploration and exploitation planning
I have a dynamical system $\mathbf{x}_{k+1}=\mathbf{f}(\mathbf{x}_k,\mathbf{u}_k)$ tracking some pre-computed trajectory, $\mathbf{x}_t = (\mathbf{x}_{t,1},\cdots,\mathbf{x}_{t,K})$. Suppose we just have a simple kinematic model with states…
2
votes
1 answer
Control that stabilizes an uknown unstable equilibrium point?
Give a non-linear ( if it helps, multi-linear ) system for the variable with $\mathbf{Z} = [\mathbf X_1, \ldots, \mathbf{X_n} ]^T$:
$$ \dot{\mathbf{Z}} = F ( \mathbf{Z}, \mathbf{u} ) $$
and an unknown equilibrium point $\mathbf{Z^*}$ (i.e. 0 = F…
shnnnms
- 343
2
votes
1 answer
Model Predictive Control and Time
As I understand Model Predictive Control (MPC) in practice takes the form of a convex QP something like
$$\min_{u_1,...,u_T,x_1,...,x_T} \sum_{t=1}^{T}(x_t-r_t)^{T}Q_t(x_t-r_t) + u_t^{T}R_tu_t$$
$$s.t. \ Ax_t+Bu_t=x_{t+1} \ \forall t \in…
2
votes
1 answer
Difference between Model Predictive Control and Rolling Horizon Optimization
Lately I've been reading numerous papers regarding Energy Hub optimization, and often the authors talk about rolling horizon optimization for taking into account uncertainty.
For instance:
"A rolling horizon optimization framework for the…
2
votes
2 answers
What's the difference between Generalized Predictive Control and Model Predictive Control?
As I know, the Generalized Predictive Control(GPC) is older than Model Predictive Control(MPC).
But what is the real difference between them? I know that GPC contains some kind of system identification, which make GPC as an adaptive controller. But…
euraad
- 3,052
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- 79
1
vote
1 answer
What is the exact connection between PID and state feedback controllers?
Suppose we are dealing with a control problem where the reference trajectory is $0$, then the PID controller is a function,
$$u = K_1 x + K_2 \dot x + K_3 \int_0^t x dt$$
where $x$ is your state.
But this looks almost exactly like state feedback…
Your neighbor Todorovich
- 8,472
1
vote
0 answers
Region around previous trajectory which contains optimal solution
I am currently working on Model Predictive Control. I somehow want to bound the region in which the optimal solution of the optimization problem will lie in. I though that this could maybe be done based on the previous solution: Under some…
L208
- 11
1
vote
0 answers
Safe set term in control theroy
The general process in the discrete-time linear time-invariant (DLTI) direct feedthrough state-space model form is considered:
\begin{equation}
\begin{cases}
\boldsymbol{x}(k+1) = \boldsymbol{A} \boldsymbol{x}(k) + \boldsymbol{B}…
ConT
- 11
1
vote
1 answer
Algorithms/Solvers for Hard Constrained Non-Linear Optimization Problems - Model Predictive Control Example
I have an autonomous robotic swarm path planning/control problem where a set of "leader" robots have predefined (nontrivial) dynamics in the control set, and "follower" robots are subject to optimization in their control. $u_i = (u_{l_i}^T \ …
1
vote
0 answers
Model Predictive Control with Linear Programming VS Quadratic Programming
Model Predrictive Control is often used with Quadratic Programming. But I have tried Model Predictive Control with Linear Programming and it works very well.
Let's begin with the discrete SISO state space model:
$$x(k+1) = A_ax(k) + B_au(k)$$
$$y(k)…
euraad
- 3,052
- 4
- 35
- 79
1
vote
1 answer
Converting a nonlinear model predictive problem to parametric optimization problem
It is very well known that a linear model predictive control problem
\begin{align}
\label{eq:linear-original problem}
\begin{aligned}
&\text{minimize}_{(u_{t})_{t=0}^{N-1}} &&…
thenewguy
- 101
1
vote
1 answer
Fast optimization solvers for using in a website tool
We are developing a website tool that, given some parameters by the user, solves the following optimal control problem online:
$$\boxed{\begin{array}{cl}
\displaystyle \min_{u\in\mathcal{U}} & \displaystyle L(u) := \frac{1}{T} \int_0^T v^\top x(t;…
unobservable_node
- 511
- 3
- 14