Questions tagged [model-predictive-control]

Model Predictive Control (MPC) is a process control method considering the system model and its predicted future optimization while respecting the defined constraints.

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Use probability theory to estimate the successors of an event out of a countable finite sample space?

Scenario: There exists to two façades in a system: façade zero, and façade one. When façade zero builds a LinearDataStructure, that object contains elements of ...
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72 views

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 ...
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51 views

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}} & \...
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Recommended python solver for an online optimization problem

I need to implement a load scheduling algorithm that involves solving an online optimisation problem from a research paper for my Real time systems course. This convex optimisation problem is setup ...
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43 views

How to keep track of variations in states based on controls in optimal control problem?

Suppose that $x(t)$ is the state variable showing the level of water in a tank at time $t$, and water is leaking the tank with rate $\lambda$. Control is denoted by $u(t)$ which is the amount of water ...
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Linear matrix inequality derivation from Risk-averse MPC problem

TLDR I need to use what looks like the Schur complement to transform a linear matrix inequality but instead of a $2\times 2$ block matrix there are more blocks. Question I'm having trouble with a ...
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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 ...
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what is offset-free MPC?

I am reading about MPC(model predictive control) and I see offset-free MPC but I don't know what is different between ordinary MPC and offset-free MPC. If you can introduce a book that explain offset-...
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59 views

Model Predictive Control gives always zero output solution - Why? Do I need soft constraints?

I have a discrete state space model: $$x(k+1) = Ax(k) + Bu(k)$$ $$y(k) = Cx(k)$$ And I'm trying to compute the predicted inputs. The first thing I do is that I fist create the extended observability ...
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158 views

Model Predictive Control: Linear MPC with constraints: Matrix sizes unclear.

I have to put Model Predictive Control constraints in a standard form. The way to achieve this form is shown below. I am struggling with the dimensions of the final matrices $\mathcal{M}$ and $\...
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63 views

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....
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Can linear programing be used in Model Predictive Control?

I'm trying to implement Model Predictive Control onto a small micro controller. I know that is not "possible", but I want to minimize the "unnecessary" tools that are avaiable inside "regular" Model ...
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37 views

Model prediction gives stochastic inputs - Predictive Control

I have a discrete state space model: $$x(k+1) = Ax(k) + Bu(k)$$ $$y(k) = Cx(k)$$ And I'm trying to compute the predicted inputs. The first thing I do is that I fist create the extended observability ...
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1answer
59 views

Model Predictive Control: Why the horizon size, $N$, must be equal or larger than 2?

If you read "Nonlinear Model Predictive Control" by L. Grune and J. Pannek (and anywhere else), everyone says that the prediction horizon size $N$ must be larger or equal to $2$,$ N\geq2$. Why?
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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 ...
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56 views

How can I handle the delays in Generalized/Model Predictive Control?

I trying to handle delays in a model who is poorly damped but I haveing som issues to estimate its parameters due to the delay. Assume that we got a state space model, which is poorly damped: $$x(k+...
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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 ...
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163 views

Model Predictive Control with reference tracking and terminal weight

In Model Predictive Control (MPC), When a reference is supposed to be tracked, we like an objective function in form of $$J=\sum_{i=1}^N ||\boldsymbol{r}(k+i)-\boldsymbol{y}(k+i)||^2_{\boldsymbol{Q}(...
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309 views

Does Model Predictive Control update the input trajectories for every iteration?

According to Model Predictive Control, it finds the best input trajectories (input signals) for the open loop control system, or MPC can also be closed loop too. My question is a open loop MPC ...
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156 views

Does Model Predictive Control required to store the past input values?

I have five questions about Model Predictive Control. LQR control has a control law which is static for all time. As I get it, MPC has a LQR control law, which changes over time, depending on a cost ...
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68 views

How to handle asymmetric input constraints in robust model predictive control for a system with polytopic uncertainty?

Consider a linear time variant system $x(k+1) = A(k)x(k)+B(k)u(k) \\ y(k) = Cx(k)$ where $[A(k), B(k)]\in\Omega $ $\Omega$ is a polytope $\Omega = \text{Co}([A_1, B_1 ] [A_2, B_2]... [A_L, B_L])$ ...
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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 ...