# Questions tagged [control-theory]

Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems with inputs. The desired trajectory of the output of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller should manipulate the inputs to the system to obtain the desired effect on the output of the system

1,411 questions
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### existence of solution of wave equation with a feedback term

If we have a system of coupled wave equations with a feedback acting on one equation,that is $u_{tt}-\Delta u+py-\alpha(t)d^{2}(x)u_{t} =0$ $y_{tt}-\Delta y+pu=0$ $u=y=0$ on boundary $\Gamma$ with d ...
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### How can I design a (PID) Controller if I don't have a reference signal?

I have been trying to control lateral and longitudinal movement of a robot for an autonomous lane keeper project. I have no problem with the lateral movement, however I couldn2t figure out exactly how ...
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### Model reduction of estimated state space models - System identification

Assume that we have a dynamical model in form of this simple transfer function $$G(s) = \frac{1}{2s^2 + 5s + 4}$$ G = tf(1, [2 5 4]) We do a step response with ...
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### How can I reduce noise from measurement without a Kalman Filter?

I'm going to create an adaptive Model Predictive Controller (MPC). The model is a state space model. Due to noise, it's very difficult to determine the model order. I'm using subspace identification ...
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### Transversality condition for infinite time horizon; Pontryagin Maximum principle

I want to solve a optimal control problem with the Pontryagin-Maximum-Principle, given following differential equation: $\dot x(t)=(a+b-c(t))x-c(t)\\ x(0)=x_0$ Regarding to the conditions: $x\geq0$ ...
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### Example of a toy ODE control problem for chemistry/chemical engineering application?

I work in control theory. I have a student who is interested in chemistry and chemical engineering problems. I thought it would be somewhat easy to find such a problem, but apparently coming up with ...
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### Explain the controllability distribution for a pendulum

As i was reading a book & i came across this statement- As the a pendulum passes through horizontally the controllability distribution doesn't have any constant rank- what does this mean ?? ...
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### Why does non constrained MPC gives double gained input values?

Assume that we have our discrete state space model: ...
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### Solution to Average of Several Trails of Dicrete Time LQR with Noise

The solution to discrete time finite horizon LQR problem is well studied. We have the linear system $$x_{k+1}=A x_{k}+B u_{k}+w_k$$ where $w_k$ is a random variable with mean $0$ and finite second ...
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### Linear quadratic regulator via least squares

In this set of slides, the finite horizon LQR problem is stated as a least-squares problem (slide 11), and using a naive method (e.g., QR factorization), the cost to solve this problem is $O(N^3nm^2)$ ...
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### 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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### How can I solve the discrete algebraic Riccati equations?

I have heard that Schur decomposition $$A = USU^{-1}$$ can be used to solve discrete algebraic Riccati equations $$X = A^T X A -(A^T X B)(R + B^T X B)^{-1}(B^T X A) + Q$$ and also continuous ...
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### Is LQR obsolete compared to non constrained MPC?

I have heard that LQR and MCP have common similarities. The difference is that MPC is using QP-programming and LQR using Riccati Equations. With QP-programming, constraints can be applied. If we ...
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### Eigenvalues of normalized vs unnormalized Laplacian of weighted digraph

Let $G$ be a weighted digraph. What is the connection between the eigenvalues of the normalized and unnormalized Laplacians of $G$. I think there is no explicit connection. We can at most find some ...
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### How to identify a system with no overshoot in terms of poles?

I'm trying to find a standard in order to identify a system with no overshoot in term of poles. I know that there is something related to dominant poles. I was looking into a particular 4th-order ...
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### Stablility of a linearized time-delay system

I have a linearized time-delay system as follows: $$\frac{\mathrm d X}{\mathrm d t} = a[X(t)-X^*] + b [X(t-R) - X^*],$$ where $a$, $b$ are constants, $R$ is the constant delay, and $X^*$ is the ...
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### Q learning for more than one goal state

I have recently implemented a reinforcement learning (TD method) problem consisting of 19 states and 2 actions (Increase/decrease relative to previous time step action) with one goal state. Now I want ...
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### is this function regular?

I am learning nonsmooth analysis for discontinuous dynamical systems. An important concept in this field is the regularity of functions. A function $f$ is regular at $x$ if its right directional ...
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### How to find the transfer function for advection equation?

The Problem: I have to find the transfer functions of the two equations in my system and of the whole system but I am not sure about something and as I haven't had mathematics lessons for my three ...
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### A simple quadratic optimizer for only constraints on input

I'm going to implement an quadratic optimizer with C for embedded systems. I will do that because I need speed. But I have some trouble to find a quadratic optimizer for C that works with embedded ...
In the figure you can see the statespace form of a feedback interconnection system. Very quick question: is there a reason they have taken $D_1=0$ and $D_2=0$? It makes workings a lot easier but I ...