What is State space: Definition and 85 Discussions
A state space is the set of all possible configurations of a system. It is a useful abstraction for reasoning about the behavior of a given system and is widely used in the fields of artificial intelligence and game theory.
For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. A "counter" system, where states are the natural numbers starting at 1 and are incremented over time has an infinite discrete state space. The angular position of an undamped pendulum is a continuous (and therefore infinite) state space.
I'm looking to check my understanding of the information below and ultimately get a better understanding of it.
Is spectral decomposition a mathematical procedure?
Does "the state space of the measured system" refer to the possible values that the system could take, when measured?
Definition of linear operator in quantum mechanics
"A linear operator ##A## associates with every ket ##|\psi\rangle \in
\mathcal{E}## another ket ##\left|\psi^{'}\right\rangle \in\mathcal{E}##, the correspondence being linear"
We also have vector operators ##\hat{A}## (such as a position...
In the paper
C. S. Lent and P. D. Tougaw, "A device architecture for computing with quantum dots," in Proceedings of the IEEE, vol. 85, no. 4, pp. 541-557, April 1997, doi: 10.1109/5.573
about quantum dots, it is stated that the basis vectors in the space of quantum states for a single cell...
Summary:: This is similar to the examples of electrical circuit state space analysis, I have been trying to find the state space equations from the following non linear first order differentials but I keep getting stuck. Any help?
A) Started off from non linear equations:
$$y' =...
How to represent this system in state space form?
where:
$$ x' = Ax + Bu \text{ and
}y = Cx + Du$$
I am trying to create a state space model based on these equations on simulink, need to find A, B, C and D but like I mentioned, i cannot find the solution when the differentials are not of...
https://en.wikipedia.org/wiki/Observability
I am studying observability and I try to get some intuition on the topic.
Given the observable matrix, we can find the null space. However, the vectors of the null space are states but this differs from the definition of what a state vector of a...
To elaborate that summary a bit, suppose ##\mathcal H## is the Hilbert space of the particle, with ##\mathcal{H}_2\subseteq\mathcal{H}## its two-dimensional spin subspace. Now consider any ##|x\rangle\in\mathcal{H}## such that ##|x\rangle\perp\mathcal{H}_2##, i.e., ##\forall ~...
Hi,
I don't know if it is the right place to ask for the following: I was thinking about the difference between the notion of spacetime as 4D Lorentzian manifold and the thermodynamic state space.
To me the spacetime as manifold makes sense from an 'intrinsic' point of view (let me say all the...
Hi,
I have a question about a homework problem: I am not sure why I do not seem to get the same answers when using different methods.
Question: Given transfer functions G(s) = \frac{s - 1}{s + 4} and C(s) = \frac{1}{s - 1} , find the state space models for those systems. Then find the...
I'm reading a book about analytical mechanics and in particular, in a chapter on hamiltonian Mechanics it says:
"In the state space (...) the complete solutionbof the canonical equations is pictured as an infinite manifold of curves which fill (2n+1)-dimensional space. These curves never cross...
I mean the first question has derivative form and the second is linear form so what the difference here in steps of converting both to transfer function... please need some ellaboration to make sure i am solving correctly or not... is it correct to apply the same rule on both:
Transfer function=...
My questions are now... Do the steps of converting this space to transfer function include any laplace ? or just we do get [SI-A]-1 and then transfer function is = C* [SI-A]-1 * B As [1 0] * [s-1/det -0.5/det ; 0.5/det s-0.5/det] * [0; 1] = -0.5/s^2+s+0.5 I mean do we need any laplace after that...
Hi good day. I am trying to find the general Inverted Pendulum on a cart nonlinear state space equations with two degrees of freedom with x, x_dot, theta, theta_dot which represents displacement, velocity, pendulum angle from vertical, angular velocity. However from research, I am seeing...
Homework Statement
For the given circuits, identify state variables and derive a state-space model for each.
Assume the input is v(t) and the output is vL(t).
Homework Equations
The Attempt at a Solution
[/B]
So my issue is that I solved this problem using two different methods. First...
Homework Statement
I am trying to learn how to create state space representations. I am using this link to study.
http://www2.ensc.sfu.ca/people/faculty/saif/ctm/examples/pend/invpen.html
Could someone explain how to get the matrix A from my equations?
Homework Equations
The Attempt at a...
I have a system with three inductors connected together at a common point.
The unconnected ends of each inductor is connected to an independent voltage source.
Basically I want to get three expressions for the dynamics of the currents with V1, V2 and V3 as inputs.
i.e. i need to eliminate the...
Homework Statement
I have derived the differential equations of a system. They are like the following:
a\ddot{\theta} - b\ddot{x} + c \theta = 0 \\
d\ddot{\theta} + e\ddot{x} = F(t)
where a,b,c,d,e are constants.
I'm having trouble putting it into state space form, since I have the highest...
Good afternoon people. I wanted to implement a physical system using control just to put into practice what I have learned in school. To be more specific: I would like to implement an inverted pendulum like the one on the photo
In this system a control input (a force u) drives the cart (mass...
There used to be a term called 'logical space' where objects have their properties (or facts) defined by their relation to other objects in said 'logical space' along with their potential modalities included in this sort of 'space'.
Here is the definition provided here:
I've heard the modern...
Hello everyone.
Iam just Learning about State space representation and controller design and have a fundamental question about the difference between classical Control theory and modern Control theory.
I understood the state space is of advantage when dealing with MIMO systems or non-linear...
Hi All
This is in relation to the folllowing paper:
https://arxiv.org/pdf/1402.6562.pdf
See section 3 on examples where standard probability theory is discussed. Is it valid? To me its rather obvious but I had had a retired professor of probability say probability theory doesn't have a state...
Homework Statement
The question asks me to express the system shown in the image in state-space form, firstly by using the transfer function which was fine but the second part asks to express in state-space form by using the components A,B,C,D as the states x1,x2,x3,x4
Homework Equations
U(s)...
Hi guys!
I study Electrical Engineering and, don't-know-why, I don't know anything about state space. Now I'm working on a project where I have a non-linear system. The first task in the project is to separate the linear and the non-linear part of this system, and then obtain the state space...
Hello, I want to verify this question.
In short,
"Where did input matrix Bu arise from?"
I was wondering why the state equation has to be in the form of x_dot=Ax+Bu. I got to the point that the highest order terms can be expressed in the form of linear superposition of lower degree terms.
If...
Lets say a state is defined by the minimal amount of independent variables to completely describe a system.
One would come up with the (q,p)-phase-space for a point mass and as another example the Hilbert-space for quantum-states.
Consider the very simple case of a standing wave in string...
Hi, I have been trying to get my head around the effect of a time reversed hamiltonian ##H^B(t)=H(-t)=T^{-1}H^F T ## on a state ket ##|\psi>##, where ##H^F=H## is the regular hamiltonian for the system (energy associated with forward time translation) and ##H^B=H(-t)## is the time reversed...
Hi,
Having a bit of trouble with this question: "Assuming a proportional controller is used, determine the gain to achieve a damping ratio of 0.5, for the following transfer function. Hence calculate the associated natural frequency and oscillation period. G(s) = -4(s+0.4) / s^2+1.6s+14."
I...
I have been struggling to solve the following problem for days.
I was given the state space model of a circuit and asked to determine the system elements. So basically, I think I have to find a suitable circuit which describes the state space equation. I am not really sure how to approach this...
Homework Statement
The state space model of a nonlinear system is
x'_1(t) = 2x^2_2(t) - 50
x'_2(t) = -x_1(t) - 3x_2(t) + u(t)
Where x_1(t) and x_2(t) are the states, and u(t) is the input. The output of the system is x_2(t).
Find the state space model of this system linearized at the...
I'm studying for an upcoming final and this is a question from a practice exam we were given. It looks simple but for some reason I just can't wrap my brain around it. The question is attached and gives a state space representation of a system (A, B, C matrices) and asks what part of the system...
Homework Statement
Given: Initial orbital elements of a satellite
a=6652.555663km;
e=0.075;
i=28.5 degrees;
Ω=40 degrees;
w=30 degrees;
n=0 degrees;
Tasks(using MATLAB):
1. Convert orbital elements to position and velocity vectors
2. Use these vectors to initialize the Runge-Kutta...
Homework Statement
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I'm trying to 'solve' two coupled second order ODE's with the intent of putting them in state space. My specific problem is more complex and includes additional equations which are irrelevant. Essentially I can solve the problem if I know the solution to this. x1 and...
Hello,
I have a state space equation at hand.. This attached with this...
Now the term (theta double dot) is a positive step for 0,136 milli seconds and negative step for next 0,136 millisecond and 0 at all other times.
So that when I simulate I will get a graph as below:
This is the nature...
Hello,
I have a fundamental question about why state space control techniques are superior to the classical methods. I l know that you can control a system with multiple inputs and outputs for several states using state space control, however, can't the same thing be done in classical control...
Just reviewing some QM again and I think I'm forgetting something basic. Just consider a qubit with basis {0, 1}. On the one hand I thought 0 and -0 are NOT the same state as demonstrated in interference experiments, but on the other hand the literature seems to say the state space is...
Homework Statement
I'm trying to derive the equations of motion and state space as well as the transfer function for a system which has two mass spring damper systems stacked on top of each other. The system is base excited. I attached a pic of the system
Homework Equations
- Sum of the...
I would like to find the distance that a vehicle travels using a Kalman filter. The vehicle is a car that travels the road between two positions. The vehicle has a GPS/barometer/accelerometer device that collects position data, which I converted from a longitude and latitude to a North, East...
I want to get the distance between points. I have a measurement of latitude, longitude and height from GPS/barometer systen (which I converted into north east down coordinates) and I have another measurement of the vehicle's velocity in the north east and down direction. To find the distance, I...
I have this circuit and I must represent it in state space. I know the process because I have done similar ones but having trouble with this one. I have found the Kirchhoff equtations for the 2 loops and for the upper juction, whatever I do after I can't end up to two equations x'1 and x'2...
I have a state space model along with an observer and state feedback.
I need to find the transfer function connecting the r (reference) to the y (output)
I have this model on simulink. I know the A,B,C,D matrices. So, I can get the TF for the stateSpace with ss2tf function of matlab...
Let:
$$x_1=A\sin{\omega t}$$ $$x_2=\dot{x}_1=A\omega \cos{\omega t}$$ $$y=A\omega$$
We want to represent this system in a state space model. The state transition matrix read:
$$A=\begin{bmatrix} 0 & 1 &\\ -\omega^2 & 0 \\ \end{bmatrix}$$ I am not sure what the output matrix will be like. Can we...
I need help finding a state-space representation for the given system and locally linearizing it...
Objective is to control the pitch angle theta, as an output, of the helicopter by regulating the rotor angle u, as an input.
This is what I've done, but apparently it isn't correct, and I...
JL*QL'' + BL*QL' + k(QL - Qm) = 0
Jm*Qm'' + Bm*Qm' - k(QL - Qm) = u
This is the equation set I have for a motor with a load.
QL'' means second derivative and QL' means first derivative.
I need to be able to obtain the state space representation of this model where X = [QL;QL';Qm;Qm'] (This is...
I’ve been trying to understand how having indistinguishable particles in a system changes the nature of the state space.
The QM texts I have gloss over this.
A typical approach is to define the symmetric and anti-symmetric kets that serve as a basis for the eigenspace containing...
Hi,
Does anyone know a program that I can put on my TI-84 calculator that will allow me to input any transfer function and get the state space representation of the system or the other way around.
For example
G(s) = \frac{\sum(K_{i}s^{i})}{\sum(P_{i}s^{i})}
The calculator prompts you...
Homework Statement
http://imagizer.imageshack.us/v2/800x600q90/690/0tab.png [Broken] [Broken]
I'm asked to find the transfer function and then find the state space representation and seem to be stuck.
Homework Equations
The Attempt at a Solution
My textbook states that for a...
Homework Statement
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I'm given the following circuit
http://imagizer.imageshack.us/v2/800x600q90/43/bwka.png [Broken]
Homework Equations
The Attempt at a Solution
I come up with the transfer function to be G(s) = \frac{s}{2+\frac{1}{s}}. The question asks me to...
Hi guys! So this question has been bugging me a bit and I can't seem to find any textbook (at least, restricted to physics textbooks) that talks about it.
In QM, the overarching formalism is clear. We have ##L^2(\mathbb{R})## and states are given by ##|\psi\rangle \in L^2(\mathbb{R})## such...
Homework Statement
Write an IIR (or ARMA) model in state space representation:
Homework Equations
y(k) = b_1 y(k-1) + \cdots + b_p y(k-p) + a_0 u(k) + \cdots + a_r u(k-r)
The Attempt at a Solution
I found much info how to write it in space state representation but no explanation...
Homework Statement
A first-order dynamic system is represented by the differential equation,
5\frac{dx(t)}{dt} + x(t) = u(t).
Find the corresponding transfer function and state space reprsentation.
Homework Equations
The Attempt at a Solution
Putting the equation in the...