What is State-space: Definition and 19 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.

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  1. djulzz1982

    Modelling Guy Needing Refresher

    Hi everybody. I like to model dynamical systems, but over the last few years, I've been busy implementing simulations, without actually deriving their equations of motions. I'm thus here to check with members whether some systems for which I wrote the equations of motions are actually corrects.
  2. M

    Engineering Advanced control systems, state-space controllers

    ------------EDIT---------------------------------------------------------------------------- Check comment #7 for neater and faster explanation of the question statement --------------------------------------------------------------------------------------------- The symbols represent: H, water...
  3. S

    Converting a nonlinear eqn of motion to a state-space model

    Homework Statement equations above are descriptive of a system with two configuration variables, q1 and q2. inputs are tau1 and tau2. d and c values are given. the question is about conversion of above equations to a state-space equation where the state-variables are x1 = q1_dot, x2 = q1_2dot...
  4. S

    I What is the difference between phase space and state-space?

    In state space, the coordinates are the state variables of a system.So,each point in state space represents a specific value of state variables.Thus,state space representation represents the changes in a dynamical system. The state variables are the minimum number of variables which uniquely...
  5. A

    Finding the state space model of a nonlinear system

    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...
  6. Linder88

    State-Space (SS) Formulation for Equations of Motion

    Homework Statement The task is to write the following equations of motion as in equation (2) considering the inputs and outputs as in equation (3) \begin{equation} \begin{cases}...
  7. Y

    State-space modeling of a control system

    Homework Statement [/B] Here is the problem: And this is the system in question: Homework Equations G(s) = θ_0(s)/θ_i(s) = output/input (open-loop transfer function) The Attempt at a Solution I've been staring at this problem and looking through my textbook for over an hour but...
  8. Chacabucogod

    Control Theory State-Space method with derivative input

    Hi, I'm reading Ogata's Modern Control Engineering, and when he talks about the representation of a differential equation in state space he divides the method in two. The first one is when the input of the differential equation involves no derivative term, for example: x'(t)+x(t)=u(t) The...
  9. R

    State-space model of magnetically suspended ball

    Hi, I have a 'simplified' equation of the magnetically suspended ball. a = g - (i/h * M) where a - actual acceleration of the ball. h - distance from the magnet. g - gravitational acceleration, to keep it simple let g = 10 M - mass of the ball 0.05 kg i - current through the...
  10. N

    State-Space model of spring-mass system

    Homework Statement Derive the state space model of a spring-mass-damper system. Neglect friction, wind resistance, etc. Neglect the force of gravity. Assume the spring's equilibrium point is at y=0 and there is an arbitrary Homework Equations [X'] = AX + BU y = CX + DUThe Attempt at a...
  11. X

    Transformation matrix of linear n-dimensional state-space system

    Hi all, I have a linear algebra question relating actually to control systems (applied differential equations) for the linear system {\dot{\vec{{x}}} = {\bf{A}}{\vec{{x}}} + {\bf{B}}}{\vec{{u}}}\\ \\ A \in \mathbb{R}^{ nxn }\\ B \in \mathbb{R}^{ nx1 }\\ In class, we formed a...
  12. T

    State-Space Representation with Initial Conditions: Finding the Right DSP Book

    Could you advise a DSP book which explains state-space representation with initial conditions. Initial conditions part is important for me. Thanks.
  13. N

    State-space description, nonlinear system, inverted pendulum

    Homework Statement Inverted pendulum on a cart on a frictionless surface, write the state-space description of a nonlinear system. outputs are theta(t), theta'(t), y(t), y'(t). Everything is 2-dimensional. Homework Equations theta(t) is the angle between the gravity vector and pendulum y(t)...
  14. N

    Circuits, State-Space Equations, MATLAB Simulink

    SOLVED. Just making the post showed me the answer. Sorry!
  15. H

    How do I numerically compute a state-space equation?

    Suppose that, I have a linear system which is analytically defined as below: \frac{dx}{dt} = Ax + Bu \, ... \, (I) y = Cx + Du \, ... \, (II) A, B, C, D are matrices defining the system, u is input, y is output. I want to simulate this system in computer (not by using Matlab or any other...
  16. T

    Help constructing state-space model of a system

    Homework Statement A single wheel cat moving on the plane with linear velocity v angular velocity \omega can be modeled by the nonlinear system: dpx/dt = v*cos(\theta) dpy/dt = v*sin(\theta) d\theta/dt = \omega where (px,py) denote the cartesian coordinates of the wheel and...
  17. S

    Nonlinear State-Space Modeling for UAV Dynamics

    Anyone have any good online sources for nonlinear state-space modeling? I need to place nonlinear UAV dynamics into state-space form for modelling and seriously running out of good reference material for information.
  18. C

    Converting a simple mass-spring system to state-space model, how?

    Homework Statement Hi guys/girls Professor gave this very simple homework where I need to convert the system below to a state-space model. The system itself is represented by the equation m*x" + k*x = f(t) Where m = 5 and k = 1. Note that, " (doublequote) is a second-order derivative...
  19. M

    How Do You Model a Discrete Stochastic Signal Using State-Space Representation?

    Homework Statement A time discrete stocastic signal is described by s(k) = w(k-1) + aw(k-2), |a|<1 and w(n) is white gaussian noise with m_w = 0, \sigma_w^2 = 1. It is observed under influence of white noise: y(k) = s(k) + v(k) where v(n) is white gaussian noise with m_v = 0...
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