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In control engineering and system identification, a state-space representation is a mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time through first-order differential equations or difference equations. These state variables change based on their current values and inputs, while ...
In control engineering and other areas of science and engineering, state variables are used to represent the states of a general system. The set of possible combinations of state variable values is called the state space of the system. The equations relating the current state of a system to its most recent input and past states are called the ...
Thus, the thermodynamic state would range over a three-dimensional state space. The remaining variable, as well as other quantities such as the internal energy and the entropy, would be expressed as state functions of these three variables.
Vacuum World, a shortest path problem with a finite state space. In computer science, a state space is a discrete space representing the set of all possible configurations of a "system". [1] 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.
The system's evolving state over time traces a path (a phase-space trajectory for the system) through the high-dimensional space. The phase-space trajectory represents the set of states compatible with starting from one particular initial condition , located in the full phase space that represents the set of states compatible with starting from ...
Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing.
A state function describes equilibrium states of a system, thus also describing the type of system. A state variable is typically a state function so the determination of other state variable values at an equilibrium state also determines the value of the state variable as the state function at that state. The ideal gas law is a good example ...
A random variable X is a measurable function X: Ω → S from the sample space Ω to another measurable space S called the state space. If A ⊂ S, the notation Pr(X ∈ A) is a commonly used shorthand for ({: ()}).