# State Space

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## state space

[′stāt ‚spās]
(control systems)
The set of all possible values of the state vector of a system.

## State Space

The state space of a dynamical system is a space such that each point in the space is uniquely associated with a certain state of the system (in some generalized coordinates). The points of the state space are known as representative points. To each process of change of state of the system (that is, to the system’s motion in these coordinates) there corresponds a certain trajectory of the motion of the representative point in the space. The concept of state space is used most often in investigations of the motion of dynamical systems in celestial mechanics, vibration theory, and the theory of automatic control.

In many technological, biological, and economic systems, the generalized coordinates of the system being considered can assume only discrete values. The states of such systems must also be regarded as discrete, and the representative points are viewed as belonging to a discrete state space. To the changes in state of such systems (that is, to the motion of the systems) there correspond successive jumps of the representative point from one position to another.

A different case is presented by systems involving parameters (coordinates) that are distributed in space. A state space with a finite number of dimensions is not sufficient for representing the states of the system in such a way as to provide a one-to-one correspondence between the state of the system (in these coordinates) and the position of the representative point. An example of such a system is a body whose state is characterized by its temperature field. A geometric image of the state of such a system can be obtained only in a space with an infinite number of dimensions.

The state space is a special case of a phase space.

References in periodicals archive ?
The stress is therefore shifted from the parameter space of the Hamiltonian in case of Berry's construction to state space.
The following are appended: (1) SCHEV Capital Outlay Prioritization Process Chart; (2) Excerpt from SCHEV Fixed Asset Guidelines (2001); (3) National Survey Results for State Space Utilization Guidelines; and (4) Terminology and Methodology.
The problem is complicated by the fact that different action choices might appear to have lower rewards but they lead the agent to more reinforcement-rich parts of the state space.
If several qubits are combined in a quantum register, the state space of such a processor allows the handling of exponentially many data by superposition of entangled states.
In those jobs, Carter said he worked with other state space advocates, so he's looking forward to promoting his own state's space efforts.
Pure heuristic search planners can be characterized along three main dimensions: (1) the state space that is searched (either the progression or regression space), (2) the search algorithm used (most often some version of best-first or hill-climbing search), and (3) the heuristic function extracted from the problem representation.
A structural state space model-based method of seasonal adjustment presents certain advantages to seasonally adjust time series
where X(f) = {f(u) | u [element of] U} is called the state space of f and any element in X(f) is called a state of f.
Here Scott comes close to legitimating militia-like paranoia, suggesting, for instance, that ordinary municipal zoning regulations lie only a few steps up the slippery slope from "concentration camps built in wartime to create and maintain a legible, bounded, concentrated state space.
Even if the new alliance is formed, CSTA is still recognized by state law as the state's spaceport authority and it would be through that organization that the funding for state space initiatives would take place.
Since these techniques search the state space of the protocol exhaustively, the amount of memory required to manipulate the state information and the verification time grow very fast with

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