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The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector , the state vector . If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
If the size of the state space is finite, calculating the size of the state space is a combinatorial problem. [4] For example, in the Eight queens puzzle, the state space can be calculated by counting all possible ways to place 8 pieces on an 8x8 chessboard. This is the same as choosing 8 positions without replacement from a set of 64, or
State space search is a process used in the field of computer science, including artificial intelligence (AI), in which successive configurations or states of an instance are considered, with the intention of finding a goal state with the desired property. Problems are often modelled as a state space, a set of states that a problem
By Gelfand representation, every commutative C*-algebra A is of the form C 0 (X) for some locally compact Hausdorff X. In this case, S(A) consists of positive Radon measures on X, and the pure states are the evaluation functionals on X. More generally, the GNS construction shows that every state is, after choosing a suitable representation, a ...
The state of a system described by a state space representation. A state vector (geographical) specifies the position and velocity of an object in any location on Earth's surface; Orbital state vectors are vectors of position and velocity that together with their time, uniquely determine the state of an orbiting body in astrodynamics or in ...
For the simplest example of a continuous, LTI system, the row dimension of the state space expression ˙ = + determines the interval; each row contributes a vector in the state space of the system. If there are not enough such vectors to span the state space of x {\displaystyle \mathbf {x} } , then the system cannot achieve controllability.
In artificial intelligence and computer programming, state space planning is a process used in designing programs to search for data or solutions to problems. In a computer algorithm that searches a data structure for a piece of data, for example a program that looks up a word in a computer dictionary, the state space is a collective term for all the data to be searched.
A state diagram for a door that can only be opened and closed. A state diagram is used in computer science and related fields to describe the behavior of systems. State diagrams require that the system is composed of a finite number of states. Sometimes, this is indeed the case, while at other times this is a reasonable abstraction.