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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.
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 state equations, and the equations expressing the values of the output variables in terms of the state variables and inputs are called the ...
A state-space model is a representation of a system in which the effect of all "prior" input values is contained by a state vector. In the case of an m-d system, each dimension has a state vector that contains the effect of prior inputs relative to that dimension. The collection of all such dimensional state vectors at a point constitutes the ...
Example of a simple MDP with three states (green circles) and two actions (orange circles), with two rewards (orange arrows) A Markov decision process is a 4-tuple (,,,), where: is a set of states called the state space. The state space may be discrete or continuous, like the set of real numbers.
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.
fits into the abstract evolution equation framework described above as follows. The input space U and the output space Y are both chosen to be the set of complex numbers. The state space X is chosen to be the product of the complex numbers with L 2 (−τ, 0). The operator A is defined as
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
These two equations can be viewed as state space equations and look similar to the state space equations for the Kalman filter. If the functions g and h in the above example are linear, and if both W k {\displaystyle W_{k}} and V k {\displaystyle V_{k}} are Gaussian , the Kalman filter finds the exact Bayesian filtering distribution.