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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.
Field theory is centered around the idea that a person's life space determines their behavior. [2] Thus, the equation was also expressed as B = f(L), where L is the life space. [4] In Lewin's book, he first presents the equation as B = f(S), where behavior is a function of the whole situation (S). [5]
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 ...
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
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.
Furthermore, the interaction of the person (P), and the environment (E) produces this life space. In symbolic expression, B=ƒ(LS)=F(P,E). [6] An example of a more complex life-space concept is the idea that two people's experience of a situation can become one when they converse together.
For example, if the dimension of the state space is greater than the dimension of the output, then there will be a set of possible state configurations for each individual output. That is, the system can have significant zero dynamics , which are trajectories of the system that are not observable from the output.