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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 state space is then factorized according to =, where is the space of 'external' states that are 'hidden' from the agent (in the sense of not being directly perceived or accessible), is the space of sensory states that are directly perceived by the agent, is the space of the agent's possible actions, and is a space of 'internal' states that ...
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]
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 ...
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 ...
The concept first made its appearance in psychology with roots in the holistic perspective of Gestalt theories. It was developed by Kurt Lewin, a Gestalt psychologist, in the 1940s. Lewin's field theory can be expressed by a formula: B = f(p,e), meaning that behavior (B) is a function of the person (p) and their cultural environment (e). [1]
Computing these functions involves computing expectations over the whole state-space, which is impractical for all but the smallest (finite) Markov decision processes. In reinforcement learning methods, expectations are approximated by averaging over samples and using function approximation techniques to cope with the need to represent value ...
In psychology, random walks explain accurately the relation between the time needed to make a decision and the probability that a certain decision will be made. [41] Random walks can be used to sample from a state space which is unknown or very large, for example to pick a random page off the internet.