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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.
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.
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 ...
The state-transition matrix is used to find the solution to a general state-space representation of a linear system in the following form ˙ = () + (), =, where () are the states of the system, () is the input signal, () and () are matrix functions, and is the initial condition at .
Full state feedback is utilized by commanding the input vector _. Consider an input proportional (in the matrix sense) to the state vector, System with state feedback (closed-loop) _ = _. Substituting into the state space equations above, we have
A solution to a discretized partial differential equation, obtained with the finite element method. In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical ...
The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the phase space usually consists of all possible values of the position and momentum parameters.
In control theory, a state observer, state estimator, or Luenberger observer is a system that provides an estimate of the internal state of a given real system, from measurements of the input and output of the real system. It is typically computer-implemented, and provides the basis of many practical applications.