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In control engineering and system identification, a state-space representation is a mathematical model of a physical system that uses state variables to track how inputs shape system behavior over time through first-order differential equations or difference equations. These state variables change based on their current values and inputs, while ...
While the time parameter is usually discrete, the state space of a Markov chain does not have any generally agreed-on restrictions: the term may refer to a process on an arbitrary state space. [15] However, many applications of Markov chains employ finite or countably infinite state spaces, which have a more straightforward statistical analysis.
In mathematics, specifically in control theory, subspace identification (SID) aims at identifying linear time invariant (LTI) state space models from input-output data. SID does not require that the user parametrizes the system matrices before solving a parametric optimization problem and, as a consequence, SID methods do not suffer from problems related to local minima that often lead to ...
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 .
Thus the set of all states of M with the weak-* topology forms a compact Hausdorff space, known as the state space of M. In the C*-algebraic formulation of quantum mechanics, states in this previous sense correspond to physical states, i.e. mappings from physical observables (self-adjoint elements of the C*-algebra) to their expected ...
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 adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. [1] It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. [2] The adjoint state space is chosen to simplify the physical interpretation of equation ...
A two-dimensional Poincaré section of the forced Duffing equation. In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.