State Space Model
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State Space Model
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A state space is the set of all possible configurations of a system.
State space model. It is a vector which contains the state variables as elements. The state or the measurement can be either continuous or discrete. Only issue is which set of states to use there are many choices. In the earlier chapters we have discussed two mathematical models of the control systems.
Die modelle koennen auch auf nichtlineare system oder systeme mit anfangswerte ungleich null angewandt werden. In the absence of these equations a model of a desired order or number of states can be estimated from measured input output data. State space models are natural in. It describes a system with a set of first order differential or difference equations using inputs outputs and state variables.
For instance the toy problem vacuum world has a discrete finite state space in which there are a limited set of configurations that the vacuum and dirt can be in. Can be developed from transfer function model as well. State space models the data is a linear function of an underlying markov process the state plus additive noise. Creating state space models most easily created from nth order dierential equations that describe the dynamics this was the case done before.
The state is observed directly and only partially observable via the observed data. Much more on this later. A state space model is commonly used for representing a linear time invariant lti system. The term state space originated in 1960s in the area of control engineering kalman 1960.
The resulting models 1. With p displaystyle p inputs and q displaystyle q outputs we would otherwise have to write down q p displaystyle qtimes p laplace transforms to encode all the information about a system. Sie bieten ausserdem eine komfortable moeglichkeit mimo multi inputmulti output systeme darzustellen zu analysieren und zu regeln. Those are the differential equation model and the transfer function model.
State space models are models that use state variables to describe a system by a set of first order differential or difference equations rather than by one or more n th order differential or difference equations. Let us now discuss these two. A generalized state space model genss object when one or more of the matrices a b c and d includes tunable parameters such as realp parameters or generalized matrices genmat. State space model ssm refers to a class of probabilistic graphical model koller and friedman 2009 that describes the probabilistic dependence between the latent state variable and the observed measurement.
The state space representation also known as the time domain approach provides a convenient and compact way to model and analyze systems with multiple inputs and outputs. 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.
