scholarly journals A flexible state–space model for learning nonlinear dynamical systems

Automatica ◽  
2017 ◽  
Vol 80 ◽  
pp. 189-199 ◽  
Author(s):  
Andreas Svensson ◽  
Thomas B. Schön
Keyword(s):  
Dynamical Systems ◽  
State Space ◽  
Nonlinear Dynamical Systems ◽  
State Space Model ◽  
Nonlinear Dynamical ◽  
Space Model

A Probabilistic Theory of Nonlinear Dynamical Systems Based on the Cell State Space Concept

1982 ◽  
Vol 49 (4) ◽  
pp. 895-902 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Dynamical Systems ◽  
State Space ◽  
Nonlinear Dynamical Systems ◽  
Global Analysis ◽  
Cell Structure ◽  
The State ◽  
Probabilistic Theory ◽  
Nonlinear Dynamical ◽  
Linear Ordinary Differential Equations ◽  
Highly Nonlinear

Developed in the paper is a probabilistic theory for nonlinear dynamical systems. The theory is based on discretizing the state space into a cell structure and using the cell probability functions to describe the state of a system. Although the dynamical system may be highly nonlinear the probabilistic formulation always leads to a set of linear ordinary differential equations. The evolution of the probability distribution among the cells can then be studied by applying the theory of Markov processes to this set of equations. It is believed that this development possibly offers a new approach to the global analysis of nonlinear systems.

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