Optimal control for third degree polynomial systems and its automotive application

2003 ◽  
Author(s):  
M.V. Basin ◽  
M.A.A. Garcia
Keyword(s):  
Optimal Control ◽  
Polynomial Systems ◽  
Automotive Application ◽  
Degree Polynomial

State estimation for stochastic polynomial systems with switching in the state equation

2017 ◽  
Vol 40 (9) ◽  
pp. 2732-2739
Author(s):  
Miguel Hernandez-Gonzalez ◽  
Michael V Basin
Keyword(s):  
Covariance Matrix ◽  
Polynomial System ◽  
Random Variable ◽  
Polynomial Systems ◽  
State Equation ◽  
The State ◽  
Nonlinear Functions ◽  
Degree Polynomial ◽  
Error Covariance ◽  
Finite Dimensional

The problem of designing a mean-square filter has been studied for stochastic polynomial systems, where the state equation switches between two different nonlinear functions, over linear observations. A switching signal depends on a random variable modelled as a Bernoulli distributed sequence that takes the quantities of zero and one. The differential equations for the state estimate and the error covariance matrix are obtained in a closed form by expressing the conditional expectation of polynomial terms as functions of the estimate and covariance matrix. Finite-dimensional filtering equations are obtained for a particular case of a third-degree polynomial system. Numerical simulations are carried out in two cases of switching between different linear and second degree polynomial functions.

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