A new higher-order method for parameter optimization of time-varying and time-invariant linear dynamic systems

2002 ◽  
Author(s):  
S.K. Agrawal ◽  
X. Xu
Keyword(s):  
Parameter Optimization ◽  
Dynamic Systems ◽  
Higher Order ◽  
Time Varying ◽  
Order Method ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Higher Order Method ◽  
Time Invariant

Minimum-Order Mathematical Models of Discrete Linear Dynamic Systems

1972 ◽  
Vol 94 (2) ◽  
pp. 139-146 ◽  
Author(s):  
A. G. Behring ◽  
V. J. Flanigan
Keyword(s):  
Mathematical Models ◽  
Discrete Time ◽  
Dynamic Systems ◽  
Input Output ◽  
Output Data ◽  
Minimum Order ◽  
Linear Dynamic Systems ◽  
Linear Dynamic ◽  
Common Problems ◽  
Time Invariant

An orthonormal filter is used to obtain minimum-order, mathematical models of linear, multivariable, discrete, time-invariant systems from input/output data. Some common problems associated with obtaining such descriptions are considered, including the problem of noise-corrupted observations.

Linear Time-Varying Dynamic Systems Optimization via Higher-Order Method Using Shifted Chebyshev’s Polynomials

1999 ◽  
Vol 121 (2) ◽  
pp. 258-261 ◽  
Author(s):  
Xiaochun Xu ◽  
Sunil K. Agrawal
Keyword(s):  
Differential Equations ◽  
Dynamic Systems ◽  
Linear Time ◽  
Optimal Solution ◽  
Higher Order ◽  
Time Varying ◽  
Varying Coefficients ◽  
Higher Order Method ◽  
Time Varying Coefficients ◽  
Higher Order Differential Equations

For optimization of classes of linear time-varying dynamic systems with n states and m control inputs, a new higher-order procedure was presented by the authors that does not use Lagrange multipliers. In this new procedure, the optimal solution was shown to satisfy m 2p-order differential equations with time-varying coefficients. These differential equations were solved using weighted residual methods. Even though solution of the optimization problem using this procedure was demonstrated to be computation efficient, shifted Chebyshev’s polynomials are used in the paper to solve the higher-order differential equations. This further reduces the computations and makes this algorithm more appropriate for real-time implementation.

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