Ellipsoidal Reachability Sets of Linear Time-Varying Systems in Estimation and Control Problems

2019 ◽  
Vol 55 (11) ◽  
pp. 1440-1453 ◽  
Author(s):  
D. V. Balandin ◽  
R. S. Biryukov ◽  
M. M. Kogan
Keyword(s):  
Linear Time ◽  
Control Problems ◽  
Time Varying ◽  
Reachability Sets ◽  
Time Varying Systems ◽  
Estimation And Control ◽  
And Control

Iterative learning identification and control for point-to-point tracking of linear time-varying systems with unknown parameters and stochastic noise

2017 ◽  
Vol 40 (13) ◽  
pp. 3834-3845 ◽  
Author(s):  
Yan Geng ◽  
Xiaoe Ruan
Keyword(s):  
Linear Time ◽  
Tracking Error ◽  
Iterative Learning ◽  
Time Varying ◽  
Unknown Parameters ◽  
Point Tracking ◽  
Time Varying Systems ◽  
System Output ◽  
Point To Point ◽  
And Control

In this paper, an interactive iterative learning identification and control (ILIC) scheme is developed for a class of discrete-time linear time-varying systems with unknown parameters and stochastic noise to implement point-to-point tracking. The identification is to iteratively estimate the unknown system parameter matrix by adopting the gradient-type technique for minimizing the distance of the system output from the estimated system output, whilst the control law is to iteratively upgrade the current control input with the current point-to-point tracking error scaled by the estimated system parameter matrix. Thus, the iterative learning identification and the iterative learning control are scheduled in an interactive mode. By means of norm theory, the boundedness of the discrepancy between the system matrix estimation and the real one is derived, whilst, by the manner of the statistical technique, it is conducted that the mathematical expectation of the tracking error monotonically converges to nullity and the variance of the tracking error is bounded. Numerical simulations exhibit the validity and effectiveness of the proposed ILIC scheme.

Iterative Learning Identification/Iterative Learning Control for Linear Time-Varying Systems

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
Nanjun Liu ◽  
Andrew Alleyne
Keyword(s):  
Iterative Learning Control ◽  
Linear Time ◽  
Tracking Error ◽  
Learning Control ◽  
Iterative Learning ◽  
Parameter Estimates ◽  
Time Varying ◽  
Fixed Parameter ◽  
Time Varying Systems ◽  
And Control

This paper integrates a previously developed iterative learning identification (ILI) (Liu, N., and Alleyne, A. G., 2016, “Iterative Learning Identification for Linear Time-Varying Systems,” IEEE Trans. Control Syst. Technol., 24(1), pp. 310–317) and iterative learning control (ILC) algorithms (Bristow, D. A., Tharayil, M., and Alleyne, A. G., 2006, “A Survey of Iterative Learning Control,” IEEE Control Syst. Mag., 26(3), pp. 96–114), into a single norm-optimal framework. Similar to the classical separation principle in linear systems, this work provides conditions under which the identification and control can be combined and guaranteed to converge. The algorithm is applicable to a class of linear time-varying (LTV) systems with parameters that vary rapidly and analysis provides a sufficient condition for algorithm convergence. The benefit of the integrated ILI/ILC algorithm is a faster tracking error convergence in the iteration domain when compared with an ILC using fixed parameter estimates. A simple example is introduced to illustrate the primary benefits. Simulations and experiments are consistent and demonstrate the convergence speed benefit.

Feedback polynomial filtering and control of non-Gaussian linear time-varying systems

2019 ◽  
Vol 123 ◽  
pp. 108-115 ◽  
Author(s):  
Filippo Cacace ◽  
Francesco Conte ◽  
Massimiliano d’Angelo ◽  
Alfredo Germani
Keyword(s):  
Linear Time ◽  
Time Varying ◽  
Time Varying Systems ◽  
Polynomial Filtering ◽  
Non Gaussian ◽  
And Control
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