A Simple Iterative Procedure for the Identification of the Unknown Parameters of a Linear Time Varying Discrete System

1963 ◽  
Vol 85 (2) ◽  
pp. 227-235 ◽  
Author(s):  
Harold J. Kushner
Keyword(s):  
Impulse Response ◽  
Discrete System ◽  
Linear Time ◽  
Time Varying ◽  
Unknown Parameters ◽  
Random Drift ◽  
Process Dynamics ◽  
Linear Discrete System ◽  
Single Input ◽  
Time Variations

A new “steepest descent” approach to the “adaptive control system” problem of the determination of the process dynamics of a time varying system is analyzed in considerable detail. The unknown parameters are the parameters of the impulse response of a linear discrete system. The identification procedure is a first-order iterative process and is designed to operate with the natural inputs of the system to be identified. After each new (single) input, new estimates of all the unknown parameters are computed. The method is computationally simple and, in its analysis, the effects of additive noise in the observations (of both input and output), random drift with time, or neglected parameters of the impulse response are handled with relative ease and become transparent. Time variations are taken directly into account, thus eliminating the necessity of the assumption of stationarity over a period of time.

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.

Identification of Linear Time-Varying Parameters of Nonstationary Systems

2019 ◽  
Vol 20 (5) ◽  
pp. 269-265
Author(s):  
V. T. Le ◽  
M. M. Korotina ◽  
A. A. Bobtsov ◽  
S. V. Aranovskiy ◽  
Q. D. Vo
Keyword(s):  
Linear Time ◽  
Control Object ◽  
Time Interval ◽  
Identification Algorithm ◽  
Time Varying ◽  
State Variables ◽  
Unknown Parameters ◽  
Technical Problems ◽  
True Values ◽  
Stationary Control

The paper considers the identification algorithm for unknown parameters of linear non-stationary control objects. It is assumed that only the object output variable and the control signal are measured (but not their derivatives or state variables) and unknown parameters are linear functions or their derivatives are piecewise constant signals. The derivatives of non-stationary parameters are supposed to be unknown constant numbers on some time interval. This assumption for unknown parameters is not mathematical abstraction because in most electromechanical systems parameters are changing during the operation. For example, the resistance of the rotor is linearly changing, because the resistance of the rotor depends on the temperature changes of the electric motor in operation mode. This paper proposes an iterative algorithm for parameterization of the linear non-stationary control object using stable LTI filters. The algorithm leads to a linear regression model, which includes time-varying and constant (at a certain time interval) unknown parameters. For this model, the dynamic regressor extension and mixing (DREM) procedure is applied. If the persistent excitation condition holds, then, in the case the derivative of each parameter is constant on the whole time interval, DREM provides the convergence of the estimates of configurable parameters to their true values. In the case of a finite time interval, the estimates convergence in a certain region. Unlike well-known gradient approaches, using the method of dynamic regressor extension and mixing allows to improve the convergence speed and accuracy of the estimates to their true values by increasing the coefficients of the algorithm. Additionally, the method of dynamic regressor extension and mixing ensures the monotony of the processes, and this can be useful for many technical problems.

scholarly journals Commutativity of systems with their feedback conjugates

2018 ◽  
Vol 41 (3) ◽  
pp. 696-700 ◽  
Author(s):  
Mehmet Emir Koksal
Keyword(s):  
Dynamical System ◽  
Differential System ◽  
Linear Time ◽  
Relevant Literature ◽  
Time Varying ◽  
Single Input Single Output ◽  
Single Output ◽  
Single Input

After introducing commutativity concept and summarizing the relevant literature, this work is focused on the commutativity of feedback conjugates. It is already known that a linear time-varying differential system describing a single input-single output dynamical system is always commutative with its constant gain feedback pairs. In this article, it is proven that among the time-varying feedback conjugates of a linear time-varying system, constant feedback conjugates are the only commutative feedback pairs and any of the time-varying feedback conjugates cannot constitute a commutative pair of a linear time-varying system.

Central suboptimalH∞controller design for linear time-varying systems with unknown parameters

2011 ◽  
Vol 42 (5) ◽  
pp. 709-716 ◽  
Author(s):  
Michael V. Basin ◽  
Pedro Soto ◽  
Dario Calderon-Alvarez
Keyword(s):  
Controller Design ◽  
Linear Time ◽  
Time Varying ◽  
Unknown Parameters ◽  
Time Varying Systems

Design of an optimal preview controller for linear time-varying discrete systems in a multirate setting

2015 ◽  
Vol 13 (06) ◽  
pp. 1550050 ◽  
Author(s):  
Fucheng Liao ◽  
Yujian Guo ◽  
Yuan Yan Tang
Keyword(s):  
Optimal Control ◽  
Discrete System ◽  
Control Method ◽  
Linear Time ◽  
Discrete Systems ◽  
Control Input ◽  
Time Varying ◽  
Preview Control ◽  
Rate System ◽  
Error System

This paper is concerned with preview control problems for linear time-varying discrete systems in a multirate setting. First, by using the discrete lifting technique, the multirate time-varying discrete system is converted to a formal single-rate system. Then, by applying the standard linear quadratic (LQ) preview control method, we construct the expanded error system, and the optimal preview control model of the common time-varying discrete system is obtained. The optimal control input of the expanded error system is obtained by using the outcome of optimal control theory on time-varying systems. The controller with preview action is obtained when we transfer our conclusion into the original system. Finally, a numerical example is included to illustrate the validity of the proposed method.

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