Online digital prediction and control of the output of a linear time-varying system

1965 ◽  
Vol 1 (8) ◽  
pp. 220
Author(s):  
R.F. Brown
Keyword(s):  
Linear Time ◽  
Time Varying ◽  
Prediction And Control ◽  
And Control

Optimal Control for Partially Observed Nonlinear Interval Systems

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
T. E. Dabbous
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Control Problem ◽  
Linear Time ◽  
Control Process ◽  
Extension Principle ◽  
Time Varying ◽  
State Observation ◽  
Partially Observed ◽  
And Control

In this paper, we consider the optimal control problem for a class of systems governed by nonlinear time-varying partially observed interval differential equations. The control process is assumed to be governed by linear time varying interval differential equation driven by the observed process. Using the fact that the state, observation, and control processes possess lower and upper bounds, we have developed sets of (ordinary) differential equations that describe the behavior of the bounds of these processes. Using these differential equations, the interval control problem can be transformed into an equivalent ordinary control problem in which interval mathematics and extension principle of Moore are not required. Using variational arguments, we have developed the necessary conditions of optimality for the equivalent (ordinary) control problem. Finally, we present some numerical simulations to illustrate the effectiveness of the proposed control scheme.

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.

Stability and Control of a Thermoacoustic Device: The Rijke’s Tube

2014 ◽  
Author(s):  
Nejat Olgac ◽  
Umut Zalluhoglu ◽  
Ayhan S. Kammer
Keyword(s):  
Linear Time ◽  
Operating Conditions ◽  
Delayed Systems ◽  
Thermoacoustic Instability ◽  
Linear Time Invariant ◽  
Stability And Control ◽  
Characteristic Roots ◽  
Simplifying Assumptions ◽  
Prediction And Control ◽  
And Control

This study presents an intersection of two seemingly separate areas of research frontiers, “prediction and control of thermoacoustic instability” and “stability analysis of neutral-class linear-time-invariant (LTI) and time-delayed systems (TDS)”. The former is a coveted capability which has been elusive to the scientific community over 1½ centuries. Analytical capabilities have been limited due to the complex physics invoking the “combustion” phenomenon. Most available results rely on accumulated empirical knowledge. In this paper we consider a benchmark combustion test platform, which is known as Rijke’s tube. Its representation is simplified to an LTI neutral TDS, stability of which is assessed using a recent mathematical paradigm called the Cluster Treatment of Characteristic Roots (CTCR). CTCR provides a unique non-conservative and exhaustive stability declaration for a Rijke’s tube within the space of its parameters, naturally, under some simplifying assumptions. For those operating conditions which induce instability, we also propose a conventional and simple control strategy which can recover stability. This method is also analyzed using the CTCR paradigm for the first time.

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
Sign in / Sign up

Export Citation Format

Share Document