Control of Constrained Linear-Time Varying Systems via Kautz Parametrization of Model Predictive Control Scheme

Kautz parametrization of the Model Predictive Control (MPC) method has shown its ability to reduce the number of decision variables in Linear Time Invariant (LTI) systems. This paper devotes to extend Kautz network to be used in MPC Algorithm for linear time-varying systems. It is shown that Kautz network enables us to maintain a satisfactory performance while the number of decision variables are reduced considerably. Stability of the algorithm is studied under the framework of the optimal solution. The proposed method is validated by an illustrative example. In this regard, the performance of unconstrained systems as well as constrained ones is compared.

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Modeling of linear time-varying systems by linear time-invariant systems of lower order

IEEE Transactions on Automatic Control ◽

10.1109/tac.1973.1100207 ◽

1973 ◽

Vol 18 (1) ◽

pp. 50-52 ◽

Cited By ~ 9

Author(s):

H. Nosrati ◽

H. Meadows

Keyword(s):

Lower Order ◽

Linear Time ◽

Time Varying ◽

Linear Time Invariant ◽

Time Varying Systems ◽

Linear Time Invariant Systems ◽

Time Invariant

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Floquet Experimental Modal Analysis for System Identification of Linear Time-Periodic Systems

Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C ◽

10.1115/detc2007-34790 ◽

2007 ◽

Cited By ~ 8

Author(s):

Matthew S. Allen

Keyword(s):

System Identification ◽

Linear Time ◽

Time Varying ◽

Response Model ◽

State Matrix ◽

Linear Time Invariant ◽

Response Data ◽

Time Varying Systems ◽

Time Invariant ◽

Time Periodic

A variety of systems can be faithfully modeled as linear with coefficients that vary periodically with time or Linear Time-Periodic (LTP). Examples include anisotropic rotorbearing systems, wind turbines, satellite systems, etc… A number of powerful techniques have been presented in the past few decades, so that one might expect to model or control an LTP system with relative ease compared to time varying systems in general. However, few, if any, methods exist for experimentally characterizing LTP systems. This work seeks to produce a set of tools that can be used to characterize LTP systems completely through experiment. While such an approach is commonplace for LTI systems, all current methods for time varying systems require either that the system parameters vary slowly with time or else simply identify a few parameters of a pre-defined model to response data. A previous work presented two methods by which system identification techniques for linear time invariant (LTI) systems could be used to identify a response model for an LTP system from free response data. One of these allows the system’s model order to be determined exactly as if the system were linear time-invariant. This work presents a means whereby the response model identified in the previous work can be used to generate the full state transition matrix and the underlying time varying state matrix from an identified LTP response model and illustrates the entire system-identification process using simulated response data for a Jeffcott rotor in anisotropic bearings.

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Robust constrained model predictive control for linear time-varying systems with norm-bounded uncertainty

2008 5th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology ◽

10.1109/ecticon.2008.4600502 ◽

2008 ◽

Cited By ~ 1

Author(s):

Vorapon Kunnee ◽

David Banjerdpongchai

Keyword(s):

Model Predictive Control ◽

Predictive Control ◽

Linear Time ◽

Time Varying ◽

Time Varying Systems ◽

Constrained Model ◽

Bounded Uncertainty ◽

Constrained Model Predictive Control

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Data-driven model predictive control: closed-loop guarantees and experimental results

at - Automatisierungstechnik ◽

10.1515/auto-2021-0024 ◽

2021 ◽

Vol 69 (7) ◽

pp. 608-618

Author(s):

Julian Berberich ◽

Johannes Köhler ◽

Matthias A. Müller ◽

Frank Allgöwer

Keyword(s):

Model Predictive Control ◽

Predictive Control ◽

Closed Loop ◽

Linear Time ◽

Data Driven ◽

Practical Implementation ◽

Behavioral Systems ◽

Linear Time Invariant ◽

Tank System ◽

Time Invariant

Abstract We provide a comprehensive review and practical implementation of a recently developed model predictive control (MPC) framework for controlling unknown systems using only measured data and no explicit model knowledge. Our approach relies on an implicit system parametrization from behavioral systems theory based on one measured input-output trajectory. The presented MPC schemes guarantee closed-loop stability for unknown linear time-invariant (LTI) systems, even if the data are affected by noise. Further, we extend this MPC framework to control unknown nonlinear systems by continuously updating the data-driven system representation using new measurements. The simple and intuitive applicability of our approach is demonstrated with a nonlinear four-tank system in simulation and in an experiment.

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