Identifiability Issues for Parameter-Varying and Multidimensional Linear Systems

1997 ◽  
Author(s):  
Lawton H. Lee ◽  
Kameshwar Poolla
Keyword(s):  
Linear Time ◽  
Model Structure ◽  
Constant Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Estimation Algorithms ◽  
Finite Dimensional ◽  
Parameter Varying ◽  
Value Decomposition ◽  
Time Invariant

Abstract This paper considers the identifiability of state space models for a system that is expressed as a linear fractional transformation (LFT): a constant matrix (containing identified parameters) in feedback with a finite-dimensional, block-diagonal (“structured”) linear operator. This model structure can represent linear time-invariant, linear parameter-varying, uncertain, and multidimensional systems. Families of input-output equivalent realizations are characterized as manifolds in the parameter space whose tangent spaces — and orthogonal complements — can be obtained via singular value decomposition. As illustrated by a numerical example, restricting iterative parameter estimation algorithms (e.g., maximum-likelihood with nonlinear programming) to the orthogonal directions offers significant computational advantages.

Determination of Different Polytopic Models of the Prototypical Aeroelastic Wing Section by TP Model Transformation

2006 ◽  
Vol 10 (4) ◽  
pp. 486-493 ◽  
Author(s):  
Péter Baranyi ◽  
◽  
Zoltán Petres ◽  
Péter L. Várkonyi ◽  
Péter Korondi ◽  
...  
Keyword(s):  
Model Transformation ◽  
Linear Time ◽  
Convex Combination ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Wing Section ◽  
Parameter Varying ◽  
Time Invariant

The Tensor Product (TP) model transformation is a recently proposed technique for transforming given Linear Parameter Varying (LPV) models into polytopic model form, namely, to parameter varying convex combination of Linear Time Invariant (LTI) models. The main advantage of the TP model transformation is that the Linear Matrix Inequality (LMI) based control design frameworks can immediately be applied to the resulting polytopic models to yield controllers with tractable and guaranteed performance. The effectiveness of the LMI design depends on the type of the convex combination in the polytopic model. Therefore, the main objective of this paper is to study how the TP model transformation is capable of determining different types of convex hulls of the LTI models. The study is conducted trough the example of the prototypical aeroelastic wing section.

scholarly journals Feedback control of linear systems with optimal sensor and actuator selection

2020 ◽  
pp. 107754632093983
Author(s):  
Taranjitsingh Singh ◽  
Massimo De Mauri ◽  
Wilm Decré ◽  
Jan Swevers ◽  
Goele Pipeleers
Keyword(s):  
Feedback Control ◽  
Semidefinite Programming ◽  
Optimization Problem ◽  
Linear Time ◽  
Linear Parameter ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Combined Design ◽  
Parameter Varying ◽  
Time Invariant

This article demonstrates a combined [Formula: see text] feedback control design for linear time-invariant and linear parameter-varying systems and optimal sensors and actuator selection. The combined design problem is systematically constructed as a mixed Boolean semidefinite programming optimization problem. We impose Big-M reformulations to the non-deterministic polynomial-time-hard coupled problem to be solved as a convex optimization problem using the branch and bound algorithm. The combined design of dynamic output feedback control along with optimal actuator selection for a linear time-invariant seismic rejection controller design serves as an application for validation by simulation. In addition, active vibration control of a smart composite plate along with optimal sensor and actuator selection validates the developed approach for linear parameter-varying controller synthesis. On comparing this approach with exhaustive search, it is observed that mixed Boolean semidefinite programming approaches have faster computation time, and comparing with the iterative reweighted ℓ1 norm algorithm and mixed Boolean semidefinite programming using outer approximations, mixed Boolean semidefinite programming yields a global solution.

New Results on Linear Time Invariant and Parameter Varying Static Output Feedback

2008 ◽  
Vol 31 (5) ◽  
pp. 1230-1238 ◽  
Author(s):  
Ricardo S. Sanchez-Pena ◽  
Phalguna Kumar Rachinayani ◽  
Dario H. Baldelli
Keyword(s):  
Output Feedback ◽  
Linear Time ◽  
Static Output Feedback ◽  
Linear Time Invariant ◽  
Parameter Varying ◽  
Time Invariant ◽  
Static Output

Reduction in the Number of Gain-Scheduling Parameters Using Dimensional Transformation

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Haftay Hailu ◽  
Sean Brennan
Keyword(s):  
Linear Time ◽  
Gain Scheduling ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Lti System ◽  
Gain Scheduled Controller ◽  
Parameter Dependent ◽  
Time Invariant ◽  
Linear Parameter Varying System ◽  
Gain Scheduled

A method is presented that can often reduce the number of scheduling parameters for gain-scheduled controller implementation by transformation of the system representation using parameter-dependent dimensional transformations. In some cases, the reduction in parameter dependence is so significant that a linear parameter-varying system can be transformed to an equivalent linear time invariant (LTI) system, and a simple example of this is given. A general analysis of the parameter-dependent dimensional transformation using a matrix-based approach is then presented. It is shown that, while some transformations simplify gain scheduling, others may increase the number of scheduling parameters. This work explores the mathematical conditions causing an increase or decrease in varying parameters resulting from a given transformation, thereby allowing one to seek transformations that most reduce the number of gain-scheduled parameters in the controller synthesis step.

scholarly journals Quadratic Stabilization of LPV System by an LTI Controller Based on ILMI Algorithm

2007 ◽  
Vol 2007 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Xie
Keyword(s):  
Controller Design ◽  
Linear Time ◽  
Admissible Solution ◽  
Linear Matrix ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Lpv Control ◽  
Lpv System ◽  
Time Invariant ◽  
Iterative Linear Matrix Inequality

A linear time-invariant (LTI) output feedback controller is designed for a linear parameter-varying (LPV) control system to achieve quadratic stability. The LPV system includes immeasurable dependent parameters that are assumed to vary in a polytopic space. To solve this control problem, a heuristic algorithm is proposed in the form of an iterative linear matrix inequality (ILMI) formulation. Furthermore, an effective method of setting an initial value of the ILMI algorithm is also proposed to increase the probability of getting an admissible solution for the controller design problem.

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