Tangential Nevanlinna-Pick interpolation for strong stabilization of MIMO distributed parameter systems

We study the problem of finding stable controllers that stabilize a multi-input multi-output distributed parameter system while simultaneously reducing the sensitivity of the system. The plants we consider have finitely many unstable transmission zeros, but they can possess infinitely many unstable poles. Using the tangential Nevanlinna-Pick interpolation with boundary conditions, we obtain both upper and lower bounds of the minimum sensitivity that can be achieved by stable controllers. We also derive a method to find stable controllers for sensitivity reduction. In addition, we apply the proposed method to a repetitive control system. © 2012 IEEE

Sensitivity reduction by stable controllers for MIMO infinite dimensional systems via the tangential nevanlinna-pick interpolation

Cataloged from PDF version of article.We study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an MIMO infinite dimensional system. The systems we consider have finitely many simple transmission zeros in (C) over bar (+), but they are allowed to possess infinitely many poles in C+. We compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential Nevanlinna-Pick interpolation. We also obtain stable controllers attaining such an upper bound. To illustrate the results, we discuss a repetitive control system as an application of the proposed method

Sensitivity reduction by stable controllers for MIMO infinite dimensional systems via the tangential nevanlinna-pick interpolation

We study the problem of finding a stable stabilizing controller that satisfies a desired sensitivity level for an MIMO infinite dimensional system. The systems we consider have finitely many simple transmission zeros in C +, but they are allowed to possess infinitely many poles in C +. We compute both upper and lower bounds of the minimum sensitivity achievable by a stable controller via the tangential Nevanlinna-Pick interpolation. We also obtain stable controllers attaining such an upper bound. To illustrate the results, we discuss a repetitive control system as an application of the proposed method. © 1963-2012 IEEE

Sensitivity reduction by strongly stabilizing controllers for MIMO distributed parameter systems

This note investigates a sensitivity reduction problem by stable stabilizing controllers for a linear time-invariant multi-input multioutput distributed parameter system. The plant we consider has finitely many unstable zeros, which are simple and blocking, but can possess infinitely many unstable poles. We obtain a necessary condition and a sufficient condition for the solvability of the problem, using the matrix Nevanlinna-Pick interpolation with boundary conditions. We also develop a necessary and sufficient condition for the solvability of the interpolation problem, and show an algorithm to obtain the solutions. Our method to solve the interpolation problem is based on the Schur-Nevanlinna algorithm. © 2012 IEEE

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Approximation, analysis and control of large-scale systems - Theory and Applications

This work presents some contributions to the fields of approximation, analysis and control of large-scale systems. Consequently the Thesis consists of three parts. The first part covers approximation topics and includes several contributions to the area of model reduction. Firstly, model reduction by moment matching for linear and nonlinear time-delay systems, including neutral differential time-delay systems with discrete-delays and distributed delays, is considered. Secondly, a theoretical framework and a collection of techniques to obtain reduced order models by moment matching from input/output data for linear (time-delay) systems and nonlinear (time-delay) systems is presented. The theory developed is then validated with the introduction and use of a low complexity algorithm for the fast estimation of the moments of the NETS-NYPS benchmark interconnected power system. Then, the model reduction problem is solved when the class of input signals generated by a linear exogenous system which does not have an implicit (differential) form is considered. The work regarding the topic of approximation is concluded with a chapter covering the problem of model reduction for linear singular systems. The second part of the Thesis, which concerns the area of analysis, consists of two very different contributions. The first proposes a new "discontinuous phasor transform" which allows to analyze in closed-form the steady-state behavior of discontinuous power electronic devices. The second presents in a unified framework a class of theorems inspired by the Krasovskii-LaSalle invariance principle for the study of "liminf" convergence properties of solutions of dynamical systems. Finally, in the last part of the Thesis the problem of finite-horizon optimal control with input constraints is studied and a methodology to compute approximate solutions of the resulting partial differential equation is proposed.Open Acces

Mathematical and Numerical Aspects of Dynamical System Analysis

From Preface: This is the fourteenth time when the conference “Dynamical Systems: Theory and Applications” gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled “Dynamical Systems” with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled “Dynamical Systems in Theoretical Perspective” and “Dynamical Systems in Applications”