For nonlinear dynamical systems, which represent the majority of real devices, any study of stability requires the investigation of the domain of attraction of an equilibrium point, i.e. the set of initial conditions ...
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ISBN:
(数字)9780857299598
ISBN:
(纸本)9780857299581
For nonlinear dynamical systems, which represent the majority of real devices, any study of stability requires the investigation of the domain of attraction of an equilibrium point, i.e. the set of initial conditions from which the trajectory of the system converges to equilibrium. Unfortunately, both estimating and attempting to control the domain of attraction are very difficult problems, because of the complex relationship of this set with the model of the system. Domain of Attraction addresses the estimation and control of the domain of attraction of equilibrium points via SOS programming, i.e. optimization techniques based on the sum of squares of polynomials (SOS) that have been recently developed and that amount to solving convex problems with linear matrix inequality constraints. A unified framework for addressing these issues is presented for in various cases depending on the nature of the nonlinear systems considered, including the cases of polynomial, non-polynomial, certain and uncertain systems. The methods proposed are illustrated various example systems such as electric circuits, mechanical devices, and nuclear plants. Domain of Attraction also deals with related problems that can be considered within the proposed framework, such as characterizing the equilibrium points and bounding the trajectories of nonlinear systems, and offers a concise and simple description of the main features of SOS programming, which can be used for general purpose in research and teaching.
AfterasurveypaperbyUtkininthelate1970s,slidingmodecontrolmeth- ologies emerged as an e?ective tool to tackle uncertainty and disturbances which are inevitable in most of the practical systems. Sliding mode control is ...
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ISBN:
(数字)9783642034480
ISBN:
(纸本)9783642034473
AfterasurveypaperbyUtkininthelate1970s,slidingmodecontrolmeth- ologies emerged as an e?ective tool to tackle uncertainty and disturbances which are inevitable in most of the practical systems. Sliding mode control is a particular class of variable structure control which was introduced by Emel’yanov and his colleagues. The design paradigms of sliding mode c- trol has now become a mature design technique for the design of robust c- troller of uncertain system. In sliding mode technique, the state trajectory of the system is constrained on a chosen manifold (or within some neighb- hood thereof) by an appropriatecontrolaction. This manifold is also called a switching surface or a sliding surface. During sliding mode, system dynamics is governed by the chosen manifold which results in a well celebrated inva- ance property towards certain classes of disturbance and model mismatches. The purpose of this monograph is to give a di?erent dimension to sl- ing surface design to achieve high performance of the system. Design of the switching surface is vital because the closed loop dynamics is governed by the parameters of the sliding surface. Therefore sliding surface should be - signed to meet the closed loop speci?cations. Many systems demand high performance with robustness. To address this issue of achieving high perf- mance with robustness, we propose nonlinear surfaces for di?erent classes of systems. The nonlinear surface is designed such that it changes the system’s closed-loop damping ratio from its initial low value to a ?nal high value.
This volume providesa broad picture of the analysis and control of nonlinear systems for scientistsand engineers with an interest in the interdisciplinary field of systems andcontrol theory. The reader will benefit fr...
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ISBN:
(数字)9783319303574
ISBN:
(纸本)9783319303567
This volume provides
a broad picture of the analysis and control of nonlinear systems for scientists
and engineers with an interest in the interdisciplinary field of systems and
control theory. The reader will benefit from the expert participants’ ideas on important
open problems with contributions that represent the state of the art in
nonlinear control.
丛书名：
lecture notes in control and information sciences
1000年
is devoted to a single question from Linear Systems Theory: "When is it possible to find a controller that stabilizes a finite family of systems?", known as the Simultaneous Stabilization Question. This ques...
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ISBN:
(数字)9783540393214
ISBN:
(纸本)9783540198628
is devoted to a single question from Linear Systems Theory: "When is it possible to find a controller that stabilizes a finite family of systems?", known as the Simultaneous Stabilization Question. This question is satisfactorily solved when the number of systems is limited to two but is open for three or more systems. This constitutes one of the important, longstanding open problems in Linear Systems Theory. Dr. Blondel reviews partial answers and discusses partial answers with equivalent formulations of the problem. Particular emphasis is placed on interlacement conditions. The parity and the interlacing conditions are presented in a clear and unified framework. The final chapter "proves" the latest research progress and shows that, contrary to most of the questions in Linear Systems Theory, there exists no necessary and sufficient conditions for simultaneous stabilization of three or more systems that involve only the coefficients of the systems and a combination of rational operations.
丛书名：
lecture notes in control and information sciences
1000年
Industrial processes such as long-wall coal cutting and me-tal rolling, together with certain areas of 2D signal andimage processing, exhibit a repetitive, or multipass struc-ture characterized by a series of sw...
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ISBN:
(数字)9783540469995
ISBN:
(纸本)9783540552642
Industrial processes such as long-wall coal cutting and me-
tal rolling, together with certain areas of 2D signal and
image processing, exhibit a repetitive, or multipass struc-
ture characterized by a series of sweeps of passes through a
known set of dynamics. The output, or pass profile, produced
on each pass explicitly contributes to that produced on the
text. This interpass interaction can lead to the growth of
oscillations, and hence a form of instability, in the se-
quence of pass profiles which require control strategies
that explicitly incorporate the essential repetitive struc-
ture of the process in their decision making. This monograph
is unique in developing the new techniques necessary for sy-
stematic control systems design in the form of a stability
theory and computationally feasible stability tests based on
finite simulations and polynomial analysis. Its development
requires a basic knowledge of linear frequency domain and
state-space theory and a knowledge of basic functional ana-
lysis would be beneficial. The text is aimed at researchers
in the area of control and systems theory and should also be
of interest to those working in the related area of signal
and image processing.
丛书名：
lecture notes in control and information sciences
1000年
A survey is given on the state of the art in theory and numerical solution of general autonomous linear quadratic optimal control problems (continuous and discrete) with differential algebraic equation constraints. It...
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ISBN:
(数字)9783540474821
ISBN:
(纸本)9783540541707
A survey is given on the state of the art in theory and numerical solution of general autonomous linear quadratic optimal control problems (continuous and discrete) with differential algebraic equation constraints. It incorporates the newest developments on differential algebraic equations, Riccati equations and invariant subspace problems. In particular, it gives a decision chart of numerical methods, that can be used to determine the right numerical method according to special properties of the problem. The book closes a gap between mathematical theory, numerical solution and engineering application. The mathematical tools are kept as basic as possible in order to address the different groups of readers, mathematicians and engineers.
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