Advances in the control of nonlinear systems

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At the core of nonlinear control theory lie two partial differential equations PDEs. One is a first-order evolution equation called the information state equation, which constitutes the dynamics of the controller. One can view this equation as a nonlinear dynamical system.

Adaptive sliding-mode control for nonlinear systems with uncertain parameters.

While the information state PDE determines the dynamics of the controller, the PDI determines the output of the controller. The authors explore the system theoretic significance of the PDI and present its gross structure.

These equations are only a few years old and their study is an expanding area of research. This book also emphasizes the theory effecting computer solvability of the information state equation, which at the outset looks numerically intractable, but which surprisingly is in many cases tractable. For example, the theory shows that careful initialization has a major influence on computer solvability.


The authors keep the book self-contained by using the appendices to help explain certain prerequisite material. The reader should have a basic knowledge of control theory, real analysis and differential equations, nonlinear operator theory, and nonlinear PDEs.

These techniques have dominated industrial design and commonly involved trial and error. The next major issue, how this extends to nonlinear systems, is what this book addresses.

Advances and Applications in Nonlinear Control Systems

What we present is an elegant general theory and corresponding formulas. Sign in Help View Cart.

Non-Linear Control system and Advance Topic in Control system Lec-01

Manage this Book. The proposed talk is dedicated to the presentation of some recent advances in this area using the so-called Takagi-Sugeno TS models also called time-varying polytopic model or quasi-LPV model. Over the last three decades, the TS modeling framework have attracted a great attention in the control community. After a period of skepticism, justified by the absence of clear demonstrations of these model properties, this type of model is now part of the almost standard tools of control engineers.

Indeed, Takagi-Sugeno modeling has proved its effectiveness in the study of nonlinear systems.

Advances in Control Systems, Volume 2

TS models can be understood as polytopic systems, where the blending between subsystems is time varying according to the so-called weighting functions. Thanks to the convexity of the blending and to the linearity of the subsystems defining the vertices, some results can be established for nonli-near systems, using tools borrowed from the linear theory.

The flexibility of that approach will be highlighted through its ability, during the control design, to take into account actuator saturations or, in the diagnosis framework, to estimate simultaneously the state and unknown time-varying parameter of the model.

Document type : Conference papers. Identifiers HAL Id : hal, version 1.

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