By Randy A. Freeman

ISBN-10: 0817639306

ISBN-13: 9780817639303

This booklet provides advances within the conception and layout of strong nonlinear keep an eye on structures. within the first a part of the publication, the authors supply a unified framework for state-space and Lyapunov innovations via combining innovations from set-valued research, Lyapunov balance conception, and online game thought. inside this unified framework, the authors then increase a number of keep an eye on layout equipment compatible for platforms defined through low-order nonlinear usual differential equations. Emphasis is put on international controller designs, that's, designs for the total area of version validity. simply because linear idea offers good with neighborhood process habit (except for serious circumstances within which Jacobian linearization fails), the authors concentrate on attaining robustness and function for giant deviations from a given operation condition.

The function of the e-book is to summarize Lyapunov layout suggestions for nonlinear platforms and to elevate very important concerns touching on large-signal robustness and function. The authors were the 1st to deal with a few of these concerns, they usually document their findings during this textual content. for instance, they determine power resources of over the top keep an eye on attempt in Lyapunov layout thoughts and convey how such attempt will be significantly reduced.

The researcher who needs to go into the sphere of sturdy nonlinear keep watch over may use this e-book as a resource of latest learn themes. For these already lively within the box, the booklet may well function a connection with a up to date physique of vital paintings. eventually, the layout engineer confronted with a nonlinear keep an eye on challenge will enjoy the ideas provided here.

*"The textual content is essentially self-contained. The authors provide all beneficial definitions and provides a accomplished advent. simply the main easy wisdom of nonlinear research and layout instruments is needed, together with Lyapunov balance idea and optimum keep an eye on. The authors additionally supply a overview of set-valued maps for these readers who're no longer conversant in set-valued research. The ebook is meant for graduate scholars and researchers on top of things idea, serving as either a precis of modern effects and a resource of recent learn difficulties. within the opinion of this reviewer the authors do achieve achieving those objectives."***— Mathematical Reviews**

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**Extra info for Robust Nonlinear Control Design: State-Space and Lyapunov Techniques**

**Example text**

1 is to construct an admissible control such that the solutions to E are RGUAS-ft for some residual set f~. 2 The system E is r o b u s t l y a s y m p t o t i c a l l y stabiliz- a b l e when there exists an admissible control such that the solutions to E are RGUAS. The system E is r o b u s t l y p r a c t i c a l l y s t a b i l i z a b l e when for every c > 0 there exists an admissible control and a compact set ft C 2r satisfying 0 E f~ C c B such that the solutions to E are RGUAS-fL The system E is r o b u s t l y s t a b i l i z a b l e when there exists an admissible control and a compact set f~ C 2( satisfying 0 E ~ such that the solutions to E are RGUAS-fL Clearly robust asymptotic stabilizability implies robust practical stabilizability, which in turn implies robust stabilizability.

1 Upper and lower semicontinuity When X and Z are topological spaces, we can define the continuity of a set-valued map F : X ",~ Z. There are two common ways to generalize the definition of the continuity of a single-valued function to that of a set-valued map: 18 C H A P T E R 2. 1 A set-valued map F : X -,~ Z is u p p e r s e m i c o n t i n u ous (usc) a t x E X when for every open set U C Z such that F ( x ) C U there exists a neighborhood V of x such that F ( V ) C U. We say that F is u p p e r s e m i c o n t i n u o u s (usc) when it is usc at every point in X .

Next suppose G is usc with compact values, and let K C Z be closed. 12 and the continuity o f f that H : X - , ~ W d e f i n e d b y H(x) := {w E G(x) : f ( x , w ) E K } is usc. 3 t h a t F is u s c . 9 Conversely, a parameterization of a set-valued map F : X ~-~ Z is a function f : X x W - - ~ Z such that F(x) = f ( x , W ) for all x C X. 5. 22 Let X be a metric space, and let B denote the closed unit ball of 1Rn. , 11~n is continuous with nonempty compact convez values, then there exists a continuous function f : X x 1R'~ --+ j~n such that F(x) = f(x, t3) for all x e X .

### Robust Nonlinear Control Design: State-Space and Lyapunov Techniques by Randy A. Freeman

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