Ebook: Algebraic and Geometric Methods in Nonlinear Control Theory

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point"of a Pin'. van GuIik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non­ trivially) in regional and theoretical economics; algebraic geometry interacts with physics; ihe Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras ·are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

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Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Realization Theory for Nonlinear Systems; Three Approaches....Pages 3-31
The Local Realization of Generating Series of Finite Lie Rank....Pages 33-43
Realizations of Polynomial Systems....Pages 45-54
Symmetries and Local Controllability....Pages 55-75
The Intrinsic Geometry of Dynamic Observations....Pages 77-87
Design of Nonlinear Observers by a Two-Step-Transformation....Pages 89-98
Front Matter....Pages 99-99
On the Input-Output Decoupling of Nonlinear Systems....Pages 101-119
Control of Nonlinear Systems Via Dynamic State-Feedback....Pages 121-145
A Classification of Nonlinear Systems Based on the Invariant Subdistribution Algorithm....Pages 147-157
Asymptotic Expansions, Root-Loci and the Global Stability of Nonlinear Feedback Systems....Pages 159-179
Everything You Always Wanted to Know about Linearization....Pages 181-226
Feedback Linearization and Simultaneous Output Block Decoupling of Nonlinear Systems....Pages 227-241
Global Feedback Linearizability of Locally Linearizable Systems....Pages 243-256
Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Control Systems....Pages 257-284
The Extended-Linearization Approach for Nonlinear Systems Problems....Pages 285-309
About the Local Linearization of Nonlinear Systems....Pages 311-322
Front Matter....Pages 323-323
Envelopes, Conjugate Points, and Optimal Bang-Bang Extremals....Pages 325-346
Geometry of the Optimal Control....Pages 347-369
Volterra Series and Optimal Control....Pages 371-387
Optimal Control and Hamiltonian Input-Output Systems....Pages 389-407
Front Matter....Pages 409-409
Nonlinear Systems in Discrete Time....Pages 411-430
Local Input-Output Decoupling of Discrete Time Nonlinear Systems....Pages 431-439
Orbit Theorems and Sampling....Pages 441-483
Front Matter....Pages 485-485
An Infinite Dimensional Variational Problem Arising in Estimation Theory....Pages 487-498
Iterated Stochastic Integrals in Non Linear Control Theory....Pages 499-510
Approximation of Nonlinear Systems by Bilinear Ones....Pages 511-520
Front Matter....Pages 521-521
Feedback Linearization Techniques in Robotics and Power Systems....Pages 523-543
C.A.D. for Nonlinear Systems Decoupling, Perturbations Rejection and Feedback Linearization with Applications to the Dynamic Control of a Robot Arm....Pages 545-572
A Nonlinear Feedback Control Law for Attitude Control....Pages 573-595
Identification of Different Discrete Models of Continuous Non-Linear Systems. Application to Two Industrial Pilot Plants.....Pages 597-621
Bang-Bang Solutions for a Class of Problems Arising in Thermal Control....Pages 623-632
Back Matter....Pages 633-642

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Content:
Front Matter....Pages i-xii
Front Matter....Pages 1-1
Realization Theory for Nonlinear Systems; Three Approaches....Pages 3-31
The Local Realization of Generating Series of Finite Lie Rank....Pages 33-43
Realizations of Polynomial Systems....Pages 45-54
Symmetries and Local Controllability....Pages 55-75
The Intrinsic Geometry of Dynamic Observations....Pages 77-87
Design of Nonlinear Observers by a Two-Step-Transformation....Pages 89-98
Front Matter....Pages 99-99
On the Input-Output Decoupling of Nonlinear Systems....Pages 101-119
Control of Nonlinear Systems Via Dynamic State-Feedback....Pages 121-145
A Classification of Nonlinear Systems Based on the Invariant Subdistribution Algorithm....Pages 147-157
Asymptotic Expansions, Root-Loci and the Global Stability of Nonlinear Feedback Systems....Pages 159-179
Everything You Always Wanted to Know about Linearization....Pages 181-226
Feedback Linearization and Simultaneous Output Block Decoupling of Nonlinear Systems....Pages 227-241
Global Feedback Linearizability of Locally Linearizable Systems....Pages 243-256
Global Aspects of Linearization, Equivalence to Polynomial Forms and Decomposition of Nonlinear Control Systems....Pages 257-284
The Extended-Linearization Approach for Nonlinear Systems Problems....Pages 285-309
About the Local Linearization of Nonlinear Systems....Pages 311-322
Front Matter....Pages 323-323
Envelopes, Conjugate Points, and Optimal Bang-Bang Extremals....Pages 325-346
Geometry of the Optimal Control....Pages 347-369
Volterra Series and Optimal Control....Pages 371-387
Optimal Control and Hamiltonian Input-Output Systems....Pages 389-407
Front Matter....Pages 409-409
Nonlinear Systems in Discrete Time....Pages 411-430
Local Input-Output Decoupling of Discrete Time Nonlinear Systems....Pages 431-439
Orbit Theorems and Sampling....Pages 441-483
Front Matter....Pages 485-485
An Infinite Dimensional Variational Problem Arising in Estimation Theory....Pages 487-498
Iterated Stochastic Integrals in Non Linear Control Theory....Pages 499-510
Approximation of Nonlinear Systems by Bilinear Ones....Pages 511-520
Front Matter....Pages 521-521
Feedback Linearization Techniques in Robotics and Power Systems....Pages 523-543
C.A.D. for Nonlinear Systems Decoupling, Perturbations Rejection and Feedback Linearization with Applications to the Dynamic Control of a Robot Arm....Pages 545-572
A Nonlinear Feedback Control Law for Attitude Control....Pages 573-595
Identification of Different Discrete Models of Continuous Non-Linear Systems. Application to Two Industrial Pilot Plants.....Pages 597-621
Bang-Bang Solutions for a Class of Problems Arising in Thermal Control....Pages 623-632
Back Matter....Pages 633-642
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