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TitleMathematical Control Theory [electronic resource] / edited by J. Baillieul, J. C. Willems
ImprintNew York, NY : Springer New York : Imprint: Springer, 1999
Connect tohttp://dx.doi.org/10.1007/978-1-4612-1416-8
Descript XXXII, 360 p. online resource

CONTENT

1 Path Integrals and Stability -- 1.1 Introduction -- 1.2 Path Independence -- 1.3 Positivity of Quadratic Differential Forms -- 1.4 Lyapunov Theory for High-Order Differential Equations -- 1.5 The Bezoutian -- 1.6 Dissipative Systems -- 1.7 Stability of Nonautonomous Systems -- 1.8 Conclusions -- 1.9 Appendixes -- 2 The Estimation Algebra of Nonlinear Filtering Systems -- 2.1 Introduction -- 2.2 The Filtering Model and Background -- 2.3 Starting from the Beginning -- 2.4 Early Results on the Homomorphism Principle -- 2.5 Automorphisms that Preserve Estimation Algebras -- 2.6 BM Estimation Algebra -- 2.7 Structure of Exact Estimation Algebra -- 2.8 Structure of BM Estimation Algebras -- 2.9 Connection with Metaplectic Groups -- 2.10 Wei-Norman Representation of Filters -- 2.11 Perturbation Algebra and Estimation Algebra -- 2.12 Lie-Algebraic Classification of Maximal Rank Estimation Algebras -- 2.13 Complete Characterization of Finite-Dimensional Estimation Algebras -- 2.14 Estimation Algebra of the Identification Problem -- 2.15 Solutions to the Riccati P.D.E -- 2.16 Filters with Non-Gaussian Initial Conditions -- 2.17 Back to the Beginning -- 2.18 Acknowledgement -- 3 Feedback Linearization -- 3.1 Introduction -- 3.2 Linearization of a Smooth Vector Field -- 3.3 Linearization of a Smooth Control System by Change-of-State Coordinates -- 3.4 Feedback Linearization -- 3.5 Input-Output Linearization -- 3.6 Approximate Feedback Linearization -- 3.7 Normal Forms of Control Systems -- 3.8 Observers with Linearizable Error Dynamics -- 3.9 Nonlinear Regulation and Model Matching -- 3.10 Backstepping -- 3.11 Feedback Linearization and System Inversion -- 3.12 Conclusion -- 4 On the Global Analysis of Linear Systems -- 4.1 Introduction -- 4.2 The Geometry of Rational Functions -- 4.3 Group Actions and the Geometry of Linear Systems -- 4.4 The Geometry of Inverse Eigenvalue Problems -- 4.5 Nonlinear Optimization on Spaces of Systems -- 5 Geometry and Optimal Control -- 5.1 Introduction -- 5.2 From Queen Dido to the Maximum Principle -- 5.3 Invariance, Covariance, and Lie Brackets -- 5.4 The Maximum Principle -- 5.5 The Maximum Principle as a Necessary Condition for Set Separation -- 5.6 Weakly Approximating Cones and Transversality -- 5.7 A Streamlined Version of the Classical Maximum Principle -- 5.8 Clarkeโ{128}{153}s Nonsmooth Version and the ?ojasiewicz Improvement -- 5.9 Multidifferentials, Flows, and a General Version of the Maximum Principle -- 5.10 Three Ways to Make the Maximum Principle Intrinsic on Manifolds -- 5.11 Conclusion -- 6 Languages, Behaviors, Hybrid Architectures, and Motion Control -- 6.1 Introduction -- 6.2 MDLe: A Language for Motion Control -- 6.3 Hybrid Architecture -- 6.4 Application of MDLe to Path Planning with Nonholonomic Robots -- 6.5 PNMR: Path Planner for Nonholonomic Mobile Robots -- 6.6 Conclusions -- 7 Optimal Control, Geometry, and Mechanics -- 7.1 Introduction -- 7.2 Variational Problems with Constraints and Optimal Control -- 7.3 Invariant Optimal Problems on Lie Groups -- 7.4 Sub-Riemannian Spheresโ{128}{148}The Contact Case -- 7.5 Sub-Riemannian Systems on Lie Groups -- 7.6 Heavy Top and the Elastic Problem -- 7.7 Conclusion -- 8 Optimal Control, Optimization, and Analytical Mechanics -- 8.1 Introduction -- 8.2 Modeling Variational Problems in Mechanics and Control -- 8.3 Optimization -- 8.4 Optimal Control Problems and Integrable Systems -- 9 The Geometry of Controlled Mechanical Systems -- 9.1 Introduction -- 9.2 Second-Order Generalized Control Systems -- 9.3 Flat Systems and Systems with Flat Inputs -- 9.4 Averaging Lagrangian and Hamiltonian Systems with Oscillatory Inputs -- 9.5 Stability and Flatness in Mechanical Systems with Oscillatory Inputs -- 9.6 Concluding Remarks


Mathematics Calculus of variations Mathematics Calculus of Variations and Optimal Control; Optimization



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