LEADER 05377nam 2200697Ia 450 001 9910822837203321 005 20240313221917.0 010 $a981-277-607-9 035 $a(CKB)1000000000766948 035 $a(EBL)1193222 035 $a(SSID)ssj0000518211 035 $a(PQKBManifestationID)12215469 035 $a(PQKBTitleCode)TC0000518211 035 $a(PQKBWorkID)10508919 035 $a(PQKB)10390602 035 $a(MiAaPQ)EBC1193222 035 $a(WSP)00001419 035 $a(Au-PeEL)EBL1193222 035 $a(CaPaEBR)ebr10688097 035 $a(CaONFJC)MIL491692 035 $a(OCoLC)826660606 035 $a(EXLCZ)991000000000766948 100 $a20080417d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aGeometric control and nonsmooth analysis $ein honor of the 73rd birthday of H. Hermes and of the 71st birthday of R.T. Rockafellar /$fedited by Fabio Ancona ... [et al.] 205 $a1st ed. 210 $aSingapore $cHackensack, NJ $cWorld Scientific$dc2008 215 $a1 online resource (376 p.) 225 1 $aSeries on advances in mathematics for applied sciences ; v. 76 300 $aDescription based upon print version of record. 311 $a981-277-606-0 320 $aIncludes bibliographical references and index. 327 $aPreface; Conference Committees; CONTENTS; Multiscale Singular Perturbations and Homogenization of Optimal Control Problems 0. Alvarez, M. Bardi and C. Marchi; 1. Introduction; 2. Standing assumptions; 3. Ergodicity, stabilization and the effective problem; 3.1. Ergodicity and the effective Hamiltonian; 3.2. Stabilization and the eflective initial data; 4. Regular perturbation of singular perturbation problems; 5. Singular perturbations with multiple scales; 5.1. The three scale case; 5.2. The general case; 6. Iterated homogenization for coercive equations; 7. Examples 327 $a7.1. Singular perturbation of a differential game7.2. Homogenization of a deterministic optimal control problem; 7.3. Multiscale singular perturbation under a nonresonance condition; References; Patchy Feedbacks for Stabilization and Optimal Control: General Theory and Robustness Properties F. Ancona and A. Bressan; 1. Introduction; 2. Patchy vector fields and patchy feedbacks; 3. Stabilizing feedback controls; 4. Nearly optimal patchy feedbacks; 5. Robustness; 6. Stochastic perturbations; References; Sensitivity of Control Systems with Respect to Measure- Valued Coefficients Z. Artstein 327 $a1. Introduction2. Standing hypotheses; 3. The chattering parameters model; 4. The Prohorov metric; 5 . Sensitivity for relaxed controls; 6. A matching result; 7. Sensitivity for chattering parameters; 8. Remarks and examples; References; Systems with Continuous Time and Discrete Time Components A. Bacciotti; 1. Introduction; 2. Description of the model; 3. Oscillatory systems: an example; 4. Stability notions; 5. A sufficient condition for stability; 6. Sufficient conditions for asymptotic stability; References; A Review on Stability of Switched Systems for Arbitrary Switchings U. Boscain 327 $a1. Introduction2. General properties of multilinear systems; 3. Common Lyapunov functions; 4. Two-dimensional bilinear systems; 4.1. The diagonalisable case; 4.1.1. Normal forms in the diagonalizable case; 4.1.2. Stability conditions in the diagonalizable case; 4.2. The nondiagonalizable case; 4.2.1. Normal forms in the nondiagonalizable case; 4.2.2. Stability conditions in the nondiagonalizable case; 5. An open problem; Acknowledgments; References; Regularity Properties of Attainable Sets under State Constraints P. Cannarsa, M. Castelpietra and P. Cardaliaguet; 1. Introduction 327 $a2. Maximum principle under state constraints3. Perimeter estimates for the attainable set; References; A Generalized Hopf-Lax Formula: Analytical and Approxi- mations Aspects I. Capuzzo Dolcetta; 1. Introduction; 2. A generalized eikonal equation; 3. The generalized Hopf-Lax formula; 4. The Hopf-Lax formula for the Heisenberg Hamiltonian; 4.1. A singular perturbation problem on the Heisenberg group; 4.2. Convergence rate of finite diflerences approximation; References; Regularity of Solutions to One-Dimensional and Multi- Dimensional Problems in the Calculus of Variations F.H. Clarke 327 $a1. Introduction 330 $aThe aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions. 410 0$aSeries on advances in mathematics for applied sciences ; v. 76. 606 $aControl theory$xResearch 606 $aNonsmooth optimization$xResearch 606 $aSystems engineering$xResearch 615 0$aControl theory$xResearch. 615 0$aNonsmooth optimization$xResearch. 615 0$aSystems engineering$xResearch. 676 $a515/.642 701 $aAncona$b Fabio$f1964-$0738757 701 $aHermes$b Henry$f1933-$014388 701 $aRockafellar$b R. Tyrrell$f1935-$06371 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910822837203321 996 $aGeometric control and nonsmooth analysis$93958533 997 $aUNINA