{"product_id":"semiconcave-functions-hamilton-jacobi-equations-and-optimal-control-paperback","title":"Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control - Paperback","description":"\u003cp\u003eby \u003cb\u003ePiermarco Cannarsa\u003c\/b\u003e (Author), \u003cb\u003eCarlo Sinestrari\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eSemiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This volume details the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations. The first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. \u003c\/p\u003e\u003ch3\u003eBack Jacket\u003c\/h3\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eSemiconcavity is a natural generalization of concavity that retains most of the good properties known in convex analysis, but arises in a wider range of applications. This text is the first comprehensive exposition of the theory of semiconcave functions, and of the role they play in optimal control and Hamilton-Jacobi equations.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eThe first part covers the general theory, encompassing all key results and illustrating them with significant examples. The latter part is devoted to applications concerning the Bolza problem in the calculus of variations and optimal exit time problems for nonlinear control systems. The exposition is essentially self-contained since the book includes all prerequisites from convex analysis, nonsmooth analysis, and viscosity solutions.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eA central role in the present work is reserved for the study of singularities. Singularities are first investigated for general semiconcave functions, then sharply estimated for solutions of Hamilton-Jacobi equations, and finally analyzed in connection with optimal trajectories of control systems.\u003c\/p\u003e \u003cp\u003e\u003c\/p\u003e \u003cp\u003eResearchers in optimal control, the calculus of variations, and partial differential equations will find this book useful as a state-of-the-art reference for semiconcave functions. Graduate students will profit from this text as it provides a handy--yet rigorous--introduction to modern dynamic programming for nonlinear control systems.\u003c\/p\u003e\u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 304\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.63 x 9.2 x 6.24 IN\u003c\/div\u003e\u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e September 14, 2004\u003c\/div\u003e","brand":"Books by splitShops","offers":[{"title":"Default Title","offer_id":42722483765311,"sku":"9780817643362","price":174.94,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0105\/8226\/1823\/files\/0735ddc4805161439ff41ade18cac887.webp?v=1765095911","url":"https:\/\/dhlswag.com\/products\/semiconcave-functions-hamilton-jacobi-equations-and-optimal-control-paperback","provider":"BBB","version":"1.0","type":"link"}