This outstanding reference presents current, state-of-the-art research on importantproblems of finite-dimensional nonlinear optimal control and controllability theory. Itpresents an overview of a broad variety of new techniques useful in solving classicalcontrol theory problems.Written and edited by renowned mathematicians at the forefront of research in thisevolving field, Nonlinear Controllability and Optimal Control providesdetailed coverage of the construction of solutions of differential inclusions by means ofdirectionally continuous sections ... Lie algebraic conditions for local controllability... the use of the Campbell-Hausdorff series to derive properties of optimal trajectories... the Fuller phenomenon ... the theory of orbits ... and more.Containing more than 1,300 display equations, this exemplary, instructive reference is aninvaluable source for mathematical researchers and applied mathematicians, electrical andelectronics, aerospace, mechanical, control, systems, and computer engineers, and graduatestudents in these disciplines .
Table of Contents
Synthesis, presynthesis, sufficient conditions for optimality and subanalytic sets, H.J. Sussmann; upper and lower semicontinuous differential inclusions - a unified approach, Alberto Bressan; global controllability by nice controls, Kevin A. Grasse and H.J. Sussmann; integrability of certain distributions associated with actions on manifolds and applications to control problems, Eduardo D. Sontag; right and left invertibility of nonlinear control systems, Witold Respondek; equivalence and invariants of nonlinear control systems, Bronislaw Jakubczyk; dual variational methods in optimal control theory, Alberto Bressan; invariance of extremals, Stanislaw Lojasiewicz, Jr; symplectic geometry for optimal control, A.A. Agrachev and R.V. Gamkrelidze; linear systems with quadratic costs, Velimir Jurdjevic; the ubiquity of Fuller's phenomenon, Ivan A.K. Kupka; regularity properties of optimal trajectories - recently developed techniques, Heinz Schattler; graded and nilpotent approximations of input-output systems, Peter E. Crouch; high-order small-time local controllability, Matthias Kawski.