Nonlinear Control in the Year 2000: Volume 1(258 Lecture Notes in Control and Information Sciences)

Control of nonlinear systems, one of the most active research areas in control theory, has always been a domain of natural convergence of research interests in applied mathematics and control engineering. The theory has developed from the early phase of its history, when the basic tool was essentially only the Lyapunov second method, to the present day, where the mathematics ranges from differential geometry, calculus of variations, ordinary and partial differential equations, functional analysis, abstract algebra and stochastic processes, while the applications to advanced engineering design span a wide variety of topics, which include nonlinear controllability and observability, optimal control, state estimation, stability and stabilization, feedback equivalence, motion planning, noninteracting control, disturbance attenuation, asymptotic tracking. The reader will find in the book methods and results which cover a wide variety of problems: starting from pure mathematics (like recent fundamental results on (non)analycity of small balls and the distance function), through its applications to all just mentioned topics of nonlinear control, up to industrial applications of nonlinear control algorithms.

Table of Contents:
Subanalyticity of distance and spheres in sub-riemannian geometry.- Principal invariants of Jacobi curves.- The de casteljau algorithm on SE(3).- Trajectory tracking by cascaded backstepping control for a second-order nonholonomic mechanical system.- Static output feedback stabilization: from linear to nonlinear and back.- Semi-linear diffusive representations for nonlinear fractional differential systems.- Controllability properties of a class of control systems on lie groups.- Stability analysis to parametric uncertainty: Extension to the multivariable case.- External stability and continuous Liapunov functions.- Optimal control with harmonic rejection of induction machine.- Nonlinear QFT synthesis based on harmonic balance and multiplier theory.- Group invariance and symmetries in nonlinear control and estimation.- A globalization procedure for locally stabilizing controllers.- Optimal control and implicit Hamiltonian systems.- Robust absolute stability of delay systems.- Stratification du secteur anormal dans la sphère de Martinet de petit rayon.- Toward a nonequilibrium theory for nonlinear control systems.- A regularization of Zubov’s equation for robust domains of attraction.- A remark on Ryan’s generalization of Brockett’s condition to discontinuous stabilizability.- Applications of Lie algebroids in mechanics and control theory.- Observer design for locally observable analytic systems: Convergence and separation property.- An H ?-suboptimal fault detection filter for bilinear systems.- Adaptive control of feedback linearizable systems by orthogonal approximation functions.- Sampled-data low-gain integral control of linear systems with actuator and sensor nonlinearities.- State feedbacks without asymptotic observers and generalized PID regulators.-Eigenstructure of nonlinear hankel operators.- Distributed architecture for teleoperation over the internet.- Singular L-Q problems and the dirac-bergmann theory of constraints.- Robust tracking of multi-variable linear systems under parametric uncertainty.- Flatness-based control of the separately excited DC drive.- State detection and stability for uncertain dynamical systems.- Controllability properties of numerical eigenvalue algorithms.- On the discretization of sliding-mode-like controllers.- Nonlinear adaptive state space control for 2 class of nonlinear systems with unknown parameters.- An observer view on synchronization.- Regularity of the sub-Riemannian distance and cut locus.- Industrial sensorless control of induction motors.- Feedback invariants, critical trajectories and hamiltonian formalism.- Paths in sub-Riemannian geometry.- Observability of C ?-systems for L ?-single-inputs and some examples.- Robust control of a synchronous power generator.