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This book, published in honor of Professor Laurent Praly on the occasion of his 65th birthday, explores the responses of some leading international authorities to new challenges in nonlinear and adaptive control. The mitigation of the effects of uncertainty and nonlinearity – ubiquitous features of real-world engineering and natural systems – on closed-loop stability and robustness being of crucial importance, the contributions report the latest research into overcoming these difficulties in: autonomous systems;reset control systems;multiple-input–multiple-output nonlinear systems;input delays;partial differential equations;population games; anddata-driven control. Trends in Nonlinear and Adaptive Control presents research inspired by and related to Professor Praly's lifetime of contributions to control theory and is a valuable additionto the literature of advanced control.

A reset controller is a linear controller whose output is reset to zero whenever its input and output satisfy an appropriate algebraic relationship. It has widespread industrial applications and is used in many modern day control systems. This monograph provides a comprehensive survey into three parts. Part I provides an historical literature review and presents some fundamental results. Part II deals with nonplanar reset systems and covers several reset rules that may be used to augment high-order controllers for plants of any order. It also provides several simulation studies showing that reset control strategies may allow to attain better performance with respect to the optimal ones obtained by classical continuous-time controllers. Part III focuses on planar systems and reports on a nontrivial generalization of the basic mechanisms emerging in Clegg integrators and First Order Reset Elements (FORE). Relevant case studies emerging in the automotive field are included. This monograph gives an in-depth assessment of the state-of-the-art and provides the reader with a starting point for further research into the increasingly important topic of Reset Control Systems.

Control of the Safety Factor Profile in a Tokamak uses Lyapunov techniques to address a challenging problem for which even the simplest physically relevant models are represented by nonlinear, time-dependent, partial differential equations (PDEs). This is because of the spatiotemporal dynamics of transport phenomena (magnetic flux, heat, densities, etc.) in the anisotropic plasma medium.Robustness considerations are ubiquitous in the analysis and control design since direct measurements on the magnetic flux are impossible (its estimation relies on virtual sensors) and large uncertainties remain in the coupling between the plasma particles and the radio-frequency waves (distributed inputs).The Brief begins with a presentation of the reference dynamical model and continues by developing a Lyapunov function for the discretized system (in a polytopic linear-parameter-varying formulation). The limitations of this finite-dimensional approach motivate new developments in the infinite-dimensional framework. The text then tackles the construction of an input-to-state-stability Lyapunov function for the infinite-dimensional system that handles the medium anisotropy and provides a common basis for analytical robustness results. This function is used as a control-Lyapunov function and allows the amplitude and nonlinear shape constraints in the control action to be dealt with.Finally, the Brief addresses important application- and implementation-specific concerns. In particular, the coupling of the PDE and the finite-dimensional subsystem representing the evolution of the boundary condition (magnetic coils) and the introduction of profile-reconstruction delays in the control loop (induced by solving a 2-D inverse problem for computing the magnetic flux) is analyzed. Simulation results are presented for various operation scenarios on Tore Supra (simulated with METIS) and on TCV (simulated with RAPTOR).Control of the Safety FactorProfile in a Tokamak will be of interest to both academic and industrially-based researchers interested in nuclear energy and plasma-containment control systems, and graduate students in nuclear and control engineering.