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This thesis concerns with a common practical problem in the area of sampled-data control systems where the plant is described by nonlinear dynamics and input and output signals are sampled at different rates. We first follow the continuous-time (emulation) approach to propose a general stabilization framework for multirate nonlinear systems in presence of disturbances. This provides a multirate H_infinity synthesis scheme which can be used to tackle the intrinsic difficulty of unknown exact discrete-time model in nonlinear sampled-data control systems. Moreover, an alternative performance criterion is introduced based on the L_2 incremental gain as a stronger form of the usual L_2 gain that quantifies whether or not small changes in exogenous inputs such as disturbances or noise will result in small changes at the output. The second part of the thesis investigates the discrete-time approach based on model approximation to the problem of multirate nonlinear sampled-data systems. First, we establish prescriptive design principles for single-rate sampled-data nonlinear observer that is input-to-state stable in the presence of unknown exact discrete-time model as well as disturbance inputs. Our results are then applied to the so-called one-sided Lipschitz nonlinearities to develop constructive design techniques via tractable (linear matrix inequalities) LMIs. Taking the idea of input-to-state stable observer into account, we propose a general framework for multirate observer design that exploits a single-rate observer working at the base sampling period of the system together with modified sample and hold devices to reconstruct the missing intersample signals. Finally, in order to verify the advantages of multirate sampling we extend our results to the area of networked-control systems (NCSs). A general output-feedback structure is developed which utilizes the same idea as that of our multirate observer to predict the missing outputs between measured samples. The proposed multirate network-based controller is shown to be capable of preserving the dissipation inequality slightly deteriorated by some additive terms, in spite of network-induced uncertainties and disturbance inputs. By this means a stable NCS can be obtained under much lower data rate and a significant saving in the required bandwidth.
The following topics are dealt with: nonlinearity: dynamic systems; describing function method; phase plane portrait; linearisation ;nonlinear second-order system linearisation; envelope methods; Limit cycles; relaxation oscillations; Lienard's equation; gradient systems and system decomposition.
Thepastthree decadeshaveseenrapiddevelopmentin the areaofmodelpred- tive control with respect to both theoretical and application aspects. Over these 30 years, model predictive control for linear systems has been widely applied, especially in the area of process control. However, today’s applications often require driving the process over a wide region and close to the boundaries of - erability, while satisfying constraints and achieving near-optimal performance. Consequently, the application of linear control methods does not always lead to satisfactory performance, and here nonlinear methods must be employed. This is one of the reasons why nonlinear model predictive control (NMPC) has - joyed signi?cant attention over the past years,with a number of recent advances on both the theoretical and application frontier. Additionally, the widespread availability and steadily increasing power of today’s computers, as well as the development of specially tailored numerical solution methods for NMPC, bring thepracticalapplicabilityofNMPCwithinreachevenforveryfastsystems.This has led to a series of new, exciting developments, along with new challenges in the area of NMPC.
This volume is an outgrowth of the workshop "Applications of Advanced Control Theory to Robotics and Automation," organized in honor of the 70th birthdays of Petar V. Kokotovic and Salvatore Nicosia. Both Petar and Turi have carried out distinguished work in the control community, and have long been recognized as mentors as well as experts and pioneers in the field of automatic control, covering many topics in control theory and several different applications. The variety of their research is reflected in this book, which includes contributions ranging from mathematics to laboratory experiments.Main topics covered include:* Observer design for time-delay systems, nonlinear systems, and identification for different classes of systems* Lyapunov tools for linear differential inclusions, control of constrained systems, and finite-time stability concepts* New studies of robot manipulators, parameter identification, and different control problems for mobile robots* Applications of modern control techniques to port-controlled Hamiltonian systems, different classes of vehicles, and web handling systems* Applications of the max-plus algebra to system-order reduction; optimal machine scheduling problems; and inventory control with cooperation between retailers* Control of linear and nonlinear networked control systems: deterministic and stochastic approachesThe scope of the work is very broad, and although each chapter is self-contained, the book has been organized into thematically related chapters, which in some cases suggest to the reader a convenient reading sequence. The great variety of topics covered and the almost tutorial writing style used by many of the authors will make this book suitable for experts, as well as young researchers who seek a more intuitive understanding of these relevant topics in the field.
Computer Aided Design of Multivariable Technological Systems covers the proceedings of the Second International Federation of Automatic Control (IFAC). The book reviews papers that discuss topics about the use of Computer Aided Design (CAD) in designing multivariable system, such as theoretical issues, applications, and implementations. The book tackles several topics relevant to the use of CAD in designing multivariable systems. Topics include quasi-classical approach to multivariable feedback system designs; fuzzy control for multivariable systems; root loci with multiple gain parameters; multivariable frequency domain stability criteria; and computational algorithms for pole assignment in linear multivariable systems. The text will be of great use to professionals whose work involves designing and implementing multivariable systems.
Engineering systems operate through actuators, most of which will exhibit phenomena such as saturation or zones of no operation, commonly known as dead zones. These are examples of piecewise-affine characteristics, and they can have a considerable impact on the stability and performance of engineering systems. This book targets controller design for piecewise affine systems, fulfilling both stability and performance requirements. The authors present a unified computational methodology for the analysis and synthesis of piecewise affine controllers, taking an approach that is capable of handling sliding modes, sampled-data, and networked systems. They introduce algorithms that will be applicable to nonlinear systems approximated by piecewise affine systems, and they feature several examples from areas such as switching electronic circuits, autonomous vehicles, neural networks, and aerospace applications. Piecewise Affine Control: Continuous-Time, Sampled-Data, and Networked Systems is intended for graduate students, advanced senior undergraduate students, and researchers in academia and industry. It is also appropriate for engineers working on applications where switched linear and affine models are important.