الصفحة 1
الصفحة 1
Nonlinear and Optimal Control Theory : Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy June 19–29, 2004
The lectures gathered in this volume present some of the different aspects of Mathematical Control Theory. Adopting the point of view of Geometric Control Theory and of Nonlinear Control Theory, the lectures focus on some aspects of the Optimization and Control of nonlinear, not necessarily smooth, dynamical systems. Specifically, three of the five lectures discuss respectively: logic-based switching control, sliding mode control and the input to the state stability paradigm for the control and stability of nonlinear systems. The remaining two lectures are devoted to Optimal Control: one investigates the connections between Optimal Control Theory, Dynamical Systems and Differential Geometry, while the second presents a very general version, in a non-smooth context, of the Pontryagin Maximum Principle.
New Trends in Optimal Filtering and Control for Polynomial and Time-Delay Systems
0. 1 Introduction Although the general optimal solution of the ?ltering problem for nonlinear state and observation equations confused with white Gaussian noises is given by the Kushner equation for the conditional density of an unobserved state with respect to obser- tions (see [48] or [41], Theorem 6. 5, formula (6. 79) or [70], Subsection 5. 10. 5, formula (5. 10. 23)), there are a very few known examples of nonlinear systems where the Ku- ner equation can be reduced to a ?nite-dimensional closed system of ?ltering eq- tions for a certain number of lower conditional moments.
Modern Sliding Mode Control Theory : New Perspectives and Applications
This book is a collection of invited chapters covering several areas of modern sliding mode control theory. The authors identify key contributions defining the theoretical and applicative state of the art of the sliding mode control theory and the most promising trends of the ongoing research activities. The contributions is divided in four main parts: Part I: Basic Theory. Part II: Design Methods. Part III: Observers and Fault Detection. Part IV: Applications.
Modeling, Control and Implementation of Smart Structures : A FEM-State Space Approach
This monograph presents an introductory overview of smart structures, their concepts, their active involvement in the vibration control, their applications and the extensive research work done on it so far. The modelling of flexible beams using two types of beam theories, viz., the Euler-Bernoulli theory and the Timoshenko beam theory is presented, including a new concept of finite element modeling of the flexible structures using Timoshenko beam theory with the inclusion of the shear both in the piezo-patches as well as in the host structure. It presents the design of the periodic output feedback control system for smart structure systems, the design of the FOS controllers for active vibration control and the design of Discrete Sliding Mode controllers using multirate output feedback technique.
Discrete-time Sliding Mode Control : A Multirate Output Feedback Approach
Sliding mode control is a simple and yet robust control technique, where the system states are made to confine to a selected subset. With the increasing use of computers and discrete-time samplers in controller implementation in the recent past, discrete-time systems and computer based control have become important topics. This monograph presents an output feedback sliding mode control philosophy which can be applied to almost all controllable and observable systems, while at the same time being simple enough as not to tax the computer too much. It is shown that the solution can be found in the synergy of the multirate output sampling concept and the concept of discrete-time sliding mode control.
Control Design Techniques in Power Electronics Devices
The book is introduced through the very important topic of modeling switched power electronics as controlled dynamical systems. Detailed circuit layouts, schematics and actual closed-loop control responses from a representative group of the plants under discussion and generated by applying the theory are included. The control theories which feature in the book are: sliding mode control and feedback control by means of approximate linearization (linear state feedback, static and dynamic proportional-integral-differential (PID control), output feedback trough observer design, Lyapunov-based control and passivity-based control). Nonlinear control design methods represented include: exact feedback linearization, input-output linearization, differential flatness, generalized PID control and, again, passivity-based control.
Advances in Variable Structure and Sliding Mode Control
Sliding Mode Control is recognized as an efficient tool to design controllers which are robust with respect to uncertainty. The resulting controllers have low sensitivity to plant parameters and perturbations and allow the possibility of decoupling the original plant system into two components of lower dimension. In addition many controllers ensure finite time convergence to the switching surface and can be straightforwardly implemented. However, in addition to this traditional area of exploitation, sliding mode concepts are being increasingly deployed for the design of observers for estimation and identification.
