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The Model Matching Problem for Switching Max-Plus Systems: a Geometric Approach
Linear systems over the max-plus algebra can model discrete event systems where synchronization, without competition, is involved. The lack of competition can be partly circumvented by considering multiple linear models, each representing a possible choice in resource allocation, and a switching mechanism, thus obtaining a switching linear max-plus system. We propose a formulation of the model matching problem for systems of such kind. The aim is to force a given plant to match exactly the output of a given model. A sufficient condition for the solvability of the problem is obtained by extending the geometric approach to switching systems over the max-plus algebra
Niadenie nelinearnych systemov: Algebricky pristup
traduzione in slovacco del volume:
Nonlinear Control Systems, An algebraic setting, G. Conte, C.H. Moog and A.M. Perdon, Springer Lecture Notes in Control and Information Science, Springer vol. 242, (March 1999) ISBN 1-85233-151-
Preface
Structural Methods in the Study of Complex Systems helps the reader respond to the challenge of mastering complexity in systems and control. The book details the fundamental control problems arising from complex dynamical systems and shows how they can be tackled effectively by means of methods developed from graph theory, differential algebra and geometric approaches. These “structural methods” produce abstractions that fit a wide variety of applications by taking advantage of their intrinsic focus on the essential characteristics of dynamical systems, their geometric perspective and visual representation, and their algebraic formalization and ability to generate algorithmic frameworks to complement the theoretical treatment. The original work and latest achievements of the contributors, expanding on material presented at a workshop organized to coincide with the 2018 European Control Conference will assist systems and control scientists interested in developing theoretical and computational tools to solve analysis and synthesis problems involving complex dynamical systems. The contributions provide a comprehensive picture of available results along with a stimulating view of possible directions for future investigations in the field. Emphasis is placed on methods with solid computational background and on specific engineering applications so that readers from both theoretical and practical backgrounds will find this collection of use
Digital Second Order Sliding Mode Control with Uncertainties Estimation for a Class of SISO Nonlinear Systems
Second Order Chattering-Free Sliding Mode Control for some Classes of Multi-Input Uncertain Nonlinear Systems
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