A Relaxation-Based Approach to Optimal Control of Hybrid and Switched Systems

A Relaxation-Based Approach to Optimal Control of Hybrid and Switched Systems

A Practical Guide for Engineers

1st Edition - February 14, 2019

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  • Author: Vadim Azhmyakov
  • eBook ISBN: 9780128147894
  • Paperback ISBN: 9780128147887

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A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems proposes a unified approach to effective and numerically tractable relaxation schemes for optimal control problems of hybrid and switched systems. The book gives an overview of the existing (conventional and newly developed) relaxation techniques associated with the conventional systems described by ordinary differential equations. Next, it constructs a self-contained relaxation theory for optimal control processes governed by various types (sub-classes) of general hybrid and switched systems. It contains all mathematical tools necessary for an adequate understanding and using of the sophisticated relaxation techniques. In addition, readers will find many practically oriented optimal control problems related to the new class of dynamic systems. All in all, the book follows engineering and numerical concepts. However, it can also be considered as a mathematical compendium that contains the necessary formal results and important algorithms related to the modern relaxation theory.

Key Features

  • Illustrates the use of the relaxation approaches in engineering optimization
  • Presents application of the relaxation methods in computational schemes for a numerical treatment of the sophisticated hybrid/switched optimal control problems
  • Offers a rigorous and self-contained mathematical tool for an adequate understanding and practical use of the relaxation techniques
  • Presents an extension of the relaxation methodology to the new class of applied dynamic systems, namely, to hybrid and switched control systems


Academic Researchers and PhD candidates from Electrical Engineering and/or Applied Mathematics faculties (technical and regular Universities, academic Research Centers). R&D departments of electrical / electronic companies (research engineers, developers). R&D departments of aerospace engineering companies (research engineers, developers). Can also be included into a PhD qualification program in Control Engineering, Applied Mathematics, advanced Computer Science and Mathematical Economics

Table of Contents

  • 1. Introduction
    2. Mathematical Background
    3. Convex Programming
    4. Short Course in Continuous – Time Dynamic Systems and Control
    5. Relaxation Schemes in Conventional Optimal Control and Optimization Theory
    6. Optimal Control of Hybrid and Switched Systems
    7. Numerically Tractable Relaxation Schemes for Optimal Control of Hybrid and Switched Systems
    8. Applications of the Relaxation Based Approach

Product details

  • No. of pages: 434
  • Language: English
  • Copyright: © Butterworth-Heinemann 2019
  • Published: February 14, 2019
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9780128147894
  • Paperback ISBN: 9780128147887

About the Author

Vadim Azhmyakov

Vadim Azhmyakov graduated in 1989 from the Department of Applied Mathematics of the Technical University of Moscow. He gained a Ph.D. in Applied Mathematics in 1994, and a Postdoc in Mathematics in 2006 of the EMA University of Greifswald, Greifswald, Germany. He has experience in Applied Mathematics: optimal control, optimization, numerical methods nonlinear analysis, convex analysis, differential equations and differential inclusions, engineering mathematics; and Control Engineering: hybrid and switched dynamic systems, systems optimization, robust control, control over networks, multiagent systems, robot control, Lagrange mechanics, stochastic dynamics, smart grids, energy management systems.

Affiliations and Expertise

Vadim Azhmyakov Department of Mathematical Sciences, Universidad EAFIT, Medellin, Republic of Colombia

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  • VadimAzhmyakov Sun Apr 07 2019

    this book constitutes a fundamental

    this book constitutes a fundamental research monograph in optimal control of hybrid and switched systems