Skip to main content
SpringerLink
Log in

Mathematical Preliminaries

  • Chapter
  • First Online:
Model-Reference Adaptive Control

Part of the book series: Advanced Textbooks in Control and Signal Processing ((C&SP))

  • 3369 Accesses

Abstract

This chapter presents some basic mathematical fundamentals for adaptive control theory. Vector and matrix norms are defined. The existence and uniqueness of a solution of a nonlinear differential equation are stated by the Cauchy theorem and the Lipschitz condition. Positive-valued functions are an important class of functions in adaptive control theory. Positive definiteness of a real-valued function is defined. The properties of a positive-definite matrix are given.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Author information

Authors and Affiliations

  1. Intelligent Systems, NASA Ames Research Center, Moffett Field, CA, USA

    Nhan T. Nguyen

Authors
  1. Nhan T. Nguyen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nhan T. Nguyen .

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Nguyen, N.T. (2018). Mathematical Preliminaries. In: Model-Reference Adaptive Control. Advanced Textbooks in Control and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-56393-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-56393-0_3

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-56392-3

  • Online ISBN: 978-3-319-56393-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation