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1511 results in Control systems and optimization

Page 10 of 76

  • 1 - Introduction

  • Sean Meyn, University of Florida
  • Book:
    Control Systems and Reinforcement Learning
    Published online:
    17 May 2022
    Print publication:
    09 June 2022, pp 1-6
    • Chapter
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Linear Multivariable Control Systems
  • Shankar P. Bhattacharyya, Lee H. Keel
  • Published online:
    02 June 2022
    Print publication:
    13 January 2022
  • This rigorous yet accessible textbook provides broad and systematic coverage of linear multivariable control systems, including several new approaches to design. In addition to standard state space theory, it provides a new measurement-based approach to linear systems, including a generalization of Thevenin's Theorem, a new single-input single-output approach to multivariable control, and analytical design of PID controllers developed by the authors. Each result is rigorously proved and combined with specific control systems applications, such as the servomechanism problem, the fragility of high order controllers, multivariable control, and PID controllers. Illustrative examples solved using MATLAB and SIMULINK, with easily reusable programming scripts, are included throughout. Numerous end-of-chapter homework problems enhance understanding. Based on course-tested material, this textbook is ideal for a single or two-semester graduate course on linear multivariable control systems in aerospace, chemical, electrical and mechanical engineering.

  • 9 - Semi-bounded State/Signal Systems

  • Damir Z. Arov, Olof J. Staffans, Åbo Akademi University, Finland
  • Book:
    Linear State/Signal Systems
    Published online:
    05 May 2022
    Print publication:
    26 May 2022, pp 576-598

  • Summary

    This chapter is a state/signal counterpart to Chapter 8. We recall that a s/s system is bounded if and only if it has at least one bounded i/s/o representation. In the semi-bounded setting, we turn this property into a definition and say that a s/s system is semi-bounded if it has at least one semi-bounded i/s/o representation. Most of the results presented in Chapter 7 for bounded s/s systems remain valid in one form or another for semi-bounded s/s systems, but there is one major exception: in the case of a bounded s/s system, the direction of time does not play an important role, i.e., most of the results that are true in the forward time direction are also true in the backward time direction. This is no longer true in the semi-bounded case. The even larger class of well-posed s/s systems is discussed in Chapter 15, and many of the results in the present chapter remain valid even in the well-posed setting.

  • 15 - Well-Posed State/Signal Systems

  • Damir Z. Arov, Olof J. Staffans, Åbo Akademi University, Finland
  • Book:
    Linear State/Signal Systems
    Published online:
    05 May 2022
    Print publication:
    26 May 2022, pp 907-949

  • Summary

    In this chapter, we study well-posed s/s systems. By definition, a s/s system is well-posed if it has at least one well-posed i/s/o representation (and then usually infinitely many wellposed i/s/o representations). The results presented here are analogous to the corresponding well-posed i/s/o results in Chapter 14, and most of the proofs consist of showing how to reduce a particular well-posed s/s result to the corresponding well-posed i/s/o result. In the well-posed i/s/o setting, we can interpret a well-posed i/s/o system as a realization of a continuous linear causal shift-invariant exponentially bounded operator. In the well-posed s/s setting, we can instead interpret a well-posed s/s system as a realization of a well-posed future, past, or two-sided behavior. Each one of these behaviors determine, the other two uniquely. Two well-posed s/s systems are externally equivalent if and only if they have the same well-posed behaviors. At the end of this chapter, we define the notion of a passive state/signal system and show that passive state/signal systems are well-posed. A passive state/signal system is characterized by the fact that it is regular, and its generating subspace is a maximally nonnegative subspace of the Kreĭn node space.

Page 10 of 76