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Fixed Final Time and Fixed Final State Linear Quadratic Optimal Control Problem of Fractional Order Singular System

  • Tirumalasetty Chiranjeevi
  • Raj Kumar Biswas
  • Shashi Kant Pandey
Conference paper
  • 68 Downloads
Part of the Algorithms for Intelligent Systems book series (AIS)

Abstract

Linear quadratic optimal control problem (LQOCP) of fractional order singular system (FOSS) with fixed final time and fixed final state in the sense of Caputo fractional derivative (FD) is presented in this paper. Performance index (PI) is considered in quadratic form. Before applying optimal control problem, using coordinate transformation [1], we transform FOSS into standard fractional order state space system. Necessary conditions are obtained using Lagrange multiplier approach. Grünwald–Letnikov approximation (GLA) based numerical technique is used to solve the necessary conditions. To demonstrate the efficiency of formulation and solution scheme, an example is illustrated. Results are obtained for different values of α.

Keywords

Caputo fractional derivative Linear quadratic optimal control problem Fractional order singular system Grünwald–Letnikov approximation Lagrange multiplier approach 

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Tirumalasetty Chiranjeevi
    • 1
    • 2
  • Raj Kumar Biswas
    • 1
  • Shashi Kant Pandey
    • 3
  1. 1.Electrical Engineering DepartmentNIT SilcharSilcharIndia
  2. 2.Rajkiya Engineering CollegeSonbhadraIndia
  3. 3.Electrical Engineering DepartmentRajkiya Engineering CollegeSonbhadraIndia

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