Multivariable Generalization of BMRAC Algorithm by Means of Global HOSM Differentiators with Dynamic Gains

Andrei Battistel1, Tiago Roux Oliveira2, Victor Hugo Pereira Rodrigues3, Leonid Fridman4

  • 1Federal University of Rio de Janeiro
  • 2State University of Rio de Janeiro
  • 3State University of Rio de Janeiro (UERJ)
  • 4Universidad Nacional Autonoma de Mexico

Details

16:10 - 16:30 | Tue 20 Aug | Lau, 6-211 | TuC4.3

Session: Adaptive Control

Abstract

This paper presents an extension of the Binary Model Reference Adaptive Control (BMRAC) for uncertain multivariable (square) systems with non-uniform arbitrary relative degrees, using only output feedback. The BMRAC algorithm is a robust adaptive strategy which has the good transient and robustness properties of sliding mode control with the important advantage of preserving a continuous control signal free of chattering, inherited from classical adaptive systems. Unlike most of the publications which consider plants with uniform relative degree one, here we circumvent the arbitrary relative degree obstacle using a multivariable generalization of global finite-time differentiators with dynamic gains and higher-order sliding modes. State-norm observers are employed to obtain an upper bound for the unmeasured state and to update the gains of the proposed robust and exact multivariable differentiator. Global and exact output tracking is guaranteed without requiring stringent symmetry assumptions on the plant High-Frequency Gain matrix, usually assumed in other works in the literature.