Output-feedback control of linear time-varying and nonlinear systems using the forward propagating Riccati equation


Prach A., TEKİNALP O., Bernstein D. S.

JOURNAL OF VIBRATION AND CONTROL, vol.24, no.7, pp.1239-1263, 2018 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 24 Issue: 7
  • Publication Date: 2018
  • Doi Number: 10.1177/1077546316655913
  • Journal Name: JOURNAL OF VIBRATION AND CONTROL
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.1239-1263
  • Keywords: Nonlinear control, output feedback, Riccati equation, internal model principle, command following, MODEL-PREDICTIVE CONTROL, BENCHMARK PROBLEM, STATE, EQUIVALENCE, PASSIVITY, DESIGN, STABILIZATION, COMPENSATORS, DYNAMICS, BALL

Abstract

For output-feedback control of linear time-varying (LTV) and nonlinear systems, this paper focuses on control based on the forward propagating Riccati equation (FPRE). FPRE control uses dual difference (or differential) Riccati equations that are solved forward in time. Unlike the standard regulator Riccati equation, which propagates backward in time, forward propagation facilitates output-feedback control of both LTV and nonlinear systems expressed in terms of a state-dependent coefficient (SDC). To investigate the strengths and weaknesses of this approach, this paper considers several nonlinear systems under full-state-feedback and output-feedback control. The internal model principle is used to follow and reject step, ramp, and harmonic commands and disturbances. The Mathieu equation, Van der Pol oscillator, rotational-translational actuator, and ball and beam are considered. All examples are considered in discrete time in order to remove the effect of integration accuracy. The performance of FPRE is investigated numerically by considering the effect of state and control weightings, the initial conditions of the difference Riccati equations, the domain of attraction, and the choice of SDC.