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

Date

2018-04-01

Author

Prach, Anna
Tekinalp, Ozan
Bernstein, Dennis S.

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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.

Subject Keywords

Nonlinear Control, Output Feedback, Riccati Equation, Internal Model Principle, Command Following

URI

https://hdl.handle.net/11511/42573

Journal

JOURNAL OF VIBRATION AND CONTROL

DOI

https://doi.org/10.1177/1077546316655913

Collections

Department of Aerospace Engineering, Article

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Citation Formats

A. Prach, O. Tekinalp, and D. S. Bernstein, “Output-feedback control of linear time-varying and nonlinear systems using the forward propagating Riccati equation,” JOURNAL OF VIBRATION AND CONTROL, pp. 1239–1263, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/42573.