Title: Adaptive control designed by online solving for Riccati and Lyapunov equations with nonlinear flight body

Authors: Mohamed Fawzy Ahmed; Hassen Taher Dorrah

Addresses: Faculty of Engineering, Cairo University, Egypt ' Faculty of Engineering, Cairo University, Egypt

Abstract: The aim of this paper is to control the path for nonlinear missile model in the pitch channel using model reference adaptive control (MRAC) and L₁ adaptive control with linear quadratic regulator time-varying (LQRTV) strategy. Linear time-varying (LTV) model is designed where their parameters are varying with time. The nonlinear flying body, LTV model, and two adaptive control structures are modelled mathematically in the MATLAB-Simulink environment. LQRTV optimal control is designed using LTV model by online solving of Riccati Equation to get time-varying state feedback gain K(t). Adaptive control structures are designed using closed loop LTV model by online solving of Lyapunov equation to get time-varying Lyapunov gain matrix P(t). LQRTV and Lyapunov weight matrixes are tuned by Simulink design optimisation method. The results of two adaptive controls with the nonlinear flying body are compared. The wind effect and the dynamic uncertainties are researched.

Keywords: nonlinear missile model; linear time-varying model; LTV; linear quadratic regulator time-varying; LQRTV; model reference adaptive control; MRAC; L₁ adaptive control; simulink design optimisation method; wind effect; dynamic uncertainties.

DOI: 10.1504/IJAAC.2020.107086

International Journal of Automation and Control, 2020 Vol.14 No.3, pp.304 - 332

Received: 10 Feb 2018
Accepted: 30 Sep 2018
Published online: 04 May 2020 *

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