Title: Optimal control of a four-wheel steering car using state-dependent Riccati equation controller

Authors: H. Tourajizadeh; S. Ordou; M. Efafi; M. Sarvari

Addresses: Faculty of Engineering, Department of Mechanical Engineering, Kharazmi University, Tehran, 15719-14911, Iran ' Faculty of Engineering, Department of Mechanical Engineering, Kharazmi University, Tehran, 15719-14911, Iran ' Faculty of Engineering, Department of Mechanical Engineering, Kharazmi University, Tehran, 15719-14911, Iran ' Faculty of Engineering, Department of Mechanical Engineering, Kharazmi University, Tehran, 15719-14911, Iran

Abstract: Optimal control of a four-wheel steering car model is performed in this paper using two strategies: linear quadratic regulator (LQR) and state-dependent Riccati equation (SDRE). In such vehicles, the system is over-constrained, so the solution of inverse dynamics is not unique. Extracting the optimal control input satisfies the desired vehicle performance while minimising a specific objective function. The bicycle model with two steering inputs is used to model the four-wheel steering car and its nonlinear behaviour. A new approach for kinematic modelling is also proposed. Two closed-loop optimal control strategies are applied: one linear and valid near its operating point, and the other global and nonlinear. Their results are analysed and compared. Model correctness is investigated via comparison with CarSim. The effectiveness of the proposed optimal control strategies and the superiority of the nonlinear SDRE over traditional methods are validated using MATLAB simulations, showing accurate path tracking with minimal energy consumption across the its full workspace.

Keywords: 4WS; four-wheel steering vehicle; optimal control; bicycle model; optimal regulation; LQR; linear quadratic regulator; SDRE; state-dependent Riccati equation.

DOI: 10.1504/IJVD.2025.149130

International Journal of Vehicle Design, 2025 Vol.98 No.1/2/3/4, pp.172 - 198

Accepted: 14 May 2025
Published online: 14 Oct 2025 *

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