This paper introduces an integrated physics-data-based approach to derive a linear parameter varying (LPV) model for nonlinear lateral vehicle dynamics. The proposed method can accurately capture the nonlinearity of the lateral vehicle dynamics using only a few data points without model training or calibrations. Specifically, a novel nonlinear tire force representation based on time-varying stiffness is first proposed. Then, from the physical principles of vehicle motions, the nonlinear lateral dynamics is expressed in the LPV formulation, where the scheduling parameters are the longitudinal speed and slip ratio. After that, a data-based LPV representation is formulated based on a small set of data points satisfying the condition of persistent excitation. The system evolution of nonlinear lateral dynamics can be precisely recovered by parametric matrices formed by these data snapshots. Simulation data from CarSim and experiment data from multiple commercial vehicles are utilized to validate the proposed physics-informed data-based LPV model. The results demonstrate exceptional accuracy and noise-handling ability of the proposed modeling approach across multiple scenarios and vehicles.

Exhaust gas recirculation (EGR) valves used in internal combustion engines are highly nonlinear due to its nonlinear mechanism and dry friction dominated at low valve speed that could lead to large steady-state displacement errors. A multiple friction factor model is adopted in this paper using switched LPV (Linear Parameter-Varying) modeling approach, where the scheduling parameter is the friction coefficient as a function of valve speed. Switched gain-scheduling LPV controllers are designed based on hysteresis switching logic with guaranteed H-infinity performance, where Parametric Linear Matrix Inequality (PLMI) conditions are relaxed to a set of Linear Matrix Inequality (LMI) conditions for synthesizing the switched LPV controllers by convex optimization. The LPV control performance is compared with that of PID controllers through both simulation and experimental studies, showing a notable improvement in the system response performance and robustness.

A dual-loop robust control scheme and its property of performance separation are presented in this article. The dual-loop control scheme consists of two degrees of freedom for nominal and robust performances, with the nominal controller being any stabilizing controller in the observer-based state-feedback form and robust controller being a standard $H_{\infty }$ controller. When there is model error and/or disturbance, the robust controller is activated to compensate the nominal controller; otherwise, the dual-loop control returns to a single-loop nominal controller. We also show that the nominal and robust performances of the dual-loop control are independent of one another. As a result, the nominal and robust controllers can be designed separately offline, and then, online coordinated in the dual-loop control. Furthermore, the state-space realization and controller implementation are also provided. Finally, a two-wheeled robot with varying slip effect is considered as an illustrative example. Both simulation and experimental results show that the dual-loop control outperforms the classical robust control methods.