Robust gain-scheduling static output-feedback H∞ control of vehicle lateral stability with heuristic approach

Sparse successive approximation for nonlinear H2 and H∞ optimal control problems under residual errors

Successive approximation techniques are effective approaches to solve the Hamilton-Jacobi-Bellman (HJB)/Hamilton-Jacobi-Isaacs (HJI) equations in nonlinear H2 and H∞ optimal control problems (OCPs), but residual errors in the solving process may destroy its convergence property, and related numerical methods also pose computational burden and difficulties. In this paper, the HJB/HJI partial differential equations (PDEs) for infinite-horizon nonlinear H2 and H∞ OCPs are handled in a unified formulation, and a sparse successive approximation method is proposed. Taking advantage of successive approximation techniques, the nonlinear HJB/HJI PDEs are transformed into sequences of easily solvable linear PDEs, to which the solutions can be computed point-wise by handling simple initial value problems. Extra constraints are also incorporated in the solving process to guarantee the convergence under residual errors. The sparse grid based collocation points and basis functions are then employed to enable efficient numerical implementation. The performance of the proposed method is also numerically demonstrated in simulations.

Prediction of Clearance Vibration for Intelligent Vehicles Motion Control

Motion control analysis should consider the system’s uncertainty to ensure the intelligent vehicle’s autonomy. The clearance structure of the transmission shaft is modeled as a cantilever beam with double clearance to predict the clearance vibration for mitigating the nonlinearity. Based on the Kelvin–Voigt collision model, a clearance model was developed using time-varying parameters identified by the wavelet transform. Comparing the frequency response functions (FRF) of the initial model with constant parameters and the updated model with time-varying parameters, the experimental results from the updated model indicate that the modal assurance criterion (MAC) is increased by 42.92%, 31.08%, 38.97%, and 50.74% in the first-four order. Cross-signature assurance criteria (CSAC) and cross-signature scale factor (CSF) have been increased by 6.55% and 12.37%. The control method based on the clearance model has been verified. In the case of 120 km/h, compared with model-predictive control (MPC) and sliding mode control (SMC), the peak of the lateral position error was reduced by 35.7% and 14.3%, and the peak of the heading error was reduced by 50% and 15.6%.