Stability and $H_\infty$ Control Synthesis of Electric Ground Vehicle Lateral Dynamics Through LPV Sampled-Data Systems

For electric ground vehicles, yaw moment gain-scheduling controller cannot adequately characterize vehicle handling information, especially longitudinal acceleration and calculation cost. This will increase effects of the front steering angle on vehicle stability and make the vehicle handling performance worse. Thus in our work, through LPV sampled-data systems, a yaw moment controller considering longitudinal acceleration is proposed to maximize handling performance and meanwhile minimize computational cost of vehicles. First, a novel integral inequality with the cubic term of integral interval length instead of the reciprocal one is constructed by non-orthogonal polynomials. This can fully utilize slack matrix variables and additional information about sawtooth structural sampling pattern of vehicle handling. Then, based on the constructed integral inequality, a cubic-term-dependent discontinuous exponent discontinuous Lyapunov-Krasovskii functional (LKF) including additional vehicle handling information is designed. To better estimate the upper bound of LKF derivative further, multiple convex function approximation (MCFA) approach is investigated. It can be applied to handle the two-variable polynomial negative definite problem by separating the variable interval into multiple sub-intervals. Thus, sufficient conditions with better performance of vehicle handling are derived for the feasibility of an
$H_\infty$
yaw moment sampled-data controller. In addition, an iterative algorithm is constructed through the inner convex approximation solution technique. And the parameter-dependent bilinear matrix inequalities can be further transformed into linear ones. Hence, it is easy to obtain the desired yaw moment sampled-data controller gain. Finally, the validity and superiority of our developed approaches can be verified, by comparing with previous results and implementing practical experiments.
Note to Practitioners
—In existing yaw moment controllers, vehicle longitudinal acceleration is not considered. This will destroy vehicle handling stability. Hence a yaw moment controller considering longitudinal acceleration is proposed through LPV systems. Meanwhile, to sufficiently make use of the bandwidth of vehicle, sampled-data controller is designed. As is well known, if the allowable maximum sampling intervals of sampled-data systems are increased, the computational cost of the vehicle can be reduced. To maximize vehicle handling performance and allowable maximum sampling intervals, a novel integral inequality is proposed and an appropriate LKF constructed. Because the constructed LKF derivative is a two-variable polynomial, MCFA is proposed to handle its negative definite problem. The sufficient stability condition via MCFA approach is bilinear matrix inequalities, which are difficult to deal with. Thus, an inner convex approximation algorithm is developed. Then the optimal yaw moment controller of vehicle lateral dynamics can also be obtained without using nonlinear solvers. Hence, a certain degree of freedom can be ensured. In summary, a yaw moment sampled-data controller can maximize vehicle handling performance while minimizing vehicle computational cost by the proposed integral inequality, MCFA approach and an inner convex approximation algorithm in this work.