Fixed-time dynamic control allocation for the distribution of braking forces in a vehicle ESC system

This paper proposes a design technique for vehicle lateral stability control. In this structure, reference variables are first determined based on the driver’s input. Using a fixed-time control technique, an upper controller, also known as virtual control, is designed to ensure vehicle stability for the desired yaw moment. Subsequently, optimal braking forces, also known as lower controls, are designed by virtual control and are utilized to generate the control inputs for the actuators. The optimal braking forces, which are constrained, are designed using a fixed-time dynamic control allocation method. This ensures their convergence to optimal values in a fixed time. Unlike static optimization methods, the proposed control allocation method introduces a dynamic update law. This approach not only reduces computational complexity but also guarantees the fixed-time convergence of braking forces to the optimal solution. The overall closed-loop stability in constant time is also achievable via the Lyapunov stability method. Simulations were conducted on a 10-DOF nonlinear dynamic vehicle model for standard test maneuvers of the electronic stability control system. The results indicate that the proposed method outperforms numerical optimization-based methods such as weighted least squares, weighted pseudoinverse, and asymptotic dynamic control allocation in terms of efficiency.