Neural Network-Based Supervisory Control for Quarter-Car Suspension with Nonlinearity and Uncertainty

This paper addresses a neural network (NN)-based vibration control problem for a quarter-car suspension model with nonlinearity and uncertainty. First, combining the state system and the disturbance exosystem, an augmented system is constructed. Thus, an optimal regulator problem of the augmented system is built. After using Pontryagin minimum principle and the dynamic programming approach, an approximative optimal vibration control (OVC) is obtained, which is derived from a Riccati equation and two vector differential equations. A feedforward compensator is designed to suppress the vibration. And through defining the adjoint vectors, the nonlinearity and uncertainty are compensated and the physical realization problem of the disturbance compensation term can be solved. Therefore, supervised by the designed OVC and trained by the designed update rule, the Neural Network-based optimal vibration control (NNOVC) is constructed. Consequentially, the NNOVC enables making the system satisfy performance requirements easily. The related proof is given. Moreover, some numerical simulations are made. It is verified that the NNOVC can replace OVC to control the suspension effectively in face of road excitation and vehicle velocity changes. The effectiveness, flexibility, and the intelligence of NNOVC are illustrated.