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

Abstract

This paper addresses a neural network (NN)-based vibration control problem for aquarter-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.

Proportional + integral + derivative control of nonlinear full-car electrohydraulic suspensions using global and evolutionary optimization techniques

“…Implementation of nonlinear techniques like feedback linearization requires guarantee of stable zero dynamics in the system; backstepping requires repeated differentiation of the system's nonlinear function and their implementation practically is usually characterized by chattering. [19][20][21][22][23] Combining nonlinear control schemes with computational intelligence techniques have largely been demonstrated to be effective, 24 but it comes with the additional computational complexity that is associated with each scheme in the process. Demonstrating system stability can also be very challenging.…”