Neural Network Adaptive Output-Feedback Optimal Control for Active Suspension Systems

The adaptive neural network (NN) output-feedback optimal control issue has been investigated for a quarter-car active electric suspension systems, where the suspension stiffness is unknown and partial state variables are unavailable for measurement. NNs are utilized to identify unknown nonlinearities, and an NN state observer is devised to estimate the unmeasurable states. For each backstepping step, via reinforcement learning (RL), a critic–actor architecture is designed to get the approximation solution of Hamilton–Jacobi–Bellman (HJB) equations and actual and virtual optimization controllers are designed, in which the input saturation constraint and road interference are considered. It is analytically proved that all controlled system signals remain bounded, while the power of the control input signal, as well as the amplitude of the vertical displacement, has been minimized. A comparative simulation is eventually given to elaborate the feasibility of the developed control algorithm.