In this paper, a new non-linear tracking controller for vehicle active suspension systems is analytically designed using an optimization process. The proposed scheme employs a realistic non-linear quarter-car model, which is composed of a hardening spring and a quadratic damping force. The control input is the external active suspension force and is determined by minimizing a performance index defined as a weighted combination of conflicting objectives, namely ride quality, handling performance and control energy. A linear skyhook model with standard parameters is used as the reference model to be tracked by the controller. The robustness of the proposed controller in the presence of modeling uncertainties is investigated. The performed analysis and the simulation results indicate that both vehicle ride comfort and handling performance can be improved using the minimum external force when the proposed non-linear controller is engaged with the model. Meanwhile, a compromise between different objectives and control energy can easily be made by regulating their respective weighting factors, which are the free parameters of the control law.