Multi-Objective Finite-Frequency H_∞/GH₂ Static Output-Feedback Control Synthesis for Full-Vehicle Active Suspension Systems: A Metaheuristic Optimization Approach

In this paper, the problem of multi-objective control for active suspension systems with polytopic uncertainty is addressed via $H_{\infty }/GH_{2}$ static output feedback with a limited-frequency characteristic. For the overall analysis of the performance demanding both the vehicle-ride comfort related to vertical- and transversal-directional dynamics and the time-domain constraints related to the driving maneuverability, a seven-degree-of-freedom full-vehicle model with an active suspension system is investigated. The robust static output-feedback control strategy is adopted because some state variables may not be directly measured in a realistic implementation. In designing this control, the finite-frequency $H_{\infty }$ performance using the generalized Kalman-Yakubovich–Popov lemma is optimized to improve the passenger’s ride comfort, while the $GH_{2}$ performance is optimized to guarantee the constraints concerning the suspension deflection limitation, road-holding ability, and actuator saturation problem. This control synthesis problem is formulated as non-convex bilinear matrix inequalities and requires simultaneous consideration of different finite-frequency domain ranges for vertical and transversal motions for evaluating the $H_{\infty }$ performance. These design difficulties are overcome by the proposed multi-objective quantum-behaved particle swarm optimizer, which efficiently explores the relevant trade-offs between the considered multiple performance objectives and eventually provides the desired set of Pareto-optimal solutions. Further, the numerical simulation cases of a full-vehicle active suspension system are presented to illustrate the effectiveness of the proposed control synthesis methodology in both frequency and time domain.