A novel method to obtain a real-time control force strategy using genetic algorithms for dynamic systems subjected to external arbitrary excitations

The paper deals with a discrete differential dynamic programming type of problem. It is an optimal control problem where an external disturbance is controlled over the time horizon by a control force constituted with the well-known convolution approach. The paper presents a simple and novel idea to achieve an optimally controlled response when a linear system is subjected to an arbitrary external disturbance. The proposed approach uses the convolution concept and states that if a control method can be established to restore a unit external disturbance, then the convolution integral can be applied to generate an overall control strategy to control the system when it is subjected to an arbitrary external disturbance. In spite of its simplicity, such a strategy has not been encountered in the literature. The only requirement for this method to be useful is to obtain an optimal control strategy to suppress the vibration of the system when it is subjected to unit response disturbance. To accomplish this, a method from classical optimal control theory such as linear quadratic regulator (LQR) that involves solving the Riccati equation of the associated system can be used. However, genetic algorithm (GA) can be adopted as an alternative way to obtain an optimal control strategy against impulse input. As any arbitrary excitation can be divided into impulses, the convolution concept will constitute the overall optimal control strategy for any arbitrary excitation with simply shifting, scaling and summation (or integration) of the GA-optimized control strategy for each impulse of the arbitrary excitation. The proposed method can be used for real time control applications. Once the control strategy for the impulse disturbance is established, the results can then be used at each time step when online control is performed. Computer simulations were carried out to control the response of a quarter-vehicle active suspension system using the proposed method. The obtained results were compared to those of linear quadratic regulator (LQR) and passive suspension applications. The overall results demonstrated the effectiveness of the proposed method for active suspension systems, especially in suppressing the vehicle body displacement when compared to both the LQR based and passive systems. Furthermore, such a control system proves to be simpler requiring less information to process, which is crucial for real-time applications.