A wavelet-based time-varying adaptive LQR algorithm for structural control

A modified form of the conventional linear quadratic regulator (LQR) control algorithm has been proposed in this paper. The formulation of the modified LQR algorithm uses the information derived from the wavelet analysis of the response in real time, to obtain the local energy distribution over frequency bands. This information reflecting the effect of excitation on the structural system are used to adaptively design the controller by updating the weighting matrices to be applied to the response energy and the control effort. The optimal LQR control problem is solved for each time interval with updated weighting matrices, through the Ricatti equation, leading to time-varying gain matrices. The advantage of the proposed control algorithm is that, it does not require an a priori (offline) choice of the weights as in the classical case and adaptively calculates the gains using the weights decided on the response characteristics in real time (online). The proposed wavelet-based adaptive time-varying LQR (TVLQR) controller is applied to both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) systems and the results are compared with the case of conventional LQR controller. Simulations based on single and multiple controllers indicate that the proposed TVLQR controller achieves significant reduction in the displacement response of the structures as compared to the reduction obtained from the use of LQR controller in some cases with acceptable increment in peak control force and marginal increment in control energy demand.