Covariance tracking method for designing a robust receding horizon controller

Abstract

In this paper, a novel covariance tracking receding horizon (CTRH) process is proposed to design a robust control algorithm. Some drawbacks of the equivalent robust algorithms, including infeasibility, computational complexity, and non-optimality, are alleviated in this process. Hence, first, covariance analysis is applied to rephrase the dynamic equation of the system to model the structural uncertainties. Afterward, this approach is extended to the future time horizons as the discrete-time formulations are to be embedded in the receding horizon controller framework. Then, a new constrained quadratic programming cost function is proposed considering the covariance matrix to mitigate the trajectory dispersion along with the control action. The final control rule is estimated by solving the new cost function using the Hildreth method. The efficiency of the developed robust algorithm is demonstrated by numerical simulation of two benchmark buildings equipped with active tendon systems subjected to earthquake excitations. The competency of the proposed method (CTRH) is then proven using nominal and various perturbed scenarios and outputs compared to the linear–quadratic–Gaussian (LQG) controller, sliding mode control (SMC), H∞, and conventional receding horizon (CRH) controllers, and comparative results are presented. The outcomes indicate that the proposed method not only well reduces the controlled responses compared to uncontrolled one but also demonstrate a high level of robustness against various other control approaches. Less computational complexity due to not adding any linear matrix inequalities and constraints is also one of the prominent features of the proposed approach.