Adaptive control of nonlinear smart base-isolated buildings using Gaussian kernel functions

Abstract

In this paper, a direct adaptive control scheme using Gaussian kernel functions is presented for the active control of nonlinear base-isolated buildings. The control scheme is based on direct adaptive control where the system response is made to follow a desired trajectory. The number of kernel functions is adaptively estimated using a growing and pruning strategy which results in the reduction of the computational overhead. Stable adaptive parameter update laws for Gaussian kernels are derived using Lyapunov approach. Performance of the proposed control scheme is evaluated on the recently developed nonlinear three-dimensional base-isolated benchmark structure. The analytical model of the benchmark structure is highly complex due its three-dimensional nature incorporating lateral and torsional responses, the biaxial interaction of the nonlinear bearings at the isolation layer, and strong coupling between the isolation level forces and the superstructure responses. Control action is provided by eight actuators distributed at the isolation level in each principal direction of the structure, and utilizing the state information corresponding to the base of the structure only. Results are presented using a comprehensive set of the performance indices to realistically quantify the trade-offs associated with the control of nonlinear base-isolated buildings. The main advantages of the adaptive controller presented in this paper are: (i) the control algorithm does not require estimating the system parameters, specifically, mass, stiffness and damping, (ii) the exact nature of the nonlinear dynamics need not be known, and (iii) the control synthesis is noniterative, and on-line. Copyright © 2007 John Wiley & Sons, Ltd.