Hybrid MPC: An Application to Semiactive Control of Structures

In clipped LQR, a common strategy for semiactive structural control, a primary feedback controller is designed using LQR and a secondary controller clips forces that the semiactive control device cannot realize. However, when the primary controller commands highly non-dissipative forces, the frequent clipping may render a controller far from being optimal. A hybrid system model is better suited for semiactive control as it accurately models the passivity constraints by introducing auxiliary variables into the system model. In this paper, a hybrid model predictive control (MPC) scheme, which uses a system model with both continuous and discrete variables, is used for semiactive control of structures. Optimizing this control results in a mixed integer quadratic programming problem, which can be solved numerically to find the optimal control input. It is shown that hybrid MPC produces nonlinear state feedback control laws that achieve significantly better performance for some control objectives (e.g., the reduction of absolute acceleration). Responses of a typical structure to historical earthquakes, and response statistics from a Monte Carlo simulation with stochastic excitation, are computed. Compared to clipped LQR, hybrid MPC is found to be more consistent in the reduction of the objective functions, although it is more computationally expensive.