Mystery World Contributors Amit and Minakshi Sanyal

One of the most successful techniques to arise from modern control theory works in the following way. Using current measurements of states of the system, control values are determined that make the output of the system follow a desired trajectory over a specifi ed interval of time into the future. Assuming suffi cient computational power and a suffi ciently accurate model of the system, numerical algorithms are used to compute these control values. The computations are usually generated by an optimization method and can take into account constraints that must be satisfi ed, for example, on the states and controls. Of the computed control values, only the fi rst value is implemented. The procedure is repeated at the next time instant and so forth. This method is known as either receding horizon control or model predictive control. A receding horizon controller does not necessarily resemble a PID control law or even an LQG or H` control law. In effect, the control law is an extremely nonlinear feedback control law, and there may be no way to represent it by an explicit formula. Nevertheless, in 1988, Elmer Gilbert and Sathiya Keerthi showed that, under fairly mild assumptions, receding horizon control can stabilize a system; it is, after all, a closedloop control strategy. Consequently, Digital Object Identifier 10.1109/MCS.2011.940722 Mystery World