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This thesis presents several contributions to tube-based model predictive control (MPC) for linear parameter-varying (LPV) systems. A common feature of the presented approaches

is their anticipative capability: that is, the capability of exploiting available information on the possible future trajectories of the scheduling variable to improve control performance.
The LPV system concept can be used to model physical systems whose dynamics depend
on an external parameter or on the current operating point. In an LPV system, the dynamical mapping between the control input and the output is linear, but this mapping depends on a so-called scheduling variable. The dynamics of an aircraft, for instance, can vary with its airspeed and altitude: these two quantities can therefore considered to be scheduling variables. It is also possible to “embed” a non-linear system in an LPV representation. In that case, the scheduling variable is used to capture the non-linear behavior. In engineering, systems are often subject to constraints. These constraints can include hard limitations on the control actuation inputs that can be applied, and limitations on the allowed resulting behavior of the system. MPC is a control design approach that can ensure that the constraints will not be violated. A central feature of MPC is its explicit use of a mathematical model to predict the future response of the system. At each sampling instant, this prediction model is used in an optimization procedure to decide which control input should be applied. In the LPV setting that is adopted in this thesis, the current value of the scheduling variable can be measured, but its future evolution is considered uncertain. Therefore, at each sampling instant, an LPV MPC must compute a control action that guarantees closed-loop stability with respect to all possible future realizations of the scheduling variable. In some applications, however, future scheduling trajectories are not completely uncertain, but some knowledge about their possible future behavior is available. In this thesis, a thermal control problem from semiconductor lithography is considered in which the scheduling variable corresponds to an exposure trajectory that is approximately known in advance. Because the temperature which is to be controlled depends on the scheduling variable, to achieve the best possible performance, it is necessary to use this information in predicting the future response of the system and deciding which control input should be applied.

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