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The aim of the thesis is to provide techniques for computing and application of explicit
model predictive control of processes in real-time. Explicit model predictive control is a
method for optimal control of processes with constraints where the control law is given
in an explicit form. It is an optimization based approach where a process model is used
to predict the future. In the presented approach the model is derived using a hybrid
modeling framework. It will be shown how that hybrid models are capable of modeling
wide class of processes with a sufficient precision. Based on the hybrid model, it is possible
to formulate an optimal control problem which considers varying dynamical properties
of the plant and moreover, takes the operating constraints into account. If the optimal
control problem is solved for the whole set of initial conditions, an explicit solution is
obtained. The explicit solution characterizes the optimal control law as a function of given
initial conditions. This allows the control law to be easily realized in practice, just by
evaluating the function for given value of initial conditions. Therefore, the explicit model
predictive controller designed in this way is especially suitable for applications with fast
dynamical changes which require low implementation cost. The thesis describes essentials
for understanding ingredients of explicit model predictive control. In particular, the main
part concerns with construction of hybrid models and their deployment in formulation of
optimization problems. Consequently, efficient algorithms for computing explicit solutions
to time optimal control problems are proposed. Obtained results are applied in real-time
experiments that show desired optimal performance and the controller satisfies all operating
constraints.