This chapter concentrates on how to implement predictive controllers for processes with constrained input and output signals. Most of the controlConstraintscontrol problems formulated in the previous chapters considered all signals to possess an unlimited range. This is not very realistic because in practice all processes are subject to constraints. ActuatorsActuators have a limited range of action and a limited slew rate, as is the case of control valves limited by a fully closed and fully open position and a maximum slew rate. Constructive or safetySafety reasons, as well as sensor range, cause bounds in process variables, as in the case of levels in tanks, flows in pipes, and pressures in deposits. Furthermore, in practice, the operating points of plants are determined to satisfy economic goals and lie at the intersection of certain constraints. The control system normally operates close to the limits and constraint violationsConstraints–violations are likely to occur.