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An algorithm for adaptive predictive control of chemical process systems is presented. A least squares based identifier with regularization prevents the covariance matrix from becoming singular and an adaptive deadzone is applied to help prevent parameter drift and output bursting. Furthermore, the estimated parameters are projected into a compact convex set which contains the true plant parameters. The proposed estimation algorithm can be used in conjunction with pole assignment, optimal, and predictive control provided that the projection procedure is implemented so that all estimated plants are stabilizable and the control policy remains feasible. A proof of bounded input, bounded output stability of an adaptive pole assignment algorithm in the presence of output disturbances and model mismatch is presented. The result can be extended to unconstrained predictive control. The application of the proposed approach to a constrained distillation control and optimization problem proposed by the SHELL Development Co. is discussed.