| In the last decade predictive control has become one of the primary techniques used to regulate multi-variable chemical processes. This popularity is usually attributed to the economic advantages provided by the algorithm's ability to regulate at or near the physical and operational limits of the process (i.e., near process constraints). While regulation of a continually operating process suggests the use of an infinite interval performance measure, the implementation requirements of the predictive algorithm (i.e., through numerically based on-line optimization) have lead the chemical process control community to a number of truncation and/or approximation schemes. These sub-optimal methods have resulted in a host of theoretical as well as practical difficulties, including; an inability to guarantee closed-loop stability, a reduced and ill-defined domain of attraction, inconsistencies between the predicted trajectory and the closed-loop output (even in the absence of disturbances and model mis-match), and tuning challenges associated with horizon size selection.; The objective this work is to investigate the computational feasibility of employing infinite-horizon performance measures in the design of predictive controllers. In particular, disturbance free linear and input affine nonlinear processes will be considered as well as linear systems subject to stochastic and worst-case disturbance inputs. In many cases, it can be shown that the constrained infinite-time closed-loop optimal control policy can be determined exactly by solving an appropriate finite-time open-loop optimization. Additionally, it will be shown that feedback implementation of these policies not only provide closed-loop stability, but also result in the largest possible domains of attraction. These improvements in performance suggest that the presented results will form a basis for the next generation of predictive controllers. |
