Traditionally, scheduling and control are viewed as two related but disparate engineering activities. For scheduling, the main decisions are typically discrete yes/no choices; the models capture only important discrete events and transitions but include many units; and, the objective is generally economic in some sense (minimize, e.g., cost or earliness). For control, the decisions are almost always continuous in nature; the models describe detailed temporal dynamics of the system but are local in scope; and, the objective function is artificially designed to maintain the system at a predetermined setpoint. Despite these differences, both problems an be addressed by formulating a mathematical optimization and solving it repeatedly as new information is received. For control systems, re-optimization is necessary to compensate for unknown disturbances and model errors, or to respond to changes in setpoint, and these same general considerations also trigger rescheduling. While the timescales may be quite different (in terms of both the horizon of optimization and how frequently optimization is performed), this similarity raises the question of whether the two disciplines can be unified under a single mathematical treatment. In this presentation, we advance the idea that certain classes of scheduling and control problems are indeed two variants of the same overall problem that differ only in their respective system dynamics and decision space, and thus can be analyzed using a common set of tools.
To exploit this connection, we revisit previous work that shows how a common scheduling model can be written in state-space form. This abstraction allows the model to be viewed as a dynamic system rather than as a set of combinatorial constraints. Next, we discuss results showing that, with suitable assumptions, the presence of discrete-valued control inputs does not affect the stability properties of model predictive control (MPC). Combining these ideas, we show that economically optimizing scheduling and control problems can both be viewed as cases of dynamic real-time optimization or economic MPC, which has important ramifications for closed-loop implementation. These connections are illustrated throughout the talk with simple, easy-to-understand chemical production scheduling problems.
Speaker: James Rawlings, UC Santa Barbara
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