Modelling in the contexts of verification and design/12. Control Design

Here, on a level of abstraction the steps to take to derive a control for a given plant. In the end, the control synthesis problem is reduced to a schedule synthesis problem, which is known to be hard. This is even more the case, as we typically will not have standard cases of scheduling problems, like job-shop, but complex ones with many sorts of dependencies and restrictions between tasks.

We identified the method for a cook&kitchen example, which provides most intuition, but can be mapped to other application areas easily. In this terminology a kitchen with all its pans, knifes, ovens, etc. corresponds to an instrumental view of a system. A recipe describes the basic steps that have to be taken to prepare a dish. A recipe can be executed in different kitchens, and also within one kitchen there are different possibilities to cook according to one recipe. An order of a menue consists of different dishes that have to be served at certain moments of time. The control design corresponds to the problem to describe at which time which steps in the kitchen have to be performed, using which tools, such that the menu is prepared correctly.

With this intuition we describe the steps for control design as follows:

1. Construct an instrumental decomposition of the system.
2. Provide a recipe-based decomposition: for this, identify elementary steps in the recipe. Describe the elementary steps, their pre- and post- conditions, ordering, timing behaviour.
3. Provide a mapping from the elementary recipe-steps to the instrumental components of the system.
4. Extend the set of conditions, and behavioural properties inherited from the instrumental components to the elementary recipe-steps.
5. Identify the orders of the systems (possibly the overall requirement).
6. Let a scheduler find possible execution orders of basic recipe steps in the available physical system, such that in the end the order is satisfied.
7. Design control fragments for the elementary recipe steps mapped on the available physical system.
8. Compose the control fragments according to the results of the scheduler.