Since its beginnings, the dyn group has not only addressed the traditional field of continuous control but also the practically very relevant field of systems with discrete elements, i.e. logic control, hybrid systems, and production planning and scheduling.

Logic control code, including exception handling, switching between sensors and controllers etc., and sequence control represents the dominant part of the control software and exhibits a large complexity that makes it very difficult to verify its correctness, especially when the logic controllers are interacting with physical systems with continuous dynamics.

Despite significant research efforts, also by our group, a break-through in the systematic development and verification of logic controllers has not yet been achieved. Our most recent work concerned the systematic and intuitive specification of logic controllers and automatic generation of SFC code from the specification. For this, the DC/FT tool has been developed and is available for test users. In the European project MULTI-FORM, we have worked on model transformations and tool chains to support the design of automated systems which forms the basis of the development of the DYMASOS simulation and validation framework.

In scheduling, our focus since long is on dealing with uncertainties in an anticipatory manner by employing the two-stage stochastic programming approach, and in a reactive manner by fast rescheduling in the framework of rolling horizon scheduling based upon timed-automata models. The recent work in this area connects scheduling and logic control design to react to unexpected events in a flexible and efficient manner.

**Publications**

Hüfner, M., Fischer, S., Sonntag, C., Engell, S.: Integrated Model-based Support for Design of Complex Controlled Systems. Computer Aided Chemical Engineering. 31, 2012, 1672–1676.

Fischer, S., Teixeira, H., Engell, S.: Systematic Specification of a Logic Controller for a Delayed Coking Drum. Computer Aided Chemical Engineering. 31, 2012, 355–359.

Scheduling problems in which some information about the future evolution is uncertain at the time of the first decisions, but where more information arrives over time, can be modeled adequately by two-stage stochastic mixed-integer programs. Here the uncertainty is modeled by a discrete set of scenarios. The first-stage decisions have to be the same for all scenarios while the second-stage decisions can be adapted to the future evolution. The presence of these recourse decisions is taken into account when the first-stage decisions are optimized.

With an increasing number of scenarios, the resulting optimization problems become computationally very hard to solve in a monolithic fashion. In our previous work, we employed a stage decomposition approach where the first-stage decisions are optimized by an evolutionary algorithm and the scenario problems are solved by MILP methods.

In the context of the Research Training Group (DFG Graduiertenkolleg) “Discrete optimization of technical systems under uncertainty”, the dyn group is investigating whether the ideas behind Ordinal Optimization: ‘*Order is easier than Value*’ and ‘*Nothing but the best is very costly*’ can be used to improve the computation times further. The key idea is to replace the exact MILP solution of the scenario problems by fast non-exact solutions and to perform a ranking (with small errors) of different promising first stage solutions. According to the theory of Ordinal Optimization, with a high probability one of the best solutions of this ranking is among the best solutions for the original optimization problem, hence good solutions can be found in relatively short computation times.

**Publications**

Sand, G.; Engell, S.: Modeling and solving real-time scheduling problems by stochastic integer programming. Comput. Chem. Eng., 28(6-7), 2004, 1087–1103.

Tometzki, T.; Engell, S.: Systematic Initialization Techniques for Hybrid Evolutionary Algorithms for Solving Two-Stage Stochastic Mixed-Integer Programs. IEEE Trans. Evol. Comput., 15(2), 2011, 196–214.

In all cases where resources (reactors, machines, robots, pallet movers) are used for different tasks or jobs that arrive in an irregular fashion, proper planning and scheduling is needed in order to achieve an efficient processing of the jobs, good resource utilization and customer satisfaction. In practice, schedules are often created manually or by applying simple heuristics which results in fast but suboptimal solutions. On the other hand, extensive scientific work has been done on formulating and solving scheduling problems by mathematical programming, but this is not yet widely applied. One of the reasons for this is that modelling is not intuitive and that realistic problems can only be solved by tailored algorithms.

In the last decade, we have explored an alternative approach: the modeling and solution of scheduling problems using timed automata. Timed-automata models are graphical and modular and the problem-specific parameters can be changed easily. Optimal schedules can be computed by the so-called reachability analysis for timed automata which computes the shortest path from an initial state to the final state where all jobs are finished by graph-search. The dyn group has developed the tool TAOpt that provides an intuitive modeling interface and advanced algorithms for graph search that solve medium-sized scheduling problems very efficiently. An advantage of the timed automata approach is that good solutions are provided very fast. Thus it is well suited for reactive scheduling problems where short response times are needed. For larger problems, time-scale decomposition by means of a rolling horizon approach can be applied.

**Publications**

Subbiah, S., Schoppmeyer, C., Engell, S.: An intuitive and efficient approach to process scheduling with sequence-dependent changeovers using timed automata models. Ind. Eng. Chem. Res., 50(9), 2011, 5131–5152.

Schoppmeyer, C., Subbiah, S., De La Fuente Valdès, J. M., Engell, S.: Dynamic Scheduling of Shuttle Robots in the Warehouse of a Polymer Plant Based on Dynamically Configured Timed Automata Models. Ind. Eng. Chem. Res., 53(44), 2014, 17135–17154.

Integrating reactive scheduling with recipe control

The increasing demand for customized products with short life-cycles and the pressure to produce cheaper, faster, and more flexibly call for an efficient scheduling and a robust operation of multiproduct batch plants. Usually, the planning of the production is done for the next months, and a detailed scheduling is performed for each day. Currently, the scheduling and recipe control layers are not integrated so that disturbances and more severe errors that cannot be compensated by the recipe control layer and thus require quick rescheduling (e.g. machine breakdowns) cannot be handled efficiently.

To overcome this problem, the dyn group is working on operations management systems that integrate scheduling and recipe control by embedding timed automata-based schedule optimization into recipe-driven production based on sequential control logic combined with interlocks. The two levels are integrated by a feedback structure in which the scheduling level passes start signals to the corresponding elementary sequences of the recipe control level which in turn reports end and error signals to the scheduling level.

Experiments on a lab scale multiproduct pipeless batch plant have shown that this integrated system is able to respond quickly and robustly to uncertain events that occur during production.

**Publication**

Schoppmeyer, C.; Fischer, S.; Steimel, J.; Wang, N.; Engell, S.: Embedding of Timed Automata-based Schedule Optimization into Recipe Driven Production. In Proc. 24th European Symposium on Computer Aided Process Engineering (ESCAPE), 2014, 415-420.

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