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| Dynamic and Embedded Optimization |
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| Members |
When dynamic systems described by ordinary differential equations (ODE), differential-algebraic equations (DAE), or difference equations shall be controlled optimally, an optimal control, or dynamic optimization problem has to be solved. Challenges for dynamic optimization are the large-scale and hybrid nature of many real-world systems, their nonlinearity, and the desire to find solutions which are robust with respect to uncertainties. Very often, most prominently in Model Predictive Control (MPC), dynamic optimization problems need automatically to be solved again and again, for changing problem data, e.g. within a process control system, leading to the field of embedded optimization. Challenges for embedded optimization are the fast and reliable online computation of optimal solutions without any human interaction, the design of embedded control systems including state and parameter estimation and exception handling, as well as efficient software-hardware designs. A further challenge are large-scale networks – e.g. electricity or telecommunications networks – which are too large to be treated by a single processing unit for which distributed optimization and control technologies are necessary.
The aim of this working group is to develop numerical methods for the reliable and fast solution of dynamic and embedded optimization problems, to code these methods within open-source state-of-the-art software, and to test them at real-world applications with high societal impact.
The focus of the Dynamic and Embedded Optimization research at OPTEC is:
- Robust Dynamic Optimization Formulations and Algorithms: We develop formulations and numerical methods to address uncertainty in nonlinear dynamic optimization problems. These appear in particular in security sensitive applications in chemical, civil, and aerospace engineering but also in mechatronic and robotic applications with high accuracy requirements despite model-plant-mismatch. The formulations are based on the robust optimization paradigm [1] in combination with linearizations when uncertainties enter nonlinearly [2].
- Microsecond Embedded Optimization Algorithms: In order to achieve ultra-short sampling times for mechatronic MPC applications we tailor numerical methods to the requirements and possibilities of embedded control hardware and even of FPGAs, exploiting features like parallelism and pipelining. Applications are in fast MHE and MPC of numerous fast mechatronic and aerospace systems.
- Distributed optimization algorithms: We will develop computational methods that allow to decouple a central optimization task into a multitude of local problems in a hierarchical or distributed manner and still guarantee convergence to the centralized optimum. The methods will be developed for both parallel computers, and distributed real-world problems which do not allow centralized computations, like in electricity networks. The applications are within external European and industrial projects and regard hydro power valley control (EDF), electricity networks (HD-MPC), and DSL networks (Alcatel).
The goal of the research is to push the international state-ofthe-art in numerical methods for dynamic and embedded optimization as well as their application to real-world problems forward.
