Moritz Diehl

ABSTRACT In this paper, we discuss robust optimal control techniques for dynamic systems which are affine in the uncertainty. Here, the uncertainty is assumed to be time-dependent but bounded by an L-infinity norm. We are interested in finding a tight upper bound for the worst case excitation of the inequality state constraints requiring to solve a parameterized lower-level maximization problem. In this paper, we suggest to replace this lower level maximization problem by an equivalent minimization problem using a special version of modified Lyapunov equations. This new reformulation offers advantages for robust optimal control problems where the uncertainty is time-dependent, i.e. infinite dimensional, while the inequality state constraints need to be robustly regarded on the whole time horizon.

Based on thorough experiences with distributed experiment control systems and fieldbus applications we are developing a control system especially targeted at neutron scattering experiments. Main characteristic is that frontend equipment and control machine are coupled by the industrial fieldbus standard PROFIBUS (DIN 19245, EN 50170). This significantly reduces the amount of cabling necessary. Further, it provides the proven error recovery

Comput Visual Sci DOI 10.1007/s00791-011-0158-4 Nested multigrid methods for time-periodic, parabolic optimal control problems Dirk Abbeloos · Moritz Diehl · Michael Hinze · Stefan Vandewalle Received: 16 January 2011 / Accepted: 24 May 2011 © Springer-Verlag 2011 ...

ABSTRACT In this paper we present a systematic and efficient approach to deal with uncertainty in Nonlinear Model Predictive Control (NMPC). The main idea of the approach is to represent the NMPC setting as a real-time decision problem under uncertainty that is formulated as a multi-stage stochastic problem with recourse, based on a description of the uncertainty by a scenario tree. This formulation explicitly takes into account the fact that new information will be available in the future and thus reduces the conservativeness compared to open-loop worst-case approaches. We show that the proposed multistage NMPC formulation can deal with significant plant-model mismatch as it is usually encountered in the process industry and still satisfies tight constraints for the different values of the uncertain parameters, in contrast to standard NMPC. The use of an economic cost function leads to a superior performance compared to the standard tracking formulation. The potential of the approach is demonstrated for an industrial case study provided by BASF SE in the context of the European Project EMBOCON. The numerical solution of the resulting large optimization problems is implemented using the optimization framework CasADi.

ABSTRACT The performance of an open volumetric air receiver depends on the quality of the flux density distribution on the receiver surface and on the use of irradiated power in the receiver. Whereas flux density distributions can be optimized using aim point optimization e.g. with ant colony optimization algorithms, a method for the thermal optimization of the receiver is presented using dynamic programming as powerful optimization algorithm. The total mass flow rate of the receiver is maximized with given desired air outlet temperature by choosing the optimal combination of mass flow rates and air temperatures in the subreceivers under consideration of flux density and temperature restrictions. The optimization method is demonstrated successfully in five simulation cases and possible application fields like receiver design, development of operation strategies for receiver and heliostat field are discussed. A combined optimization of aim point optimization and thermal optimization is planned for the future.

ABSTRACT We demonstrate how CasADi, a recently developed, free, open-source, general purpose software tool for nonlinear optimization, can be used for dynamic optimization in a flexible, interactive and numerically efficient way. CasADi is best described as a minimalistic computer algebra system (CAS) implementing automatic differentiation (AD) in eight different flavors. Similar to algebraic modeling languages like AMPL or GAMS, it includes high-level interfaces to state-of-the-art numerical codes for nonlinear programming, quadratic programming and integration of differentialalgebraic equations. CasADi is implemented in self-contained C++ code and contains full-featured front-ends to Python and Octave for rapid prototyping. In this paper, we discuss CasADi from the perspective of the developer or advanced user of algorithms for dynamic optimization for the first time, leaving out details on the implementation of the tool. We demonstrate how the tool can be used to model highly complex dynamical systems directly or import existing models formulated in the algebraic modeling language AMPL or the physical modeling language Modelica. Given this symbolic representation of the process models, the resulting optimal control problem can be solved using a variety of methods, including transcription methods (collocation), methods with embedded integrators (multiple shooting) as well as indirect methods.

ABSTRACT Algorithms for fast real-time Nonlinear Model Predictive Control (NMPC) for mechatronic systems face several challenges. They need to respect tight real-time constraints and need to run on embedded control hardware with limited computing power and memory. A combination of efficient online algorithms and code generation of explicit integrators was shown to be able to overcome these hurdles. This paper generalizes the idea of code generation to Implicit Runge-Kutta (IRK) methods with efficient sensitivity generation. It is shown that they often outperform existing auto-generated Explicit Runge-Kutta (ERK) methods. Moreover, the new methods allow to treat Differential Algebraic Equation (DAE) systems by NMPC with microsecond sampling times.

A nonlinear model predictive control (NMPC) formulation is used to prevent an exothermic fed-batch chemical reactor from thermal runaways even in the case of total cooling failure. Detailed modeling of the reaction kinetics and insight into the process dynamics led to the formulation of a suitable optimization problem with safety constraints which is then successively solved within the NMPC scheme.

We develop a state-of-the-art nonlinear model predictive controller (NMPC) for periodic unstable systems, and apply the method to a dual line kite that shall fly loops. The kite is described by a nonlinear unstable ODE system (which we freely distribute), and the aim is to let the kite fly a periodic figure. Our NMPC approach is based on the “infinite

Model Predictive Control (MPC) is a control technique capable of accounting for constraints on inputs, outputs and states, and traditionally makes a trade-off between output error and input cost. Originally developed for slow processes, MPC is nowadays also applied to faster systems such as mechatronic systems, thanks to increased computer power and more advanced algorithms. For these systems however, time optimality is often of the utmost importance, a feature that is not present in traditional MPC. This paper therefore presents and validates a new type of MPC, time optimal MPC (TOMPC), which minimizes the settling time. An experimental validation of TOMPC on a linear drive system with a sampling time of 5ms is performed and comparison with traditional MPC and linear feedback systems is given.