**Duration:** 4 years.

**Financial terms:** 550 EUR monthly scholarship +
additional bonuses based on performance.

List of available projects:

In Model Predictive Control (MPC), control inputs are determined by solving an optimization problem, which takes process constraints and economic criteria into account. Because optimization is time consuming, implementation of MPC in real time can be cumbersome if cheap control platforms are employed or when the system's dynamics is fast. One way around this issue is to pre-compute the optimal control input using parametric programming and store such a pre-computed solution in a look-up table. Implementation of MPC then reduces to finding an element of the table which contains measurements of the process variables. This project has two main objectives. First, to develop and to construct a set of test beds that represent systems with a fast dynamics. Examples of such systems include mechanical systems (e.g., an inverted pendulum), or chemical processes with fast chemical reactions. The second objective is then to develop tailored MPC strategies for control of such systems. Such controllers must be simple enough as to allow for their fast implementation, and robust enough to cope with nonlinearities and disturbances.

The goal of the project is to design, implement and validate control systems which guarantee a safe operation of the controlled plant even in the presence of uncertainties, disturbances or targeted attacks on the control infrastructure. This goal will be achieved by a suitable combination of theoretical, computational and implementation tools and procedures with the objective to provide a formal certificate of a safe and correct operation of the control system. Theoretical concepts will be based on optimal and predictive control. Implementation procedures will use parametric and convex optimization. Resulting safe control systems will be implemented on hardware platforms typically used in process automation.

In Model Predictive Control (MPC), control inputs are determined by solving an optimization problem, which takes process constraints and economic criteria into account. Because optimization is time consuming, implementation of MPC in real time can be cumbersome if cheap control platforms are employed. One way around this issue is to pre-compute the optimal control input using parametric programming and store such a prec-computed solution in a look-up table. Implementation of MPC then reduces to finding an element of the table which contains measurements of the process variables.

Even though implementation of MPC by table lookup is simple, the downside being that once the table becomes more complex, more time is required to search through it and the more memory the table consumes. Therefore it is of great practical importance to develop novel techniques and methods to reduce the table size and to speed up its lookup. The project therefore aims at attacking two goals, which are closely related. The first one is to reduce the size of the look-up table, e.g. using algorithms from computer graphics (graphical and fractal compression, hash tables, etc.). The other goal is to devise novel algorithms capable of performing the table lookup more efficiently (e.g. by employing search trees, looking for the nearest neighbor, etc.).

Hybrid systems represent a relatively new approach to control of physical processes using digital control systems. The idea of hybrid systems is to combine two fundamentally different approaches to system modeling. While the physical part of the system is usually described by differential or difference equations involving continuous variables, the digital controller typically involves IF-THEN-ELSE switching actions, which involve mainly binary variables. Hybrid systems are nowadays a proven concept with many applications ranging from air traffic control, through modeling and control of cars using adaptive cruise control, regulation of power transmission lines, up to control design for complex processes of the chemical and petrochemical industry.

The aim of the project is to develop a systematic approach to modeling and control of hybrid systems using optimization methods. The modeling part will be focused at finding new theoretical and computational approaches to automatic linearization of nonlinear functions using multiple linearization points. This will allow to describe even complex physical systems using relatively simple mathematical models. These models will be subsequently used for control design using the model predictive control principle. The objective is to extend existing and develop new methods which would allow the resulting optimization problems (which involve continuous and binary variables) to be solved in real-time. Finally, the methods and concepts developed throughout this work will be verified, experimentally, on various chemical plants (including chemical reactors, distillation columns, heat exchangers, etc.) and on autonomous robots.

In networked control systems, control inputs are transmitted to the controlled plant via a communication network, which can be prone to various adversary effects. These effects range from directed attacks, through signal corruption and delays due to packet loss, up to total loss of communication capabilities. In a better case, such a disruption leads to deterioration of performance, but, in the worst case, can even damage the controlled plant. Therefore the project aims at securing networking control systems agains the above mentioned effects. This involves detecting the attacks and compensating for the undesired behavior. One possible way of achieving this goal is to combine model predictive control with Lyapunov stability theory to devise a protecting block which "filters" the received control command and safe-guards it.