The project will advance our knowledge in all system-theoretic aspects of hybrid systems in order to provide control engineers with new conceptual, mathematical and CAD tools for building controllers for such systems. Special emphasis will be put on computationally effective control results, that is not only existential mathematical results and abstract synthesis algorithms, but methods that can be implemented using current software and hardware technology. The project will progress according to the following major axes.
Survey of Hybrid Control (SC Package)
We intend to investigate some major classes of control applications and see how hybrid phenomena manifest themselves in the modeling and controller synthesis for such applications. In particular we will learn how industrial control engineers overcome the limitations of classical models in order to cope with discontinuous models. Since control systems can be found practically everywhere, we do not intend to be exhaustive, but such a survey can be beneficial beyond this particular project. In addition, we believe that there is a lack of mutual understanding between communities interested in hybrid control problems and even inside the same community due to the lack of a reference framework where different models, assumptions and algorithms could be related to each other and even compared. We believe this is actually slowing down the progress of the field and we plan to spend time trying to place models and algorithms in a unifying framework.
Hybridization of Control (CH Package)
Under this title we put the adaptation of the basic system-theoretic notions, control synthesis and optimization techniques to the hybrid setting. The principal object of study will be linear hybrid systems, in both continuous and discrete time, for which we will try to develop control and optimal control synthesis techniques. Due to the hardness of the combinatorial optimization problems implied by the hybrid nature of the system, approximations of the optimal solution must be considered as well. A special care will be given to the computational complexity trade-off between on-line and off-line computations of the feed-back function.
Reachability-based Methods (RM Package)
We intend to continue with the effort of devising controller synthesis methods based on generalized search strategies over the state-space of the system. This approach is particularly attractive for defining "switching surfaces" between several continuous modes of operation. So far it has been applied mostly to the verification of safety properties but we intend to extend it to controller synthesis for additional properties and performance criteria. In order to develop such techniques, geometrical properties of dynamical systems will be studied along with classes of geometrical objects (simplices, orthogonal polyhedra, ellipsoids) which are used to reason about the system dynamics or to approximate reachable states. A special effort will be directed toward efficient data-structures and algorithms for manipulating these objects. These techniques can also be used to verify controllers that have already been synthesized using ad-hoc methods.
Tools (TL Package)
The developed techniques will be implemented into prototype tools that can be used by engineers to test the applicability of the ideas in the design process. Such tools will feature a user-interface for easy definition of hybrid control systems and a collection of algorithms for automatic and semi-automatic controller synthesis and verification.
In order to maintain a good contact with industrial reality, we will investigate two classes of case-studies to be supplied by the three industrial partners. They will come from domains where practitioners have already recognized the need for hybrid techniques. The first will be related to the rapidly developing domain of engine control in vehicles, using hybrid models of internal combustion engines and power-train systems. The second class will involve models of an integrated electrical power production and distribution systems. We will investigate optimal policies for activating and shutting off production units according to changes in the demands and costs while maintaining system stability.