Hybrid models describe systems composed of both continuous and discrete components. The former are typically associated with physical first principles, the latter with logic devices, such as switches, digital circuitry, software code. A typical instance are real-time systems, where physical processes are controlled by embedded controllers. Our research focuses, among other topics, on the synthesis of optimal controllers for hybrid systems, the formal verification for safety and stability analysis, and the development of efficient software tools for modeling and control of hybrid systems. We introduced a new framework for modeling of hybrid systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are hybrid systems described by linear discrete-time dynamic equations subject to linear inequalities involving real and integer variables. We developed the declarative language HYSDEL (HYbrid System DEscription Language) which fully automatizes the construction of MLD and Piecewise Affine (PWA) forms from a high level description of the hybrid system. For hybrid systems we study constrained optimal controllers which are able to stabilize hybrid systems on desired reference trajectories while obeying operating constraints, and possibly take into account previous qualitative knowledge. The potential of the method was demonstrated on a number of industrial applications. We have shown how optimal controllers can be expressed explicitly as piecewise affine control laws by solving multiparametric programs. In this form the controllers are suitable for implementation on fast hybrid processes. Almost all algorithms developed by our group are available in the Multi-Parametric Toolbox. |