Research On Some Main Technique Of Hybrid Dynamical System

Hybrid dynamical system has a rich application background and the broadly theory supporting, which make it be research hot topic in the fields of the control theory and engineering, and also in computer science. It made us to solve the synchronization problem for the diversity of signal type and the dynamical character in which appeared in the hybrid system. It is indispensability process to locate the state event for solving the synchronization problem. This thesis begins with the supervisory control framework and hybrid automata and focused on the state event triggered by the interaction of the continuous and discrete dynamical, and solved some main problem existed in studying the state event. The content is as following:1. Presented a survey for the hybrid dynamical system in depth. The feature problem including how to express the time, synchronization problem, and the determination of the solution for solving the system equations were analyzed. It also talked about the research the statues in quo about the modeling, verification, stability analysis, controller design, and the tools for verification and simulation of the hybrid dynamical system.2. Discussed the supervisory control framework and hybrid automata for modeling the hybrid dynamical system, which including its application, its plant described, its control goat, interface and controller designing technique. Furthermore, also discussed the indetermination problem and the abstract technique in which appeared in adopting the supervisory control framework. The relationship between hybrid automata and supervisory control framework was also discussed.3. Based on the monotony of dynamical evolution and event condition for hybrid dynamical systems, and on the probability of taking place the state event, a layered state event detection method was presented to improve the efficiency of state event detecting. The analysis and simulation result shows it was validity when the multi-event happened.4. A step-by-step approaching method was presented for locating the state event during designing the interface or simulating the hybrid dynamical system. The rational integrate step adjust strategy was also presented by studying the dynamical trajectory of the hybrid systemevent condition. It solved the problem that the usual locate method could locate the state event precisely when the "discontinuity sticking" phenomena appeared, and also overcome the limitation when using the "discontinuity locking" technique.5. An interval sets rapid searching method was presented to improve the state event locating precision and to solve the discontinuity sticking phenomena, which is caused by the coupling of modes and states, and by the location error transferring among the modes for the hybrid dynamical systems. Given the error bound of location state, this method can accurately locate the state events rapidly.6. Based on the result of inverse for the generalized Vandermonde matrices, the strict transformation relationships between the continuous-time model and the discrete-time model when they have multiple poles are proofed. The transformation results can directly be expressed as the relationship between the numerator polynomial coefficients of the two models, and it exists the unified transformation forms as to the different type of the holders.Finally, the further research topic was put forward in the fields about this thesis.