Nonlinear Generalized Minimum Variance Control Of Hybrid Systems

Hybrid systems are a class of unified dynamic systems that consist of a combination of discrete event dynamic systems and continuous variable dynamic systems. There are many complicated industrial control processes that can be modeled by hybrid systems, such as intelligent transportation systems, computer integrated manufacturing systems, industrial production control and scheduling systems and modern flight control systems.Hybrid systems can be modeled in a lot of ways, for example hybrid automata, piecewise affine systems, mixed logic dynamical systems, linear complementary systems and so on. The control of linear hybrid automata (LHA) is studied in this thesis. Taking it into account that many hybrid models (i.e. piecewise affine systems and mixed logical dynamical systems) can be transformed into equivalent hybrid automata, hybrid automata are more complex and general models. Thus the research on control of hybrid systems has more general meanings.In this thesis hybrid automata are transformed into its equivalent state-dependent space models where equivalence refers to that the two systems create the same trajectories. While LHA are a class of non-deterministic models, state-dependent space models are deterministic systems with input. During our research, it can be proved that the uncertainty in the process of LHA control mode transition could be totally represented by introducing new input variables. Then we will get the equivalent state-dependent space models of LHA. Afterward, the nonlinear generalized minimum variance (NGMV) control law will be used to control the state-dependent space models and its simulation results are satisfactory. The systems models of NGMV generally can be composed of three parts:delay terms in signal transmission channels, a stable nonlinear input subsystem and an output subsystem represented by state-dependent space model or polynomial matrix, which could be unstable. An optimal controller is obtained by minimizing the variance of the signal consisted of error weighting, control inputs weighting and state variables weighting.By analyzing the simulation results of NGMV control of LHA, it can be seen that this algorithm can effectively control hybrid systems. However, NGMV control method is not mature enough and is still under development and improvement. Especially, the robustness and stability of the systems require further exploration and research.