A Numerical Method For Solving Optimal Con-trol Of Hybrid Systems And Its Application To Nonlinear System Control

Hybrid systems exist extensively in practical engineering. Optimal control for hybrid sys-tems is one of the most important problems of hybrid system theory. It has both great theoretical meanings and extensive practical background. In this dissertation, a numerical method for solv-ing optimal control for hybrid systems is developed, and its application to nonlinear control is studied. The main contributions are as follows:1. A simultaneous method based on the orthogonal collocation on finite element is proposed for the numerical solution of optimal control problem for hybrid systems. There are many complex constraints in the optimal control for hybrid systems, so explicit solutions can not be easily obtained. Numerical solutions are usually obtained by solving mix-integer pro-gramming, which results from discretizing the optimal control problem for hybrid system. Euler method is the most popular method to this day, such as MLD-MPC method and so on. The discretization step length can be reduced to improve the numerical precise, while the computation will be lowered down. Additionally, the MLD-MPC method is based on the logical events, so it just can be used to solve the proposition of optimal control for hybrid system, whose mode switching is controlled. To overcome these shortcomings, a simultaneous method based on the orthogonal collocation on finite element is proposed for the numerical solution of optimal control problem for hybrid systems based on previous research. Compared with the Euler method, the proposed method in this thesis can acceler-ate the solving process significantly. Compared with the MLD-MPC method, the proposed method can be used to solve the optimal control problem of hybrid system, where mode switching is either controlled or autonomous.2. The proposed simultaneous method based on the orthogonal collocation on finite elemen-t for optimal control problem of hybrid systems is applied to nonlinear control. So far, the control problem of nonlinear system is still one of the most difficult problems in con-trol science and engineering. Usually the multimodel control method is used to avoid the harmful effect of nonlinearity, while it is difficult to schedule submodels/subcontrollers, and oscillation may occur during switching. In order to overcome these drawbacks and keep the advantage of multimodel method that multiple linear model are used to approxi-mate a nonlinear system and reduce its nonlinearity, the optimal control method for hybrid system is applied to nonlinear systems in a unified model framework and with a uniform objective function to get a better control performance.3. Receding-horizon strategy is employed to resist random disturbances and make up model-plant mismatches during discretization. In practice, almost every process confronts with uncertain disturbances, which may have negative effects on system evolution. And the model-plant mismatches may affect system stability and control accuracy. In order to over-come these shortcomings, the receding-horizon strategy is employed to remedy model-plant mismatches and resist the uncertain disturbances. And simulations approve of the proposed method.