Optimal Sliding Mode Control For A Class Of Affine Nonlinear Systems With Uncertainties

Nonlinearities and uncertainties are general for real models. Linear quadratic performance index can synthetically manifest the requirement of the system performance. The optimal control theory based on Linear Quadratic Regular (LQR) for linear systems has developed well, and achieved significant results. But it is difficult to get the analytical solutions, when it is used to deal with the optimal problems of nonlinear systems. In addition, the optimal controller is usually designed for systems based on precise mathematical models. When the system is subject to uncertainties, such as parameter variations and external disturbances, the system performance criterion will deviate from the desired values, even becomes unstable. Sliding mode control (SMC) is considered to be an effective robust control approach, one of the most advantages of SMC is that during the sliding mode, the SMC system has robustness to matched parameter uncertainties and external disturbances.Considering the problems above, the problems of optimal control, optimal sliding mode design and global robust optimal sliding mode control are investigated for a class of affine nonlinear systems with uncertainties in this dissertation. The main studies are as follows:1. The optimal control problem for a class of affine nonlinear systems is studied by SDRE (State Dependent Riccati Equation) method andθ- Dmethod. The SDRE method simulates the LQR formulation for linear system, transforming the nonlinear system into the state dependent coefficient (SDC) form, then gets the approximate optimal control law; Theθ- D method is carried out by solving the HJB (Hamilton Jacobi Bellman) equation approximately which is achieved by adding perturbations to the cost function. Simulation results demonstrate the effectiveness and superiority of two proposed methods.2. The optimal sliding mode control problem for a class of uncertain linear systems is considered. First, the optimal control law based on LQR is obtained for nominal system, then, the sliding mode control theory is used to robustify the designed optimal controller, thus the dynamic system exhibits global robustness to the uncertainties, satisfies requirement of given optimal performance criterion. The proposed approach is applied to a magnetic levitation system, and simulation results show its effectiveness.3. The problem of global robust optimal sliding mode control for a class of affine nonlinear system is designed. Theθ- Dmentioned above is adopted to solve the optimal (suboptimal) control law, which is used to stabilize and optimize the nominal system; the construction of integral sliding mode surface remove the reaching phase of conventional SMC effectively; the discontinuous law is designed, which provides complete compensation for uncertainties of the system. So the global robust optimal sliding mode control is realized. A ball-beam system is considered to demonstrate effectiveness of the proposed strategy.