The Algorithmic Research Of Optimal Control Problem On Uncertainty Linear System

Some unknown elements always exist in the analysis process for the control systems, such as unmodeled dynamics, parametric uncertainties, changes of the operating environment, model reduction and linearization approximations etc., or external disturbance. So it is almost impossible to obtain an accurate mathematics model for the practical industrial process. Therefore, the based-model modern control is hardly used widely in a practical control system, but the appearance of the based-robustness optimal Control give the modern control theory a new future, it solves the problem between modern control and engineering applications. So the robustness analysis and the design of the optimal controller become the main task in the control theory research.Meantime, engineering systems usually run with fixed bounds, and control actions must satisfy the strict limitations. Therefore, the constrained control problem emerges. When constraints are ineluctable factors, we must deal with constraints while designing the controller of systems, otherwise, the expected index could not be obtained or bring tragedies sometimes. This thesis researches stabling and optimal control problems of linear constrained uncertainty system after the introductions of the linear constrained system and linear uncertainty system's optimal control.Linear matrix inequalities are special form of convex polyhedral sets, which connect constrained conditions of the system and play an important role in design of controller. The uncertainty control problem of linear systems with constraints of control, state and initial state is studied. First, based on Lyapunov stability theory, use linear matrix inequality and matrix analysis as the main mathematical tools, the linear constrained uncertainty system's control problem transformed to the an optimal problem with the LMI form, using the optimal solver of the LMIs from the dynamic system, state feedback controller is designed so that initial states transfer asymptotically while all constraints are satisfied. Second, measure the states of the system, treat them as the new initial states and solve the new optimal problem which contains the system's states, obtain the next control law and so on. The control gain is different from time to time, reduce the conservation and enhance the robustness confronting the external disturbances.In addition to the above main result, we also consider the control problem of a class of high-speed sampling systems with convex polytopic uncertainties. Based on the linear matrixinequality (LMI) approach, sufficient conditions are derived for given H_∞ cost of the systems via parameter-dependent Lyapunov functions. Furthermore, the computation problems of the optimal H_∞ cost are formulated as a convex optimization problem with LMI constraints. It'll bring an important significance for the high-speed sampling systems' research.