Numerical Methods For Robust Control Of Interval Parameter Systems

Robustness means the ability a system with uncertainties to maintain normal working performance and it is always taken as an important index to evaluate controller. With the development of control algorithms and techniques, uncertainty problems, especially the controls of system subjected to limited parameter uncertainties, have attracted more and more attention of scholars home and abroad. For robust design of systems subjected to parameter uncertainties, one of the most important approaches is to solve the matrix Riccati equations. Therefore, precise solution of matrix Riccati equations is necessary not only in control theories but also in actual engineering applications.Analogy theories between structural mechanics and optimal control provide a new approach to achieve robust control of systems subjected to parameter uncertainties. The precise integration method of the structure mechanics, which is used to solve matrix Riccati equations, can not only gives high accurate solution but also keep the consistency of the computed results even with a large integration step. Moreover, the parameters of state transfer matrix and controllability matrix of the closed-loop system are computed when solving the Riccati equation. In addition, Lyapunov function method with interval analysis adopted is also one effective way to study robust stability of parameter systems.Uncertain parameters always satisfy certain bounds in actual control systems. Therefore, the key of robust control of time-invariant systems subjected to parameter uncertainties is to deal with limited uncertain parameters as known intervals to study. Based on the Lyapunov interval function and the Lyapunov stability theory, a new method is proposed to analyze robust stability of interval systems. Besides, observability and controllability of linear interval systems are discussed through interval analysis approach as well as the performance criterions. Interval matrix Riccati equation is solved accurately through precise integration method with the interval solutions of system response attained at the same time. So simulation of the closed-loop systems with interval parameters can be executed.