Observer Design Of Nonlinear Differential-Algebraic Sub-systems

Nonlinear Differential-Algebraic Equations systems are also known as Singular systems or Descriptor systems. It has been found that many problems are modeled by Differential-Algebraic Equations systems, such as robotics, electrical circuits, computer aided design. The controlled plants are usually treated as isolated systems, where are not considered influences between the controlled plants and the rest of the large-scale systems. Based on state feedback, most of controllers are designed. However for many practical controlled plants, there exist mutual constraints and influences, where are affected by the interconnection inputs of the rest of the large-scale systems. The controlled plants are nonlinear Differential-Algebraic sub-systems within large-scale systems and only the output signals can be feedbacked when the control scheme is designed. Therefore, the problems of nonlinear Differential-Algebraic sub-systems state observer design are particularly important.Motivated by this, in this paper the problems of state observer design are researched for a class of a nonlinear Differential-Algebraic sub-systems of index one and interconnection inputs local measurable. Many practical systems such as power systems components just fall into the category studied in this paper. Main contents in this paper are as follows:1. The single-input single-output nonlinear Differential-Algebraic equations sub-systems observer design problems are studied, given initialized observer and non-initialized observer design programs.(1) By a system diffeomorphism, the equivalent system transformation is achieved. The problems of observer design are studied based on equivalent system by the characteristics index1and interconnection input variables local measurable of nonlinear Differential-Algebraic equations sub-systems making the observer state error asymptotically converges to zero. Initialized observer needs the initial state of the observer to satisfy the algebraic equations.(2) Non-initialized observer design method by a diffeomorphism, the equivalent system transformation is achieved. Based on the equivalent system, making the system satisfied the Lipschitz nonlinear conditions by index1and interconnection input variables local measurable of nonlinear Differential-Algebraic equations sub-systems, the problems of observer design are studied The observer state error is asymptotically converges to zero. The initial states of observer do not need to restrict to the algebraic equations. 2. The single-input single-output nonlinear Differential-Algebraic equations sub-systems observer design is expanded. The multi-input multi-output observer design problems are syudied, given initialized observer and non-initialized observer design programs.(1) The equivalent system transformation is achieved by a system diffeomorphism. The problems of observer design are studied based on equivalent system. For any bounded input u, Lipschitz nonlinear conditions, Lyapunov stability theorem and nonlinear differential-algebraic sub-system properties are used, making the observer state error asymptotically converges to zero by the characteristics index1and interconnection input variables local measurable of nonlinear Differential-Algebraic equations sub-systems. The observer state error is asymptotically converges to zero. Initialized observer needs the initial state of the observer to satisfy the algebraic equations.(2) The proposed non-initialized observer design method by a diffeomorphism, the equivalent system transformation is achieved. Based on the equivalent system, non-initialized observer is proposed and proved the observer exponential convergence to zero. For the original system, the problems of observer design are studied for any bounded input u, making the system satisfied the Lipschitz nonlinear conditions, Lyapunov stability theorem, the Lyapunov function and nonlinear Differential-Algebraic equations sub-systems properties. The observer state error is asymptotically converges to zero. The initial states of observer do not need to restrict to the algebraic equations.