Control Design for Nonlinear System Described by Differential-Algebraic Equations

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In this research, we study controller design of nonlinear systems described by differential-algebraic equations (DAE). In nonlinear cases, it is hard to convert the system to ordinary differential equations (ODE) without redundancy, because nonlinear algebraic equations cannot be solved analytically in general.First, for nonlinear DAE systems with index one, a design method of exact I/O-linearizing control and observer is proposed, where the global-stability condition of the observer is also obtained. The estimated state variables in the observer converge to an invariant manifold determined by the algebraic equations in finite time.Secondly, we show two methods transforming from a nonlinear DAE system with high index to a redundant ODE system, where the DAE system may include an impulsive mode. One is a differentiation method in which algebraic equations are differentiated with dynamic extension of input. The other is an extension of regularizing method that cancels impulsive modes using state feedback. The latter method and the original regularizing method are not applicable for systems with partial observation.By using the former method, we show an I/O-linearizing controller and an observer design for nonlinear high-index DAE systems. Since the system can be transformed to ODE system, many state feedback design methods can be applied to the system. However, for the redundant ODE system, conditions of the observer design, for example existence of polytope covering nonlinear dynamics, may not be satisfied. Therefore, we extend the method for systems with index one to this case. Moreover, the dimension of the observer dynamics is reduced by using the values of input-integrators included by the controller. The proposed observer can estimate all redundant state variables, where the restriction described by the algebraic equations for the estimated variables is satisfied in finite time.