The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix ...The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.展开更多
This paper presents a novel nonlinear continuous-time observer based on the differential state-dependent Riccati equation (SDRE) filter with guaranteed exponential stability. Although impressive results have rapidly e...This paper presents a novel nonlinear continuous-time observer based on the differential state-dependent Riccati equation (SDRE) filter with guaranteed exponential stability. Although impressive results have rapidly emerged from the use of SDRE designs for observers and filters, the underlying theory is yet scant and there remain many unanswered questions such as stability and convergence. In this paper, Lyapunov stability analysis is utilized in order to obtain the required conditions for exponential stability of the estimation error dynamics. We prove that under specific conditions, the proposed observer is at least locally exponentially stable. Moreover, a new definition of a detectable state-dependent factorization is introduced, and a close relation between the uniform detectability of the nonlinear system and the boundedness property of the state-dependent differential Riccati equation is established. Furthermore, through a simulation study of a second order nonlinear model, which satisfies the stability conditions, the promising performance of the proposed observer is demonstrated. Finally, in order to examine the effectiveness of the proposed method, it is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines. The simulation results verify how effectively this modification can increase the region of attraction and the observer error decay rate.展开更多
基金supported by the National Natural Science Foundation of China(60874114)
文摘The relationship between the technique by state- dependent Riccati equations （SDRE） and Hamilton-Jacobi-lsaacs （HJI） equations for nonlinear H∞ control design is investigated. By establishing the Lyapunov matrix equations for partial derivates of the solution of the SDREs and introducing symmetry measure for some related matrices, a method is proposed for examining whether the SDRE method admits a global optimal control equiva- lent to that solved by the HJI equation method. Two examples with simulation are given to illustrate the method is effective.
文摘This paper presents a novel nonlinear continuous-time observer based on the differential state-dependent Riccati equation (SDRE) filter with guaranteed exponential stability. Although impressive results have rapidly emerged from the use of SDRE designs for observers and filters, the underlying theory is yet scant and there remain many unanswered questions such as stability and convergence. In this paper, Lyapunov stability analysis is utilized in order to obtain the required conditions for exponential stability of the estimation error dynamics. We prove that under specific conditions, the proposed observer is at least locally exponentially stable. Moreover, a new definition of a detectable state-dependent factorization is introduced, and a close relation between the uniform detectability of the nonlinear system and the boundedness property of the state-dependent differential Riccati equation is established. Furthermore, through a simulation study of a second order nonlinear model, which satisfies the stability conditions, the promising performance of the proposed observer is demonstrated. Finally, in order to examine the effectiveness of the proposed method, it is applied to the highly nonlinear flux and angular velocity estimation problem for induction machines. The simulation results verify how effectively this modification can increase the region of attraction and the observer error decay rate.
