Abstract
ABSTRACTMost real systems can be considered as a nonlinear and parameters of the systems may have uncertainties and external disturbances. Hence, in this paper, using the power series algorithm (PSA) based on State Dependent Riccati Equations (SDRE) and considering the proposed conditions that guarantee the asymptotic stability, the optimal regulator problem for a particular class of nonlinear systems is solved. Also, according to the specified pattern in the modified PSA (MPSA) method, weighting matrices are used as a function of state variables to achieve the better regulatory responses. Simulations are carried out on the Lorenz's chaotic system with uncertainties and external disturbances. The efficiency of optimal regulators the PSA and the MPSA methods in eliminating the external disturbances and being robust to uncertainties are compared together. The results show that the values of the performance index and the control cost in the MPSA method are smaller than the PSA method. Then the regulatory response in the MPSA method is more efficient.
Highlights
Due to the wide range of nonlinear systems, the problem of optimal control of nonlinear systems has attracted the attention of control engineers in recent years
The optimal control of the State Dependent Riccati Equations (SDRE) has been investigated by Cloutier, D’Souza, and Mracek (1996), Khaloozadeh and Abdollahi (2002)
Using the power series algorithm (PSA) based on SDRE equations and considering the proposed conditions that guarantee the asymptotic stability, the robust optimal regulator is designed, such that it can be used to cover a wide range of nonlinear systems, it is robust to the uncertainties and external disturbances
Summary
Due to the wide range of nonlinear systems, the problem of optimal control of nonlinear systems has attracted the attention of control engineers in recent years. Shen et al established a unified framework to investigate both the quantized and the saturated control problems for a class of sampleddata systems under noisy sampling intervals (Li, Shen, Liang, & Shu, 2015) In all of these methods it is assumed that the nonlinearities of states are only linear dependent. It is important to design the optimal control law that stabilized the wide range of nonlinear systems but, robust to the uncertainties and the external disturbances. Using the power series algorithm (PSA) based on SDRE equations and considering the proposed conditions that guarantee the asymptotic stability, the robust optimal regulator is designed, such that it can be used to cover a wide range of nonlinear systems, it is robust to the uncertainties and external disturbances.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
