Adaptive control of time‐varying uncertain non‐linear systems with input delay: a Hamiltonian approach

The adaptive control problem of a class of time-varying non-linear systems with uncertainties and input delay is addressed via a Hamiltonian approach in this study. The delay is assumed to be a constant and the uncertainties are small parametric perturbations. First, the non-linear system is equivalently transformed into a Hamiltonian system form and the Casimir-like function is proposed to help shaping the Hamiltonian as a candidate of Lyapunov function in the extended systems. Second, the adaptive control problem is investigated based on the time-varying dissipative Hamiltonian system with input delay. The feedback controller is designed to guarantee the stability of the closed-loop system for all admissible uncertainties, as well as constant delay. Sufficient conditions are presented to ensure the rationality of the proposed control law, which are derived based on Lyapunov function method. Stabilisation problem is also considered while there are no uncertain parameters in the delay non-linear systems. Finally, several examples are presented to illustrate the effectiveness of the results obtained in this study.

[1]  Weiwei Sun,et al.  Robust Adaptive Control of Uncertain Stochastic Hamiltonian Systems with Time Varying Delay , 2016 .

[2]  Wei Wei Sun,et al.  Stabilization analysis of time-delay Hamiltonian systems in the presence of saturation , 2011, Appl. Math. Comput..

[3]  Abdesselem Boulkroune,et al.  State and output feedback fuzzy variable structure controllers for multivariable nonlinear systems subject to input nonlinearities , 2014 .

[4]  Gang Feng,et al.  On finite-time stability and stabilization of nonlinear port-controlled Hamiltonian systems , 2012, Science China Information Sciences.

[5]  Kazunori Sakurama,et al.  Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations , 2001, Autom..

[6]  Kang G. Shin,et al.  Robust trajectory planning for robotic manipulators under payload uncertainties , 1987 .

[7]  Gerardo Espinosa-Pérez,et al.  Performance evaluation of energy-shaping approach controllers for synchronous generators using a finite-element model , 2004 .

[8]  Daizhan Cheng,et al.  Stabilization of time-varying Hamiltonian systems , 2006, IEEE Transactions on Control Systems Technology.

[9]  Sing Kiong Nguang,et al.  Robust stabilization of a class of time-delay nonlinear systems , 2000, IEEE Trans. Autom. Control..

[10]  Shengwei Mei,et al.  Co-ordinated H∞ control of excitation and governor of hydroturbo-generator sets: a Hamiltonian approach , 2004 .

[11]  Zairong Xi.  Adaptive stabilization of generalized Hamiltonian systems with dissipation and its applications to power systems , 2002, Int. J. Syst. Sci..

[12]  Ian R. Petersen,et al.  Robust control of uncertain systems: Classical results and recent developments , 2014, Autom..

[13]  Yuzhen Wang,et al.  Stability for a class of nonlinear time-delay systems via Hamiltonian functional method , 2012, Science China Information Sciences.

[14]  C. Peng,et al.  Improved delay-dependent robust stability criteria for uncertain systems with interval time-varying delay , 2008 .

[15]  Weiwei Sun,et al.  Observer-based robust adaptive control for uncertain stochastic Hamiltonian systems with state and input delays , 2014 .

[16]  Arjan van der Schaft,et al.  Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems , 2008, IEEE Transactions on Automatic Control.

[17]  Alessandro Astolfi,et al.  Transient stabilization of multimachine power systems with nontrivial transfer conductances , 2005, IEEE Transactions on Automatic Control.

[18]  Leipo Liu,et al.  Universal stabilisation design for a class of non-linear systems with time-varying input delays , 2015 .

[19]  Arjan van der Schaft,et al.  Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

[20]  S. Gutman.  Uncertain dynamical systems--A Lyapunov min-max approach , 1979 .

[21]  Daizhan Cheng,et al.  On Hamiltonian realization of time-varying nonlinear systems , 2007, Science in China Series F: Information Sciences.

[23]  Weiwei Sun,et al.  L2 disturbance attenuation for a class of time-delay Hamiltonian systems , 2011, J. Syst. Sci. Complex..

[24]  Gang Feng,et al.  Finite-time stabilization and H∞ control for a class of nonlinear Hamiltonian descriptor systems with application to affine nonlinear descriptor systems , 2014, Autom..

[25]  Daizhan Cheng,et al.  Stabilization of Hamiltonian systems with dissipation , 2001 .

[26]  A. Boulkroune,et al.  A projective synchronization scheme based on fuzzy adaptive control for unknown multivariable chaotic systems , 2014 .

[27]  R. Pasumarthy,et al.  Brief Paper Stability analysis of interconnected Hamiltonian systems under time delays , 2012 .

[28]  Emilia Fridman,et al.  On input-to-state stability of systems with time-delay: A matrix inequalities approach , 2008, Autom..

[29]  Shuzhi Sam Ge,et al.  Robust adaptive control of nonlinear systems with unknown time delays , 2004, Proceedings of the 2004 IEEE International Symposium on Intelligent Control, 2004..

[30]  Robert F. Stengel,et al.  Robust control of nonlinear systems with parametric uncertainty , 2002, Autom..

[31]  Tielong Shen,et al.  Adaptive feedback control of nonlinear time-delay systems: the LaSalle-Razumikhin-based approach , 2005, IEEE Transactions on Automatic Control.

[32]  Romeo Ortega,et al.  Further deleterious effects of the dissipation obstacle in control-by-interconnection of port-Hamiltonian systems , 2015, Autom..