Practically stable nonlinear receding-horizon control of multi-model systems

The objective of the paper is the design of a stabilizing switching control scheme for a class of nonlinear systems. Such systems are characterized by means of a finite set of nonlinear discrete-time models and for each model a finite set of receding-horizon nonlinear control laws is defined. This highlights a major feature of the considered class of switched systems with respect to previous works, namely, the possibility of switching both between different system models and between different controllers. Some practical stability concepts are then introduced and compared with classical stability definitions. The analysis of the different stability properties is carried out yielding theoretical constraints to be satisfied by the switching strategies in order to guarantee stable modes of behavior of the multi-model switched system. Some simulation results are finally reported showing the effectiveness of the proposed control scheme.

[1]  Panos J. Antsaklis,et al.  Practical stabilization of integrator switched systems , 2003, Proceedings of the 2003 American Control Conference, 2003..

[2]  Hai,et al.  Uniformly Ultimate Boundedness Control for Uncertain Switched Linear Systems , 2022 .

[3]  João Pedro Hespanha,et al.  Switching between stabilizing controllers , 2002, Autom..

[4]  Kumpati S. Narendra,et al.  Adaptive control using multiple models , 1997, IEEE Trans. Autom. Control..

[5]  A. Michel,et al.  Stability theory for hybrid dynamical systems , 1998, IEEE Trans. Autom. Control..

[6]  Thomas Parisini,et al.  Nonlinear stabilization by receding-horizon neural regulators , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[7]  G. Nicolao,et al.  Stabilizing receding-horizon control of nonlinear time-varying systems , 1998, IEEE Trans. Autom. Control..

[8]  Thomas Parisini,et al.  A hybrid receding-horizon control scheme for nonlinear systems☆ , 1999 .

[9]  R. Decarlo,et al.  Perspectives and results on the stability and stabilizability of hybrid systems , 2000, Proceedings of the IEEE.

[10]  M. Branicky.  Multiple Lyapunov functions and other analysis tools for switched and hybrid systems , 1998, IEEE Trans. Autom. Control..

[11]  Guisheng Zhai,et al.  On practical stability of switched systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[12]  Thomas Parisini,et al.  A receding-horizon regulator for nonlinear systems and a neural approximation , 1995, Autom..

[13]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[14]  H. Michalska,et al.  Receding horizon control of nonlinear systems , 1988, Proceedings of the 28th IEEE Conference on Decision and Control,.

[15]  Thomas Parisini,et al.  Nonlinear stabilization by receding-horizon neural regulators , 1998 .

[16]  S. Sacone,et al.  Stable multi-model switching control of a class of nonlinear systems , 2004, Proceedings of the 2004 American Control Conference.

[17]  Thomas Parisini,et al.  Stable hybrid control based on discrete-event automata and receding-horizon neural regulators , 2001, Autom..

[18]  A. Michel.  Recent trends in the stability analysis of hybrid dynamical systems , 1999 .