Optimal impulse control of systems with control constraints and application to HIV treatment

In this paper, conditions for optimal impulse control of an impulsive system with constraints on control are derived. These hold for a system whose states can be changed instantaneously at discrete times with impulses while a continuous control is being applied between those times. The conditions derived are applied to the problem of optimal HIV treatment. Simulation results are presented to show the treatment procedure. The results obtained show that the intervention method developed leads to good results

[1]  Pini Gurfil,et al.  Optimal control of HIV infection with a continuously-mutating viral population , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[2]  Hyungbo Shim,et al.  Control of immune response of HIV infection model by gradual reduction of drug dose , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[3]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[4]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[5]  Christine Chevallereau,et al.  Low energy cost reference trajectories for a biped robot , 1998, Proceedings. 1998 IEEE International Conference on Robotics and Automation (Cat. No.98CH36146).

[6]  J.A.M. Felippe de Souza,et al.  Optimal control theory applied to the anti-viral treatment of AIDS , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[7]  E. B. Lee,et al.  Time-optimal control of the swing using impulse control actions , 1998, Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207).

[8]  Xiaohua Xia,et al.  CONTROLLABILITY ANALYSIS OF THE CHEMOTHERAPY OF HIV/AIDS , 2002 .

[9]  Elmer G. Gilbert,et al.  A class of fixed-time fuel-optimal impulsive control problems and an efficient algorithm for their solution , 1971 .

[10]  M. Nowak,et al.  Specific therapy regimes could lead to long-term immunological control of HIV. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[11]  M A Spartalis,et al.  How HIV causes AIDS. , 1995, Journal of the National Medical Association.

[12]  Shigui Ruan,et al.  Mathematical Biology Digital Object Identifier (DOI): , 2000 .

[13]  Stefano Baccarin,et al.  Optimal impulse control for cash management¶with quadratic holding-penalty costs , 2002 .