An optimal dynamic inversion-based neuro-adaptive approach for treatment of chronic myelogenous leukemia

Combining the advanced techniques of optimal dynamic inversion and model-following neuro-adaptive control design, an innovative technique is presented to design an automatic drug administration strategy for effective treatment of chronic myelogenous leukemia (CML). A recently developed nonlinear mathematical model for cell dynamics is used to design the controller (medication dosage). First, a nominal controller is designed based on the principle of optimal dynamic inversion. This controller can treat the nominal model patients (patients who can be described by the mathematical model used here with the nominal parameter values) effectively. However, since the system parameters for a realistic model patient can be different from that of the nominal model patients, simulation studies for such patients indicate that the nominal controller is either inefficient or, worse, ineffective; i.e. the trajectory of the number of cancer cells either shows non-satisfactory transient behavior or it grows in an unstable manner. Hence, to make the drug dosage history more realistic and patient-specific, a model-following neuro-adaptive controller is augmented to the nominal controller. In this adaptive approach, a neural network trained online facilitates a new adaptive controller. The training process of the neural network is based on Lyapunov stability theory, which guarantees both stability of the cancer cell dynamics as well as boundedness of the network weights. From simulation studies, this adaptive control design approach is found to be very effective to treat the CML disease for realistic patients. Sufficient generality is retained in the mathematical developments so that the technique can be applied to other similar nonlinear control design problems as well.

[1]  M.H. Hassoun,et al.  Fundamentals of Artificial Neural Networks , 1996, Proceedings of the IEEE.

[2]  E. Afenya,et al.  Normal cell decline and inhibition in acute leukemia: a biomathematical modeling approach. , 1996, Cancer detection and prevention.

[3]  Richard S. Sutton,et al.  Neural networks for control , 1990 .

[4]  Robert F. Stengel,et al.  Optimal Control and Estimation , 1994 .

[5]  Robert M. Sanner,et al.  Gaussian Networks for Direct Adaptive Control , 1991, 1991 American Control Conference.

[6]  Jitendra R. Raol,et al.  Modelling and Parameter Estimation of Dynamic Systems , 1992 .

[7]  A. Isidori,et al.  Nonlinear system I , 1999 .

[8]  Radhakant Padhi,et al.  IMPLEMENTATION OF PILOT COMMANDS IN AIRCRAFT CONTROL: A NEW APPROACH BASED ON DYNAMIC INVERSION , 2003 .

[9]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[10]  Aurelio Piazzi,et al.  Point-to-Point Motion Planning for Servosystems With Elastic Transmission Via Optimal Dynamic Inversion , 2001 .

[11]  S. N. Balakrishnan,et al.  Robust Neurocontrollers for Systems with Model Uncertainties: A Helicopter Application , 2005 .

[12]  Kumpati S. Narendra,et al.  Adaptation and learning using multiple models, switching, and tuning , 1995 .

[13]  Thomas Kailath,et al.  Linear Systems , 1980 .

[14]  Anthony J. Calise,et al.  Nonlinear flight control using neural networks , 1994 .

[15]  George M. Siouris,et al.  Applied Optimal Control: Optimization, Estimation, and Control , 1979, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  Peter J. Gawthrop,et al.  Neural networks for control systems - A survey , 1992, Autom..

[17]  Radhakant Padhi,et al.  Model Following Robust Neuro-Adaptive Control Design for Non-Square, Non-Affine Systems , 2004 .

[18]  E K Afenya,et al.  Some perspectives on modeling leukemia. , 1998, Mathematical biosciences.

[19]  Helen Moore,et al.  A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction. , 2004, Journal of theoretical biology.

[20]  Klaus H. Well,et al.  Attitude Control of a Reentry Vehicle with Internal Dynamics , 2002 .

[21]  Hassan K. Khalil,et al.  Output feedback control of nonlinear systems using RBF neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[22]  Anneli Folkesson,et al.  Numerical methods for engineers , 2007 .

[23]  Anthony J. Calise,et al.  Adaptive output feedback control of a class of non-linear systems using neural networks , 2001 .

[24]  Anthony J. Calise,et al.  Analysis of Adaptive Neural Networks for Helicopter Flight Control , 1997 .

[25]  A. Calise,et al.  Adaptive Output Feedback Control of a Class of Nonlinear Systems Using Neural Networks , 1999 .

[26]  John Carl Panetta,et al.  Optimal Control Applied to Cell-Cycle-Specific Cancer Chemotherapy , 2000, SIAM J. Appl. Math..

[27]  Steven C. Chapra,et al.  Numerical Methods for Engineers , 1986 .

[28]  Narasimhan Sundararajan,et al.  Neuro-controller design for nonlinear fighter aircraft maneuver using fully tuned RBF networks , 2001, Autom..

[29]  Zhongwu Huang,et al.  Robust adaptive critic based neurocontrollers for helicopter with unmodeled uncertainties , 2001 .

[30]  Z. Estrov,et al.  Chronic Myelogenous Leukemia: Biology and Therapy , 1999, Annals of Internal Medicine.

[31]  M. Gopal,et al.  Modern Control System Theory , 1984 .

[32]  Singiresu S. Rao.  Engineering Optimization : Theory and Practice , 2010 .

[33]  Aurelio Piazzi,et al.  Optimal dynamic-inversion-based control of an overhead crane , 2002 .

[34]  Dan Bugajski,et al.  Dynamic inversion: an evolving methodology for flight control design , 1994 .

[35]  Panos J. Antsaklis,et al.  Neural networks for control systems , 1990, IEEE Trans. Neural Networks.

[36]  Donald E. Kirk,et al.  Optimal control theory : an introduction , 1970 .

[37]  M. Baccarani,et al.  Hematologic and cytogenetic responses to imatinib mesylate in chronic myelogenous leukemia. , 2002, The New England journal of medicine.