State Dependent Riccati Equation Based Model Reference Adaptive Stabilization of Nonlinear Systems with Application to Cancer Treatment

Abstract The paper suggests a new approach to Model Reference Adaptive Control (MRAC) design for stabilization of a class of uncertain nonlinear systems. The proposed MRAC design methodology is based upon a stable nonlinear reference model which is produced by a state feedback controller using the so-called State Dependent Riccati Equation (SDRE) techniques. Based on states of the reference model, the designed stabilizer for the nonlinear reference model is then adapted for the nonlinear plant dynamics with a suitable adaptation mechanism, again by using the SDRE methodology. The proposed technique is illustrated to develop an optimal chemotherapy drug administration for cancer treatment using a tumor growth mathematical model. Simulation results show the effectiveness of the proposed SDRE-based MRAC method for the stabilization of nonlinear systems.

[1]  Petros A. Ioannou,et al.  Robust Adaptive Control , 2012 .

[2]  D. T. Stansbery,et al.  Position and attitude control of a spacecraft using the state-dependent Riccati equation technique , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[3]  Graham Goodwin,et al.  Discrete time multivariable adaptive control , 1979, 1979 18th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[4]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[5]  Dennis S. Bernstein,et al.  Discrete-Time Adaptive Command Following and Disturbance Rejection with Unknown Exogenous Dynamics , 2006, CDC.

[6]  Karl Johan Åström,et al.  Adaptive Control , 1989, Embedded Digital Control with Microcontrollers.

[7]  M. Tadi.  State-dependent Riccati equation for control of aeroelastic flutter , 2003 .

[8]  Tayfun Çimen,et al.  Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method , 2010, Annu. Rev. Control..

[9]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[10]  A. G. Alleyne,et al.  Experimental real-time SDRE control of an underactuated robot , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[11]  Ami Radunskaya,et al.  The dynamics of an optimally controlled tumor model: A case study , 2003 .

[12]  Metin U. Salamci,et al.  SDRE optimal control of drug administration in cancer treatment , 2010 .

[13]  Curtis P. Mracek.  SDRE AUTOPILOT FOR DUAL CONTROLLED MISSILES , 2007 .

[14]  Gang Tao,et al.  Adaptive Control Design and Analysis , 2003 .

[15]  D. Mayne.  Nonlinear and Adaptive Control Design [Book Review] , 1996, IEEE Transactions on Automatic Control.

[16]  Dennis S. Bernstein,et al.  Lyapunov‐stable discrete‐time model reference adaptive control , 2005 .

[17]  Metin U. Salamci,et al.  Sliding mode control design with time varying sliding surfaces for a class of nonlinear systems , 2006, 2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006 IEEE International Symposium on Intelligent Control.