Controlling Drug Infusion Biological Systems FREN with Sliding Bounds Chidentree Treesatayapun Abstract—In this paper, a direct adaptive control for drug infusion of biological systems is presented. The proposed controller is accomplished using our adaptive network called Fuzzy Rules Emulated Network (FREN). The structure of FREN resembles the human knowledge in the form of fuzzy I F-THEN rules. After selecting the initial value of network’s parameters, an on-line adaptive process based on Lyapunov’s criteria is performed to improve the controller performance. The control signal from FREN is designed to keep in the region which is calculated by the modified Sliding Mode Control (SMC). The simulation results indicate that the proposed algo- rithm can satisfy the setting point and the robust performance. I. INTRODUCTION The infusion of sodium nitroprusside in order to lower blood pressure in patients after surgery is an example of the drug infusion problem. There are two general methods for administering the drug [1]. The first one is a bolus injection and the second is a continuously controlled release of the drug. The controller must find the correct dose to decrease the blood pressure to the desired level with out the risk of a drug overdose. The model of a patient’s response have been represented in [2]. This model has been used by several controller design studies. The model reference adap- tive controller was introduced in [3]. Many multiple-mode adaptive controllers were presented in [4] and [5]. A robust direct model reference adaptive controller was described in [6], in which the control of a dog’s mean arterial blood pressure was investigated. Unfortunately, theirs result are based on a linearized nonlinear model and need the accurate mathematical model. In this paper, our adaptive controller inspired by the hy- brid Sliding Mode Control(SMC) [7], [8], [9] and a recently proposed adaptive controller called Fuzzy Rules Emulated Network (FREN) [10], [11] is presented to cope those problems. The mathematical model of the controlled drug system is not necessary. The structure of FREN resembles the human knowledge in the form of fuzzy control rules and its initial setting of network parameters is intutively selected. After setting its parameters, an on-line adaptation is performed during its operation to fine tune the values. Hence, the controller is able to adapt itself to the change of environment. During the control effort is generated by FREN, the stability can be guaranteed by the bound signals calculated by the modified SMC. This paper is organized as follows. Section II introduces the overview of the drug infusion model. The bound of the C. Treesatyapun is with Faculty of Electrical Engineering, Chiang-Mai, Thailand. tree471@yahoo.com control effort is presented in section III. Then, in section IV, the structure of FREN is introduced. Its usage as a controller is explained in the next subsection. During the operation, all FREN’s parameters are adjusted in order to minimize the control error signal. This adaptive method based on the steepest descent or gradient search is presented in subsection IV-B. The criteria for learning rate selection is discussed next. Then the computer simulation results when applying FREN to control the change in blood pressure to the infusion rate of sodium nitroprusside are shown in section V. In the final section, some conclusions are given. II. THE DRUG INFUSION MODEL In [2], a model of a patient’s response to the infusion of sodium nitroprusside has been perforned. The transfer function is ΔP d (s) I (s) = Ke -Tis (1 + αe -Tcs ) τs +1 , (1) where ΔP d (s) is the change in mean arterial blood pressure in mmHg and I (s) is the drug infusion rate in mlh -1 . Other parameters can be defined as follows: K Sensitivity of the patient to the drug  mmHg mlh -1  , T i Initial transport delay (sec), T c Recirculation transport delay (sec), α Recirculation (-), τ Lag time constant (sec). In this paper, the simulation will be done with a discret-time model. Let ΔP d (k) and I (k) be the k th sampling of Δp d (t) and i(t), where Δp d (t) and i(t) are invert Laplace transform of ΔP d (s) and I (s), respectively. The plant simulation is depicted in Fig. 1, where ΔP d (k) and I (k) are denoted by Y (s) and U (s), respectively. The disturbance is generated to follow the patient’s environment as shown in Fig. 2. 1 Y(s) 1 40s+1 p1 0.4 alpha Ti Tc Sum -K- Gain 1 U(s) Fig. 1. Drug system From (1), the controlled drug system can be rewritten as ΔP d (k + 1) = f (P d (k),φ)+ g(P d (k),φ)I (k)+ d(k), (2) or in state equation form as  x 1 (k + 1) x 2 (k + 1)  =  0 1 0 0  x 1 (k) x 2 (k)  +  0 g(.)  u(k)+  0 f (.)  +  0 d(k)  , (3) Proceeding of the 2004 American Control Conference Boston, Massachusetts June 30 - July 2, 2004 0-7803-8335-4/04/$17.00 ©2004 AACC ThA10.2 2278