1210 
MONITORING 
to work, but each has its own advantages and 
disadvantages. In general the more precisely 
one wishes to maintain control the more it will 
cost in terms of system complexity. We are 
studying the various trade offs involved with 
several approaches now. 
One simple approach is to let the model indi- 
cate through its weight profile when the re- 
sponse is over, thereby using it as a means of 
measuring the delay. 
One can then measure the response to a given 
change in input after the delay as indicated by 
the model. From this response one can deter- 
mine the system's gain. By storing the gain and 
delay thus determined and updating them after 
each control attempt, one can realize adaptive 
steady state control. This would be a means of 
solving the problem of delay adaption in the 
case of our initial heuristic attempts to adap- 
tively control blood pressure. Such a simple ap- 
proach would not utilize this model's ability to 
begin adaption before a response is complete, 
and therefore, it would adapt more slowly than 
necessary. 
To avoid this objection, we arrive at steady 
state control in a different manner. To state this 
more succinctly, note that one can determine 
the required steady state input by the following 
relationship: 
T 
k = l 
where L = an integer constant, the delay be- 
tween taps in the delay line, we currently use 5 
seconds 
N = number of taps 
j = current time 
T = LN + j 
This solution we call phase I. 
One then uses as input values based upon 
the relationship : 
Xi = Xss for all i = j + 1, j + 2 . . . T. 
where X; is the value actually used and X^s is 
the value computed. This solution may never be 
optimum, but it will always be stable. It will be 
better than any nonadaptive approach because 
of its ability to determine the steady state gain 
and delay and use these in predicting drug re- 
sponse. 
To expand on this last point, note that even 
though this is called a steady state solution, the 
weights can be varying from sample time to 
sample time and with each of these changes a 
new Xss will be determined. Thus, the only 
thing steady state is the desired end result. 
The steady state solution takes the system 
under control from one steady state setting to 
another as commanded. How it goes from one 
level to the next is not determined. 
In order to cause the system to go from one 
steady state value to another as quickly as pos- 
sible (or in any prescribed way) , the plant's dy- 
namics must be used. If we make the transition 
follow the input command as closely as possible 
we have, by definition, optimum control. In 
mathematical terms, optimum control attempts 
to minimize the function : 
(yi-ri)2 
where rj = instantaneous, desired output 
yi = actual output of the control model 
In the next phase, phase II, one sets 
(yi-ri)2 = 0 for all i = j + 1, j + 2 . . . T 
Xi now equals Xi in 
N 
ri- 2 W,Xi-k+i 
so long as Xi is within bounds. These bounds 
are limits set upon the range of the input func- 
tion by practice (e.g., no negative IV rates and 
none above, say, 50 drops/minute). If Xi is 
within bounds for all i, an optimal solution is 
possible and we can stop. That is, one can use 
this value for Xi at each point in Xi where i = 
j + 1, j+2 . . . T and he will have an optimal 
result. Phase II control is rarely possible. 
If Xi does not maintain itself within bounds, 
it must be limited. Studies yet not implemented 
• Where W, is the first non zero weight and the delay line has 
N-Nq elements where Nq is the number of zero valued weights. 
