Parameter Estimation Using Dynamic Optimization

Abstract

Until now, we have studied the stability, instability, and oscillatory behaviors of the 5 system (2.81) (Chap. 2) and mechanisms that can regulate the instability charac- 6 teristics of the systems in Chaps. 4-7. We have observed that due to the variations 7 in nutrient supply (inflow) and washout (outflow), the system is subject to disturbances. In fact, this has lead to formulation of various models (2.1)-(2.6) and the mechanisms in earlier chapters. The inflow and outflow rates are represented by the parameter D in our models. Thus, on the whole, D seems to be king pin in deter11 mining the characteristics of these biological models. Such a parameter is called a key parameter. But if we know that the system can be brought under control by re- 13 stricting this parameter, we may call this D; a control parameter. Then it becomes 14 very important to estimate this control parameter. OnceD is estimated, the tendency 15 (stability or instability) of the system under consideration may be understood from 16 the results of Chaps. 2 and 3. Accordingly the control parameter may be varied to 17 change the dynamics of the system from instability to stability or vice-versa. Even in 18 case D is only a key parameter and cannot be controlled by us, its estimation helps 19 us in deciding whether mechanisms are required and which mechanism, if required.