ABSTRACT
So far, we have only examined problems with one control and one dependent state variable. Often, though, we will wish to consider more variables. For example, consider a system modeling antibiotics used to fight a viral infection. In addition to the number of viral particles in the blood, we might also want to follow the number of antibodies or white blood cells. These quantities would be represented as additional state variables. Further, suppose the patient was taking two different antibiotics that caused the body to generate antibodies at different rates or times. These would need to be separate control variables; see [90]. Further, we could examine an SIR epidemic model with vaccination levels as a control [13, 93, 137, 149, 157, 180], or a tuberculosis epidemic model involving decisions in allocating efforts [95]. In this chapter, we will discuss how to handle such problems.
