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Unformatted text preview: Homework 6 - MAE143B Spring 2010: due Thursday May 20 This week’s homework will consist of three parts all dealing with the same problem; the control of the nonlinear predator-prey model described in ˚ Astr¨om & Murray pp. 90-91, 181-183. This model describes the dynamical evolution of the populations of snowshoe hares, H t , and lynxes, L t , in Canada. The open-loop, uncontrolled behavior is described by the coupled logistic equations (3.31) on p. 90, where the various parameters are explained. The analytical responses are indicated by marginal A, while the matlab responses are indicated by m. As a farmer, you are concerned by the periodic explosion in the hare population illustrated in Figure 3.20; the little blighters eat you crops. Likewise you are concerned by the periodic precipitous plummeting of the lynx population, because they get hungry and eat your offspring. So you decide to explore the management of a stable population of both species. There are just two issues, • Because lynxes only eat hares – and the occasional small Canadian – it is only possible to regulate the food available to the hares, which is done by controlling the amount of herbage made available to them. You cannot directly control the lynx food. The controlled system equation are given at the beginning of Example 6.5 on page 181 and differ from (3.31) through the inclusion of a control term u affecting the birth rate of the hares. • Because the hares live in burrows and move around, they are much harder to count than the home-loving lynxes. So your only reliable population measure is the lynx population, L t . You must infer the hare population. To compensate for these shortcomings, you recall that you received an A+ in MAE143B in 1976; the last time an A+ was awarded, you understand. So you try to use those ideas. To assist you, a kindly professor has made available some matlab files on the sole condition that you do not laugh at his coding skills ... it is pretty rudimentary, I can tell you. population dydt.m The function file from the book website providing the uncontrolled ( u = 0 ), open-loop behavior of the predator-prey model (3.31) with the nominal parameter values shown in Figure 3.20. It must be called using ode45 in matlab as follows for example....
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- Spring '10
- Linear state feedback, linear state-estimate feedback