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Predators and prey in the population of an ecosystem can be evaluated and investigated with mathematical explorations. Intermediate elementary students explore Fibonacci sequences in relation to prey and discuss models to maintain a balance between the species through mathematics by modifying variables. iSTEM (Integrating Science, Technology, and Engineering in Mathematics) authors share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K-grade 6 classroom.
This chapter provides a concise and up-to-date analysis of the foundations of performance robustness of a linear-quadratic class of cooperative decision-making with respect to variability in a stationary and stochastic environment. The dynamics of large-scale and interconnected dynamical systems corrupted by a standard stationary Wiener process include decision activities that are controlled by decentralized decision makers. Basic assumptions will be that cooperative decision makers form a coalition and have access to the current value of the states of the systems. The performance robustness and uncertainty of the coalition is now affected by other non-cooperative participants such as model deviations and environmental disturbances, named Nature. A decentralized model-following approach where interactions among coalitive decision makers are represented by reduced order models, is taken to derive various local decisions without intensive information interchanges. Decentralized decision strategies considered here collaboratively optimize an advanced multi-objective criterion over time where the optimization takes place with high regard for possible random sample realizations by Nature who may more likely not be acting in concert. The implementation of decision gain parameters in the finite horizon case is shown to be feasible. The inherent decision structure now has two degrees of freedom including: one, state feedback gains with state measurements that are robust against performance uncertainty; and two, interactive feedback gains that minimize differences between the actual and desirable interactions. 153554b96e