Sepsis, a manifestation of the body's inflammatory response to injury and infection, has a mortality rate of between 28%-50% and affects approximately 1 million patients annually in the United States. Currently, there are no therapies targeting the cellular/molecular processes driving sepsis that have demonstrated the ability to control this disease process in the clinical setting. We propose that this is in great part due to the considerable heterogeneity of the clinical trajectories that constitute clinical "sepsis," and that determining how this system can be controlled back into a state of health requires the application of concepts drawn from the field of dynamical systems. In this work, we consider the human immune system to be a random dynamical system, and investigate its potential controllability using an agent-based model of the innate immune response (the Innate Immune Response ABM or IIRABM) as a surrogate, proxy system. Simulation experiments with the IIRABM provide an explanation as to why single/limited cytokine perturbations at a single, or small number of, time points is unlikely to significantly improve the mortality rate of sepsis. We then use genetic algorithms (GA) to explore and characterize multi-targeted control strategies for the random dynamical immune system that guide it from a persistent, non-recovering inflammatory state (functionally equivalent to the clinical states of systemic inflammatory response syndrome (SIRS) or sepsis) to a state of health. We train the GA on a single parameter set with multiple stochastic replicates, and show that while the calculated results show good generalizability, more advanced strategies are needed to achieve the goal of adaptive personalized medicine. This work evaluating the extent of interventions needed to control a simplified surrogate model of sepsis provides insight into the scope of the clinical challenge, and can serve as a guide on the path towards true "precision control" of sepsis.