We consider the task of developing algorithms for cyber-physical systems (CPS) for proactively managing the state of unstable systems with a chaotically evolving state vector. Examples of such processes are changes in the state of gas- and hydrodynamic environments, stock price evolution, thermal phenomena, and so on. The main problem of this type of CPS is creating forecasts that would allow us to compare the efficiency of different feasible control actions. The presence of a chaotic element in the state dynamics of unstable systems does not allow to build of control CPS based on conventional statistical extrapolation algorithms. Hence, in the current chapter, we consider forecasting algorithms built upon machine learning and instance-based data analysis. In the conditions of chaotic influences, which are common in unstable immersion environments, obtaining an accurate forecast is highly complicated. Within the conducted computational experiment that employed direct averaging by three after-effects of analog windows, the average forecast accuracy oscillates between 15 and 20%. Effective forecasting of a chaotic process of a complicated inertia-less nature based on the considered computational schemes has not been achieved yet. This means that additional research, based on multidimensional statistical measures, is required.