The dynamic system of control of technological innovations is considered. Its dynamics is described by a vector linear discrete recurrent ratio and influenced by control parameters (controls) and an uncontrollable parameter (vector of risks or obstacles). In this case, the risks in the system of control of technological innovation will imply factors that influence negatively or catastrophically the results the processes, considered in it. To solve the problem on control over technological innovations, we proposed methods based on the construction of predictive sets – reachability regions of the considered dynamic model. These are the sets of all permissible states of a phase vector of the system at an assigned moment, correspondent to the fixed program control and to all permissible vectors of risk. This procedure is accompanied by the minimax-based method for finding a guaranteed result. Its essence is that the value of the worst (maximum) vector of possible risks is the least compared with similar values for the others at minimally guaranteed optimal control. Thus, we minimize the impact of risks in the problem of control of technological innovations, where the risks are uncontrollable parameters. This is implemented based on selection of such optimal control, which would guarantee the obtained result under the influence of any maximal risk from the set of permissible risks. The proposed method enables the development of effective numerical procedures that make it possible to implement computer modeling of dynamics of the studied problem, to form program minimax control over technological innovations and to obtain an optimal guaranteed result. The results reported here could be used for economic-mathematical modeling and for solving other problems on the optimization of data forecasting and control processes under conditions of insufficient information and in the existence of risks. In addition, the developed modeling toolset could form the basis for development of appropriate software-hardware complexes to support making effective control decisions in the innovation activity.