futuresets
Futuresets are a mathematical construct used to describe the collection of states that a system could occupy at a specified future time, given current information, a model of dynamics, and uncertainties. In formal terms, let S be the state space, s0 the current state, and M a model that defines a transition map T. For a horizon t, the futureset F_t(s0) is the set of all states s in S that can be reached after t transitions from s0 under some admissible sequence of disturbances. When disturbances are uncertain, F_t is usually treated as an over-approximation, capturing all states that could occur under any allowed evolution.
Futuresets are constructed through forward reachability analysis, set-valued maps, interval or polyhedral bounds, and stochastic sampling
They may be monotone with time in systems that allow persistence, and their geometry reflects system constraints
Applications span planning under uncertainty in robotics and autonomous systems, control engineering, risk management, and scenario
See also: reachable set; set-valued forecasting; scenario planning.