Simulation-Equivalent Reachability of Large Linear Systems with Inputs

Control systems can be subject to outside inputs, environmental effects, disturbances, and sensor/actuator inaccuracy. To model such systems, linear differential equations with constrained inputs are often used, \(\dot{x}(t) = A x(t) + B u(t)\), where the input vector u(t) stays in some bound. Simulating these models is an important tool for detecting design issues. However, since there may be many possible initial states and many possible valid sequences of inputs, simulation-only analysis may also miss critical system errors. In this paper, we present a scalable verification method that computes the simulation-equivalent reachable set for a linear system with inputs. This set consists of all the states that can be reached by a fixed-step simulation for (i) any choice of start state in the initial set and (ii) any choice of piecewise constant inputs.