Construction of Robust NCR for Input-Constrained Discrete Nonlinear Systems Using Backward Reachability

In this paper, we address the problem of constructing an under-approximation of the null-controllable region for input constrained discrete nonlinear systems with additive disturbances. The robust null-controllable region (RNCR) refers to the set of states for which robust stabilization is achievable subject to input constraints. In this paper, we propose a computationally tractable algorithm for computation of the robust null-controllable region which involves computation of backward reachable sets, i.e the set of states that can be driven to an given set of states in finite time, subject to disturbances and input constraints. The key ingredient in our RNCR region construction is the efficient computation of backward reachable sets without steps like sequential linearization, guessing of linearization error, etc which are essential part of state of the art backward reachability algorithms. Finally, we demonstrate the efficacy of our algorithm through numerical examples.