Feasible trajectories of linear dynamic systems with inequality constraints using higher-order representations

Abstract

This paper proposes a method to determine trajectories of dynamic systems that steer between two end points while satisfying linear inequality constraints arising from limits on states and inputs. The method exploits the structure of the dynamic system to eliminate the state equations. The linear inequalities on inputs and states are replaced by a finite set of linear inequalities on the mode coefficients and changing the problem of trajectory generation to finding a convex polytope on the mode coefficients. The procedure is demonstrated in an example and verified experimentally.