A mixed logical dynamics actuator model for optimal control with position and rate limits

In this paper the solution of optimal control problems under actuator excursion and rate limits is considered. One way of addressing internal limits of a servomechanism in optimal control problems is through the introduction of input and state constraints. However, this modeling approach may introduce unnecessary conservatism in the optimal solution of the control problem. In the present work an actuator formulation based on Mixed Logical Dynamics (MLD) is developed to address this issue, eliminating the conservatism. These conditions are implemented through a Mixed-Integer Linear Programming (MILP) formulation with binary variables. The application of the formulation is illustrated using a model of a general transport aircraft. In this scenario both the standard optimal control formulation with state constraints and the novel MILP formulation proposed in this paper are used to maximize a heading change of the aircraft at a fixed terminal time. It is shown that the MILP encoding yields a lower cost function value compared to the standard optimal control formulation at the expense of greater computational resources.