Constraint-reduced interior-point optimization for model predictive rotorcraft control

Constraint reduction has been proposed, in the context of linear and quadratic primal-dual interior-point optimization, as an approach for efficiently handling problems in which the number of inequality constraints far exceeds that of decision variables. With such problems, it is typical that only a small percentage of constraints are active at the solution, the others being, in a sense, redundant. Computing search directions based on a judiciously selected subset of the constraints, updated at each iteration, significantly reduces the work per iteration, while global and local quadratic convergence can be provably retained. In this paper, we apply a constraint-reduced primal-dual interior-point algorithm to a case study of quadratic-programming-based model-predictive rotorcraft control in which, indeed, constraints far outnumber decision variables. A difficulty is that constraint reduction requires the availability, for each optimization problem (to be solved on-line), of an initial strictly feasible point. Indeed, such points may not be readily available in the model-predictive control context. We propose to address this difficulty by substituting a certain auxiliary, ℓ₁-penalized problem, which has the same solution as the original problem. As a by-product, this technique lends itself nicely to the use of “warm starts“ that speed up the solution of the optimization problem. Numerical results, in particular in terms of CPU time needed to solve each quadratic program, show promise that model-predictive control may soon be a practical technique for rotorcraft control.