Quasi-Newton methods are reliable and e cient on a wide range of problems, but they can require many iterations if no good estimate of the Hessian is available or the problem is ill-conditioned. Methods that are less susceptible to ill-conditioning can be formulated by exploiting the fact that quasi-Newton methods accumulate second-derivative information in a sequence of expanding manifolds. These modi ed methods represent the approximate second derivatives by a smaller reduced approximate Hessian. The availability of a reduced Hessian allows conventional quasi-Newton methods to be improved in two ways. First, it is possible to reduce the objective while the iterates are forced to linger on a manifold whose dimension can be signi cantly smaller than the manifold on which curvature is being accumulated. Second, approximate curvature in directions o the manifold can be reinitialized as the iterations proceed, thereby reducing the in uence of a poor initial estimate of the Hessian. We conclude by presenting extensive numerical results from problems in the CUTE test set. Our experiments provide strong evidence that reduced Hessian quasi-Newton are more robust and more e cient than conventional quasi-Newton methods on small-to medium-sized problems.

Abstract. Limited-memory BFGS quasi-Newton methods approximate the Hessian matrix of second derivatives by the sum of a diagonal matrix and a fixed number of rank-one matrices. These methods are particularly effective for large problems in which the approximate Hessian cannot be stored explicitly.It can be shown that the conventional BFGS method accumulates approximate curvature in a sequence of expanding subspaces. This allows an approximate Hessian to be represented using a smaller reduced matrix that increases in dimension at each iteration. When the number of variables is large, this feature may be used to define limited-memory reduced-Hessian methods in which the dimension of the reduced Hessian is limited to save storage. Limited-memory reduced-Hessian methods have the benefit of requiring half the storage of conventional limited-memory methods.In this paper, we propose a particular reduced-Hessian method with substantial computational advantages compared to previous reduced-Hessian methods. Numerical results from a set of unconstrained problems in the CUTE test collection indicate that our implementation is competitive with the limited-memory codes L-BFGS and L-BFGS-B.

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This paper describes the maturation of a control allocation technique designed to assist pilots in recovery from pilot-induced oscillations. The control allocation technique to recover from pilot-induced oscillations is designed to enable next-generation high-efficiency aircraft designs. Energy-efficient next-generation aircraft require feedback control strategies that will enable lowering the actuator rate limit requirements for optimal airframe design. A common issue on aircraft with actuator rate limitations is they are susceptible to pilot-induced oscillations caused by the phase lag between the pilot inputs and control surface response. The control allocation technique to recover from pilot-induced oscillations uses real-time optimization for control allocation to eliminate phase lag in the system caused by control surface rate limiting. System impacts of the control allocator were assessed through a piloted simulation evaluation of a nonlinear aircraft model in the NASA Ames Research Center's Vertical Motion Simulator. Results indicate that the control allocation technique to recover from pilot-induced oscillations helps reduce oscillatory behavior introduced by control surface rate limiting, including the pilot-induced oscillation tendencies reported by pilots.

This paper describes the maturation of a control allocation technique designed to assist pilots in the recovery from pilot induced oscillations (PIOs). The Control Allocation technique to recover from Pilot Induced Oscillations (CAPIO) is designed to enable next generation high efficiency aircraft designs. Energy efficient next generation aircraft require feedback control strategies that will enable lowering the actuator rate limit requirements for optimal airframe design. One of the common issues flying with actuator rate limits is PIOs caused by the phase lag between the pilot inputs and control surface response. CAPIO utilizes real-time optimization for control allocation to eliminate phase lag in the system caused by control surface rate limiting. System impacts of the control allocator were assessed through a piloted simulation evaluation of a non-linear aircraft simulation in the NASA Ames Vertical Motion Simulator. Results indicate that CAPIO helps reduce oscillatory behavior, including the severity and duration of PIOs, introduced by control surface rate limiting.