Abstract: A method, apparatus and system including the execution of an accelerated optimization method. According to an exemplary embodiment, the accelerated optimization method includes: first-order optimality conditions for a generic nonlinear optimization problem are generated as part of the terminal transversality conditions of an optimal control problem. It is shown that the Lagrangian of the optimization problem is connected to the Hamiltonian of the optimal control problem via a zero-Hamiltonian, infinite-order, singular arc. The necessary conditions for the singular optimal control problem are used to produce an auxiliary controllable dynamical system whose trajectories generate algorithm primitives for the optimization problem. A three-step iterative map for a generic algorithm is designed by a semi-discretization step. Neither the feedback control law nor the differential equation governing the algorithm need be derived explicitly.

Abstract: The disclosure provides a closed-loop controller for a controlled system comprising a comparison element generating an error e, a compensator generating a control uN value based on the error e, and a control allocator determining a manipulated parameter uM value based on the control uN. The control allocator typically utilizes a control effectiveness function and determines uM value by selecting one or more specific system x0 signals from the system state xi or system input yj values or system parameters values pk reported, defining a plurality of distributed xD around each specific system x0 signal, and minimizing an error function E(zi), where the error function E(zi) is based on errors which arise from use of the plurality of distributed xD in the control effectiveness function rather than one or more specific system x0 signals.

Abstract: The disclosure provides a robotic arm controller which determines a control parameter for at least one actuator comprising the robotic arm using a control equation having the general form Ax=b, where A is a transformation matrix A based on the geometry and Jacobian of the robotic arm, x is the control parameter x such as a torque vector at a specific joint, and b is the end effector parameter b which specifies a desired corrective state of the end effector. The methodology, by way of constructing and solving an unscented optimization problem, provides a solution to the Ax=b problem by perturbing at least one joint angle appearing in the Jacobian to generate a plurality of distributed joint angles, determining a control parameter x which minimizes an error function.

Abstract: Methods, systems and computer readable media are presented for computing a guidance control policy to transition an uncertain dynamical system from an initial state to a final state, in which a set of points are computed to provide discreet and accurate representation of uncertainty, and in which a guidance control policy is computed based on a set of equations involving the initial state, the final state, state variables, control variables, and parameters, as well as designated parameters of interest, a set of constraints corresponding to state and control variables, a performance metric, statistical distribution types corresponding to the parameters of interest, statistical moments individually corresponding to the parameters of interest, and weighting values corresponding to the parameters of interest.

Abstract: Unscented optimal control combines the unscented transform with optimal control to produce a new approach to directly manage navigational and other uncertainties in an open-loop framework. The sigma points of the unscented transform are treated as controllable particles that are all driven by the same open-loop controller. A system-of-systems dynamical model is constructed where each system is a copy of the other. Pseudo-spectral optimal control techniques may be applied to this system-of-systems to produce a computationally viable approach for solving the large-scale optimal control problem.

Abstract: Methods and apparatus are presented for spacecraft operation using non-Eigen axis attitude transitions via control momentum gyroscopes (CMGs) to avoid or mitigate singularities by providing a time-varying attitude command vector including a plurality of time-varying attitude command signals or values representing a plurality of spacecraft states and control trajectories as a guidance command input to an attitude controller of the spacecraft without modifying the spacecraft feedback control law.

Abstract: Methods and apparatus are presented for spacecraft operation in which a control problem is formulated using a control law or steering law as a path constraint or as a dynamic constraint, and the control problem is solved to provide a guidance command trajectory for use in operating spacecraft control momentum gyroscopes to guide the spacecraft from an initial state to a desired final state.