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Grantham, W. J.

Publications and source records attributed to Grantham, W. J..

3 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Lyapunov optimal feedback control of a nonlinear inverted pendulum

Liapunov optimal feedback control is applied to a nonlinear inverted pendulum in which the control torque was constrained to be less than the nonlinear gravity torque in the model. This necessitates a control algorithm which 'rocks' the pendulum out of its potential wells, in order to stabilize it at a unique vertical position. Simulation results indicate that a preliminary Liapunov feedback controller can successfully overcome the nonlinearity and bring almost all trajectories to the target.

Grantham, W. J.↗
NASA NTRS1972

A problem of collision avoidance

Collision avoidance between two vehicles of constant speed with limited turning radii, moving in a horizontal plane is investigated. Collision avoidance is viewed as a game by assuming that the operator of one vehicle has perfect knowledge of the state of the other, whereas the operator of the second vehicle is unaware of any impending danger. The situation envisioned is that of an encounter between a commercial aircraft and a small light aircraft. This worse case situation is examined to determine the conditions under which the commercial aircraft should execute a collision avoidance maneuver. Three different zones of vulnerability are defined and the boundaries, or barriers, between these zones are determined for a typical aircraft encounter. A discussion of the methods used to obtain the results as well as some of the salient features associated with the resultant barriers is included.

Vincent, T. L.↗