An efficient implementation of Generalized Predictive Control using a multi-layer feedforward neural network as the plant's nonlinear model is presented. In using Newton-Raphson as the optimization algorithm, the number of iterations needed for convergence is significantly reduced from other techniques. The main cost of the Newton-Raphson algorithm is in the calculation of the Hessian, but even with this overhead the low iteration numbers make Newton-Raphson faster than other techniques and a viable algorithm for real-time control. This paper presents a detailed derivation of the Neural Generalized Predictive Control algorithm with Newton-Raphson as the minimization algorithm. Simulation results show convergence to a good solution within two iterations and timing data show that real-time control is possible. Comments about the algorithm's implementation are also included.

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Pamela Haley and Don Solowayhis article presents experimental results of a transonic wind-T tunnel test that demonstrates the use of generalized predictive control for flutter suppression for a subsonic wind-tunnel wing model. The generalized predictive control algorithm is based on the minimization of a suitable cost function over finite costing and control horizons. The cost function minimizes not only the sum of the mean square output of the plant predictions, but also the weighted square rate of change of the control input with its input constraints. An additional term was added to the cost function to compensate for dynamics of the wing model that cause it to be invariant to low input frequencies. This characteristic results in a control surface that drifts within the specified input constraints. The augmentation to the cost function that penalizes this low frequency drift is derived and demonstrated. The initial validation of the controller uses a linear plant predictor model for the computation of the control inputs. Simulation results of the closed-loop system that were used to determine nominal ranges for the tuning parameters are presented. The generalized predictive controller based on the linear predictor model successfully suppressed the flutter for all testable Mach numbers and dynamic pressures in the transonic region in both simulation and windtunnel testing. The results confirm that the generalized predictive controller is robust to modeling errors. Pamela Haley is with the NASA Langley Research Center in Hampton, VA 23681, email: p.j.haley@larc.nasa.gov. Donsoloway is with NASA Ames Research Center in Moffett Field, CA 94035, email: don@ptolemy.arc.nasa.gov. A version of the article waspresented ai the 5th IEEE International Conference on Control Applications, Dearborn, MI, Sept. 15-18, 1996.