Data processing: vehicles – navigation – and relative location – Vehicle control – guidance – operation – or indication – Aeronautical vehicle
Reexamination Certificate
1999-02-19
2001-03-13
Nguyen, Tan (Department: 3661)
Data processing: vehicles, navigation, and relative location
Vehicle control, guidance, operation, or indication
Aeronautical vehicle
C244S003100, C280S001210
Reexamination Certificate
active
06202007
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention generally relates to a method for using exact stability integration in network designs. More particularly, the invention relates to a method for using exact stability in net-work designs for application in systems optimizing flight control of aircraft through the use of improved numerical techniques.
2. Description of the Prior Art
The idea of exact stability integration originated during the course of an U.S. Air Force study whose objective was to advance the flight control of aircraft through improved numerical techniques. One of the techniques that was investigated was a predictor-corrector approach that had exact stability for second and fourth order systems.
Mathematical literature describes integration algorithm in terms of order, i.e. first order, second order, - - - up to any order of which the computer is capable. However, integration at higher orders designs a system that is always stable and completely controllable with a deadbeat response. According to Warwick and Tham, the dead-beat response provides the required robustness of the system by causing the response of the estimation error to reach equilibrium in minimum time. Warwick, Kevin and Tham, Ming T., “Failsafe Control Systems,” Chapman and Hall, New York, 1991, p. 126,127.
The intrinsic robustness of a dead-beat response is achieveable with an exact stability system (as opposed to an absolute stability system) inasmuch as the observer is strongly decoupled from unwanted disturbances and moderately decoupled from faults resulting in a network with a dead-beat response having the desired stability, robustness and controllability response desired which can be easily obtained when exact stability is used as a design tool and using the technique of process control. According to Kalman, exact stability provides complete control if there exists a sampled-data controller which has a dead-beat response. Kalman, R. E., “On the General Theory of Control Systems”, First International Federation Automatic Control, Moscow, Butterworths, Vol. 1, pp 481-492 (1961).
Representative of the prior patent art directed to proportional integration system in combination with a dead-beat system is U.S. Pat. No. 4,979,940 (Bobo, Jr. et al.). The patent discloses an infusion system, methodology, and algorithm for identifying patient-induced pressure artifacts.
Representative of the prior patent art directed to network with order integration and controlling algorithm are U.S. Pat. No. 5,148,514 (Arima et al.), U.S. Pat. No. 5,224,203 (Skeirik), U.S. Pat. No. 5,282,261 (Skeirik), and U.S. Pat. No. 5,293,457 (Arima et al.). Arima et al. discloses neural network integrated circuit device having self-organizing function. Skeirik discloses on-line process control neural network using data pointers, and neural network process measurement and control.
Representative of the prior patent art directed to high order information processing for a network that has a controlling algorithm and order integration is U.S. Pat. No. 5,513,923 (Matsuba et al.). The patent discloses high order information processing method by means of a neural network and minimum and maximum searching method therefor.
Representative of the prior patent art of general interest are U.S. Pat. No. 5,197,114 (Skeirik) directed to computer neural network regulatory process control system and method; U.S. Pat. No. 5,629,845 (Liniger) directed to parallel computation of the response of a physical system; and U.S. Pat. No. 5,634,004 (Gopinath et al.) directed to directly programmable distribution element.
While many of the neural network systems with order integration and controlling algorithm disclosed in the prior art generally have achieved the objectives for which they were designed, none disclose a neural network system which embodies an algorithm with integration orders as high as desired for optimization problems. Consequently, the need still exists for a neural network system exact stability algorithm, with the value of integration orders restricted by computer memory capacity, that always has dead-beat control with minimal extraneous errors added to the system.
SUMMARY OF THE INVENTION
The present invention is directed to providing a method for using exact stability in network design for application in systems for optimizing flight control of aircraft through the use of improved numerical techniques. The invention also allows for application in systems for optimizing integration step size in technological and industrial environments, maximizing the benefits of such processes with the minimum amount of truncation, roundoff and random errors in the network to obtain robust realizable and stable neural networks. Moreover, the present invention can be applied to all types of linear or nonlinear filters or networks.
Through the use of improved numerical techniques, a new concept of stability was determined which was designated exact stability because randomness arising from the extraneous eigenvalues moving randomly from −1 to +1 in absolute stability was eliminated by constraining the closed loop poles to be at the origin. By constraining the parasitic eigenvalues to be zero, integration at high order was accomplished and the order was determined to be as high as the order of integration which was wanted.
The present invention utilizes exact stability in networks designs for application in systems for optimizing the flight control of aircraft through improved numerical techniques. Optimization of the flight control of aircraft is achieved by configuring an exact stability algorithm for generating a numerical integration of a high order of any type linear or nonlinear filter or network by constraining extraneous eigenvalues in the high order filter or network to be a definite value. And designing a self starting method for a numerical solution of differential equations having a main process that describes a multiplicity of states of motion and a subprocess that computes derivatives of states with an nth order numerical solution for an nth order differential equation.
Numerical integration of networks of high order using exact stability in effect gives a dead-beat response because the extraneous eigenvalues have been constrained to be a definite value. The dead-beat response provides the requested robustness of the system by causing the response of the estimation error to reach equilibrium in minimum time. Moreover, exact stability provides complete control when there exists a sampled-data controller with a dead-beat response.
The corrector method includes a self starting routine. The numerical solution of differential equations comprises a main process that describes the states of motion and a subprocess that computes the derivatives of the states.
Additional advantages of using a system with exact stability as defined by the present invention are: (A) the corrector only is used which simplifies the coding and shortens the execution time; (B) the order of the algorithm can be set as high as desired to reduce the truncation errors as low as required if the computer has enough memory; (C) the computer develops the desired algorithm after the desired order is read from the input by starting with the first order, second order, - - - , until the desired order is obtained; (D) the dead-beat approach is very robust in sensor fault detection; and (E) a filter or network with zero parasitic eigenvalues that has a dead-beat response is completely controllable.
The foregoing and other features and advantages of the present invention will become apparent to those skilled in the art upon a reading of the following detailed description when taken in conjunction with the flow of information diagram wherein there is shown and described an illustrative embodiment of the invention.
REFERENCES:
patent: 4520972 (1985-06-01), Diesinger et al.
patent: 4979940 (1990-12-01), Bobo, Jr. et al.
patent: 5005353 (1991-04-01), Acton et al.
patent: 5148514 (1992-09-01), Arima et al.
patent: 5153923 (1992-10-01), Matsuba
pat
Marzocco Ralph L.
Nguyen Tan
Tran Dalena
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