HYBRID COMPUTER TO SOLVE NONLINEAR PROGRAMMING PROBLEMS

摘要

1403375 Solving simultaneous equations INSTITUT ELEKTRODINAMIKI AKADEMII NAUK UKRAINSKOI SSR 18 May 1972 23454/72 Heading G4G A hybrid (digital/analogue) computer for solving non-linear problems involving a number of independent variables, comprises an initial condition channel 5 in which the values of the independent variables are set into the computer, and a parallel problem-solving channel 6 in which the problem is solved starting from the initial conditions. The channel 5 comprises a circuit 10 for generating analogue signals representing the initial conditions and a junction generator for generating a so-called "auxiliary junction" which is any convenient junction which becomes zero when the initial conditions generated by circuit 10 are equal to the values of the independent variables. The output of the function generator 11 is fed to a differentiator 12, 13 which produces the time derivative of the auxiliary function. The problem-solving channel 6 comprises a circuit 14 for generating analogue signals corresponding to the current values of the independent variables, these being fed to a function generator 15 which generates a second "auxiliary function" defined as any function of the independent variables having minima at those values of the variables which are solutions of the problems to be solved. The Specification gives examples of suitable forms of the first and second auxiliary functions which, in effect, yield error signals. The output of the function generator 15 is fed to circuits 16, 17 for generating the time derivative of the second auxiliary function. The outputs of the channels 5, 6 are fed alternately via a switch 7 and amplifier 9 to an A/D converter 2 which produces a digital signal indicative of the sign of the timederivative signal from amplifier 9. This signal is fed to a logical search-direction device 25, 26 which determines in accordance with successive outputs of the A/D converter 2 a search direction for the vector whose components are the set of independent variables. The search-direction device commands a set of integrators 4 each arranged to provide a continuous output corresponding to a respective one of the independent variables and which increases or decreases with time in accordance with the search directions. For a binary vector, the device may comprise three AND gates 29, 30, 31, Fig. 2 and a flip-flop 34, the gates being connected to a clock 182 and to the output 24 of the A/D converter 2 as shown. An inverter 33 is inserted between the converter 2 and the input of the gate 30. The gate 31 is connected to the SET output of the flipflop. The RE-SET output furnishes a "change direction" command and the output of the AND gate 31 furnishes a "change sign" command; the mode of generation of the two dimensional vector is indicated in Fig. 16. This figure also shows examples of ways in which successive search vectors may be generated in proceeding from initial condition points M 1 , M 2 , M 3 , M 4 and arbitrary search directions to the four solutions of the simultaneous equations: The analogue circuits 11, 12, 13 and 15, 16, 17 for generating and differentiating the first and second auxiliary functions are determined by the chosen functions. The first auxiliary function generated in the initial condition channel 5 may, e.g. be defined as where the # j are the mismatch errors in the n initial conditions and # is a constant. The network for generating this function may (Fig. 5, not shown) consist of set of diode pairs for separately summing the positive and negative errors and a differential transformer for producing the time derivative.