SU348113A1 - - Google Patents

Description

This invention relates to the field of computing.

Analog computing devices for solving systems of ordinary differential equations are known, which contain a discrete-analog converter and a derivative former with an automatic mode of operation and penal function generators connected to it.

All known devices require input of the initial information in a digital and analog computer) first blocks and a large amount of time in the preparation of work programs.

The proposed device differs from the known ones in that it contains in the circuit between the output of the discrete-analog converter and one of the formers of the penalty function which are subsequently included in the analog model of derivatives and the matching switch, the control inputs of which are connected to the outputs of the automaton of operation modes.

The drawing shows a block diagram of a hybrid computing machine.

The machine contains an analog computing device 1 for solving systems of ordinary differential equations, which includes a discrete-analog converter 2, a model analog 3 of a function system, a model analog of 4 non-triggered ones, a model quasi-analogue 5 initial conditions, a model quasi-analogue 6 inverters, matching switch 7, drivers for penalties functions 8i, 82 and 8h shaper derivative 9 and automatic modes of operation 10.

Analog computing device allows solving tasks of the form

 + F (, 0, (1)

where X is the vector of the desired variables, and

(2)

Ф - given nonlinear functions.

The model-analogue 3 of the system of functions is made in the form of a nonlinear resistive multipole and is a functional converter of many variables with the transformation type F. The presence of inverted X and non-inverted X values of the desired variables in the device allows performing these transformations without

operational amplifiers. Model-analogue of 4 derivatives is made in the form of a multipole of integrating capacitors. The quasi-analogous models 5 and 6, respectively, of the initial conditions and inverters are made in the form of a linear generator of generating signals defined by a gap, in the equation, (3) (X0 is a definable initial vector) and the constraints in equation (2). I agree, switch 7 contains terminating resistors and key elements. Shapes 8, 22, and 8z of the penalty function are implemented in the form of diode-resistive multipoles and serve to form a pair of signals / + and f from the input signals e, in accordance with the expressions /.-S, (i). f 2 /, {Bi). The transformation law f - i (i) and fi (i) is determined by the operating conditions of the analog computing device in the hybrid computing machine and is chosen such that the penalty function, -L (6) has a quadratic relationship in the zone of change 8 near zero and linear in the rest of the area. Shaper 9 of the derivative represents a transistor circuit designed to generate an output signal (from input signals / + and /) in accordance with the expression (/, 31) dt where / g is a certain multiplier. The key elements contained in the driver 9 circuitry allow the conversion (7) to be performed on signals arriving at different inputs. The machine 10 modes of operation is used to generate discrete signals that determine the mode of operation of analog computing device 1 for external commands (for example, from the operator). Analog-discrete converter 11 is designed to generate an output signal and the input signal in accordance with the expression a l-d + Sign /) and can be performed, for example, in the form of a Schmidt trigger. Discrete-to-analog converter 2 is designed as a set of controlled oscillators that vary linearly upward, then downward. The proposed device works in the following way. The inputs of the model-analogue 3 of the function system, the model-analogue of 4 derivatives, the models of quasi-dialogs of initial conditions 5 and inverters 6 are fed to the input signals of the analog computing device 1. The automatic machine 10 operating modes sets the following modes of the analog computing device: initial position, decision and stop. In the initial position mode, the problem is solved, represented by the systems of equations (2) and (3). In this mode, the signals of the model-quasi-analogue 5 initial conditions and the model-quasi-analogue 6 inverters are used. The model-quasi-analogue of 5 initial conditions produces signals corresponding to the mismatches in Eq. (3), and the model-quasi-analogue of 6 inverters, corresponding to the mismatches in Eq. (2). These discrepancies arrive at the inputs of the formers 82 and 8z of the penalty function; at the outputs of KOjopbix, bunks of penalty functions are formed in accordance with expressions (4) and (5). The total penalty function, equal to the sum of the penalty function of the initial conditions and the penalty function of the inverters, has a single minimum corresponding to the solutions of the systems of equations (2) and (3). The work of the hybrid computer in this mode consists in finding this minimum. The components of the penalty function are input to the driver of the derivative 9, where each of the pairs of components of the penalty function is transformed in accordance with expression (7) and the resulting signals are summed. A pair of output signals from the imager 8i of the penalty function in this mode is turned off by the command of the automaton 10 modes of operation. In the solution mode, a problem of the form (1), (2) is solved. On the outputs of the model-analogue 3 of the function system, the current values of the function system Φ are generated, the output signals of the model-analogue 4 derivative are the derivatives of the input signals. The output signals of the analogue model 4 and the analogue model 3 of the system of functions are fed to the inputs of the matching switch 7, the output of which produces nets in the system of differential equations (1). The outputs of the matching switch 7 are fed to the input of the driver 8i of the penalty function, the outputs of which form the components of the penalty function in accordance with expressions (4) and (5). The model-quasi-analogue of 6 inverters and the driver of the KB of the penalty function work in the same way as in the previous mode. The total penalty function f-f, + /., (9) where / n fa are the penalty functions, respectively, of the systems of equations (1) and (2), has a single minimum. The minimum coordinates vary over time due to the presence of a system of ordinary differential equations in the assignable problem. The work of the hybrid computer in this mode consists in finding the coordinates of this minimum and in tracking the minimum of the NLP change its coordinates. The components of the penalty functions from the outputs of the formers 8i and 8z of the penalty functions are fed to the inputs of the derivative 9, where each of the pairs of components of the penalty function is transformed in accordance with the expression (7) and the received signals are summed, resulting in a time derivative of the penalty functions (9). The incoming, and from the former 82 of the penalty function, the pair of signals in this mode is turned off by the command of the automaton 10 modes of operation. In the stop mode, the problem represented by system (2) and the system of differential equations, -0, is solved. dt The stop mode basically coincides with the decision mode. The only difference is in the transition from equation (1) to equation (u). This is accomplished by turning off in the matching switch 7 of the model-analogue 3 of the system of functions on command of the automaton 10 modes of operation. In all modes, the output of the imaging unit 9 derivative is the output of the analog computing device 1. The output signal / analog computing device 1 is fed to the input of the analog-discrete converter 11, which produces the output signal cr in accordance with the expression (8). The output of the analog-to-digital converter 11 is fed to the input of a digital computing device 12, which generates a series of signals as a sequence of mutually orthogonal vectors, the components of which can take only two values of +1 and -1. The outputs of the digital computing device 12 are the control signals of the discrete-analog converter 2, the outputs of which generate voltages determining the search path. The resulting trajectory has the form of a continuous broken line with mutually orthogonal straight linear sections. In general, the operation of the hybrid computing machine is characterized as follows. In a straight-line motion in a selected direction, the change in the penalty function is analyzed. If the penalty function decreases (a 0), then the movement in the selected direction is preserved, if the penalty function increases (), then first the direction of movement changes orthogonal to the previous one, then reverses in that direction, then again the transition to a new direction etc., until the penalty function starts decreasing. Such a search process makes it possible to quickly find the minimum of the penalty function. The vector Ao is used to set the initial conditions for a system of differential equations. PROPOSE: c and b) e te n and An analog computing device containing a discrete analog transducer and a derivative former with an automatic mode of operation connected to it and penal function operators In order to simplify the input of information about the source data, it contains in the circuit between the output of the discrete-analog converter and one of the formers of the penalty function a series-connected analogue model of the derivatives and a matching switch, the control inputs of which are Connected to the outputs of the machine modes.