Optimalizing control with process-dynamics identification

The meaning of the terms process identification, adaptive and optimalizing control is indicated. The basic difference between these types of control and the ordinary ones is the need for a "learning process". Using multiplication plus integration as the simplest possible type of "learning", simple schemes are obtained in which sinusoidals or random fluctuations may be used as test signals. A more detailed study and an analog simulation have been made of such an optimalizing system. This one is free from the defects of formerly proposed systems, i.e.: - the detrimental effects of system dynamics on the optimalizing control action, - the loop gain changes and even instability of the optimalizing control loop when the process dynamics change with time. This has been achieved by introducing a model of the process dynamics, the parameter(s) of which are controlled by an identifying-control loop. A typical value for the convergence speed towards the optimum of the optimalizing control can be given as follows: using a sinusoidal test signal, the transient for a step-disturbance is approximately of the form
\epsilon^{-t/\tau}
where the value of τ corresponds with three periods of the test signal used. Although the system is nonlinear and time varying, some analytical results have been obtained which check the computer results. The ideas presented can be extended to more-dimensional optimalization and more-parameter identification.