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Abstract

It is assumed that processes to be identified or controlled can be described by linear or non-linear differential equations with unknown coefficients aᵢ. For on-line identifications a model is constructed to have the same form of differential equation as the process, but with adjustable parameters αᵢ replacing the aᵢ. The parameters αᵢ are adjusted in a steepest descent fashion; they are shown to converge to the aᵢ as long as an adjustment gain K(t) is non-negative, and not identically zero. An approximate analysis is carried out to determine the best constant K which gives the fastest identification. Optimal control theory is introduced to find the best piecewise continuous K(t) in the interval 0 ≤ K(t) ≤ Kmax . From the exact solution in a special case, a switched suboptimal K which always gives fast identification is determined. Identification schemes are developed for processes which include an unknown non-linearity that, can be assumed to be piecewise linear. An adaptive control, system is developed to control processes with unknown time-varying coefficients. The system is shown to be stable as long as the process inverse is stable; the process need not be stable. Systems to control linear and non-linear unstable processes are designed and simulated. The limitations of the adaptive system are determined, and compared with the limitations of conventional feedback systems.