On a direct method for optimization of stochastic distributed parameter systems

A direct method for optimization of a class of linear distributed parameter systems with stochastic distributed disturbances is presented. The method is based on expanding control systems, Green's function and covariance matrices in terms of a finite number of elements taken from complete sets of orthonormal basis in both time and space. Practical considerations are considered in the application of the method. A minimum-variance filter is designed using noisy discrete observations from a finite number of measuring points. Then the synthesis of a pointwise controller is carried out to minimize a quadratic performance index. The optimal coefficients of control are determined via simple algebraic relations in terms of the state conditional mean. A discussion of the properties and computational aspects of the method is given.

[1]  Donald M. Wiberg,et al.  Canonical equations for boundary feedback control of stochastic distributed parameter systems , 1972 .

[2]  G. Stein,et al.  Identification of Green's function for distributed parameter systems , 1970 .

[3]  C. Leondes,et al.  Advances in Control Systems , 1966 .

[4]  V. Rosenberg,et al.  Methods for the Numerical Solution of Partial Differential Equations , 1969 .

[5]  M. Athans,et al.  Toward a practical theory for distributed parameter systems , 1970, IEEE Transactions on Automatic Control.

[6]  Y. M. El-Fattah,et al.  A direct method for synthesis of optimum distributed systems , 1973 .

[7]  H. Erzberger,et al.  On the design of optimum distributed parameter system with boundary control function , 1967, IEEE Transactions on Automatic Control.

[8]  S. E Aidarous,et al.  A direct method for optimization of stochastic distributed systems , 1975, Autom..

[9]  H. J. Kushner,et al.  On the Optimal Control of a System Governed by a Linear Parabolic Equation with White Noise Inputs , 1968 .

[10]  Michael A. Arbib,et al.  Topics in Mathematical System Theory , 1969 .

[11]  K. O. Solberg,et al.  Discrete time control of linear distributed parameter systems , 1970 .

[12]  Spyros G. Tzafestas,et al.  Optimal control of a class of linear stochastic distributed-parameter systems , 1968 .

[13]  M. Ghonaimy,et al.  A direct method for computing optimal feedback control for linear systems , 1972 .

[14]  Y. M. El-Fattah.  State estimation for linear deterministic distributed systems , 1974 .

[15]  A. G. Butkovskiĭ,et al.  Distributed control systems , 1969 .

[16]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[17]  Solomon G. Mikhlin,et al.  The numerical performance of variational methods , 1971 .

[18]  S. Prabhu,et al.  Optimal control of linear diffusion processes with quadratic error criteria , 1972 .

[19]  C. Sanathanan,et al.  Analysis and control of distributed systems using non-eigen space modes† , 1971 .