Application of the Direct Decomposition Method

In the preceding chapter, a new two-level approach to control complex processes was presented. It was shown that it leads to a control law of the mixed type, i.e. an open-loop term is added to a feedback term such that the simultaneous action of both terms ensures the optimality of the solution. This control structure is quite attractive for on-line applications where the first level acts as a regulator while the higher level or coordinator takes over the “harmonization” of the different actions. The present chapter is more directly concerned with practical considerations when applying this method on-line.

[1]  Madan G. Singh,et al.  Systems: Decomposition, optimisation, and control , 1978 .

[2]  M. Jamshidi,et al.  ON THE HIERARCHICAL CONTROL OF DISCRETE-TIME SYSTEMS WITH TIME DELAY. , 1984 .

[3]  E. J. Bauman,et al.  Multilevel Optimization Techniques with Application to Trajectory Decomposition , 1968 .

[4]  Marlin H. Mickle,et al.  Multilevel control and optimization using generalized gradients technique , 1977 .

[5]  Louis A. Hageman,et al.  Iterative Solution of Large Linear Systems. , 1971 .

[6]  Peter Falb,et al.  Some successive approximation methods in control and oscillation theory , 1972 .

[7]  Mohamed F. Hassan,et al.  A two-level costate prediction algorithm for non-linear systems , 1977, Autom..

[8]  Magdi S. Mahmoud.  Optimal control of constrained problems by the costate coordination structure , 1978, Autom..

[9]  B. Anderson,et al.  Linear Optimal Control , 1971 .

[10]  M. Jamshidi,et al.  HIERARCHICAL CONTROL FOR LARGE SCALE TIME-DELAY SYSTEMS. , 1983 .

[11]  M. F. Hassan,et al.  The optimization of non-linear systems using a new two level method , 1976, Autom..

[12]  Hiroyuki Tamura,et al.  Multistage linear programming for discrete optimal control with distributed-lags , 1977, Autom..

[13]  R. Rockafellar.  Augmented Lagrange Multiplier Functions and Duality in Nonconvex Programming , 1974 .

[14]  William L. Garrard,et al.  Design of nonlinear automatic flight control systems , 1977, Autom..

[15]  J. Gillis,et al.  Matrix Iterative Analysis , 1961 .

[16]  A. M. Geoffrion.  Duality in Nonlinear Programming: A Simplified Applications-Oriented Development , 1971 .

[17]  W. Arthur.  Control of linear processes with distributed lags using dynamic programming from first principles , 1977 .

[18]  Madan G. Singh,et al.  Modelling and hierarchical optimization for oversaturated urban road traffic networks , 1974 .

[19]  Harold J. Kushner,et al.  Accelerated procedures for the solution of discrete Markov control problems , 1971 .

[20]  B. Nicoletti,et al.  Optimal discrete systems with pure delays , 1973 .

[21]  Nicolas D. Georganas,et al.  Review of "Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding" by Gunter H. Meyer. , 1977 .

[22]  Mohamed F. Hassan,et al.  Hierarchical optimisation for non-linear dynamical systems with non-separable cost functions , 1978, Autom..

[23]  P. Spitéri,et al.  Decentralized Calculations in Optimal Control of a Large Thermic Process: Methods and Results , 1980 .