Predictive Coordination in Two Level Hierarchical Systems K. Stoilova, and T. Stoilov AbstractNew optimization method, using Non-iterative coordination in multilevel systems is developed. Coordination with prediction is considered. Decision making for optimal resource allocation in a two levels system is worked out. Appropriate model for steady state optimization is derived. Analytical relations are given, which benefit the real time management of the two level control system. Index Termsdecision making, optimization methods, operations research, mathematical programming, system engineering I. INTRODUCTION The decision-making in multilevel systems has been strongly influenced by the experience of the human beings in coordinating their efforts reaching an overall goal, which cannot be achieved individually by the persons. Thus the organization of the humans concerns one of the first and earliest human invention [1]. Following the organizational practice and rules, the multilevel theory uses decomposition and coordination principles in controlling large scale, distributed, complex technical systems. The control process of the complex hierarchical systems is described by the solution of an optimization problem. The original complex optimization problem is reduced to a set of low order optimization subproblems solved by the subsystems of the multilevel system. Thus the solution of the complex problem is found as a vector of the subproblems’ solutions. The subproblems are influenced (coordinated) by the coordination problem to generate the solution of the original problem. Hence, instead of direct solution of a high order and complex optimization problem, the multilevel theory manages and coordinates the solution of low order optimization subproblems. Such methodology, consisting of decomposition to subproblems and coordination between them, leads to hierarchical systems operation [2]. Two main coordination strategies have been worked out: goal coordination and interaction prediction [2], [3]. The goal coordination influences the local performance indices K. Stoilova - Assoc.prof., Ph.D., T. Stoilov – Professor, D.Sc., Ph.D in Institute of Computer&Communication Systems – Bulgarian Academy of Sciences, Acad G.Bonchev str. Bl.2, Sofia 1113, Bulgaria, telephone: (359 2) 979 27 74, fax: (359 2) 72 39 05; e-mail: todor@hsi.iccs.bas.bg of the subproblems. The interaction prediction assumes constant values for the global arguments or for parts of the global constraints. The coordinator performs all these influences in an iterative manner. These iterative calculations insist multiple data transmissions from the lower levels to the coordinator and vice versa, spend time for calculations and data transmissions and prevent the reactions of the hierarchical system in real time. Generally the multilevel approach is used for off-line solution of large- scale optimization problems [4], [5]. In [6], [7] the multilevel technique is successfully applied for nonlinear time delay problem, concerning nonlinear and discrete time systems. The hierarchical coordination has been applied for solving staircase, angular, overlapping structure problems in steady state optimal control [8]. Hierarchical methods were used for joint coordination in steady state control and identification [9]–[11]. The multilevel approach is used in multilevel control scheme with low level: regulating control for keeping selected process variable at set point values and higher optimization level which maintains the optimal values of the set points [12], [13]. To overcome the gaps between the iterative computations and the real time requirements a partial feedback has been worked out for the local control subsystems [14] in linear quadratic dynamical systems. But open loop compensation must be evaluated iteratively in on-line. Hence the hierarchical multilevel approach successfully deals with steady state and dynamically optimization problems concerning off-line applications like system design, off-line scheduling and off-line parameter and system optimization. But the iterative manner of computations restricts the hierarchical methodology to be used in on-line control applications. To overcome the iterative multilevel management the noniterative coordination has been worked out in [15]. Such coordination procedure applies a non- iterative “preposition – correction” protocol. The local subsystems solve and send to the coordinator their prepositions x(0) found with lack of the global constraints. The coordinator modifies x(0) towards the global optimal solution x opt and transmits it to the subsystems for implementation. The noniterative coordination founds on the explicit analytical description and approximation of the dual Lagrange problem. This coordination has been derived for linear quadratic and quadratic-quadratic steady state optimization problems [16]. 2002 FIRST INTERNATIONAL IEEE SYMPOSIUM "INTELLIGENT SYSTEMS", SEPTEMBER 2002 0-7803-7134-8/02/$10.00 © 2002 IEEE 324