Madan G. Singh

A comparison of two hierarchical optimization methods

In this note the interaction prediction method and the goal coordination method for the multi-level optimization of large-scale interconnected dynamical systems with separable quadratic coat functions and linear dynamics are compared. The vehicle for the comparison is a twelth-order complex counter-current example taken from the literature. The computational load for the two methods is compared qualitatively whereas the convergence characteristics arc tested on the example. A simple condition is also given for the convergence of the interaction prediction method. This is also tested on the example.

Correspondence item: Hierarchical optimisation for non-linear dynamical systems with non-separable cost functions

In this paper the previous hierarchical optimisation algorithm of Hassan and Singh for non-linear interconnected dynamical systems with separable cost functions is extended to the case of non-linear and non-separable cost functions. This ensures that any decomposition could be used and makes the new algorithm suitable for the optimisation of general non-linear problems.

Hierarchical optimization of non-linear systems with application to a synchronous machine

In this paper a method with wide applicability is outlined for the hierarchical control of large non-linear interconnected dynamical systems with separable cost functions, The method is applied to the problem of optimal control of synchronous machine excitation. The system considered comprises a single generator connected by a transmission line to an infinite bus-bar and for this system the trajectory of the optimal voltage to be applied to the field winding is computed using the two-level method.

Controllers for linear interconnected dynamical systems with prespecified degree of stability

The approach of Anderson and Moore for the design of controllers for linear systems having a prespecified degree of stability is extended to the case of interconnected dynamical systems. The stability and performance of such controllers is studied when the system is subjected to structural perturbations as well as to loss of coordination information. For both the cases a stability condition is derived and bounds are developed for the performance loss.

A New Three Level Algorithm for River Pollution Control

Abstract In this paper a recent three level costate prediction algorithm for the optimisation and open loop control of non-linear interconnected dynamical systems is specialised to the linear-quadratic case and is used to solve a 52nd order river pollution control problem. The new approach uses less storage and provides faster convergence than the best previous hierarchical approach. In addition, since only low order vector integrations are performed, the overall solution is both stable and accurate. The approach is also extended to compute the constant feedback gain matrix for the infinite time case and this matrix is calculated for the 52nd order river system.

A hierarchical model-following controller for certain non-linear systems

In this note a hierarchical solution is developed for non-linear dynamical systems with linear controls. The method involves defining a linear model which incorporates a desirod response for the system and then following this model without using excessive control effort. This latter problem is solved within a two-level structure using a modified pseduo-model coordination method.

Stochastic Hierarchical Control of a Large Scale River System

Abstract In this paper an application study of hierarchical methods to the solution of a 52nd order stochastic river pollution control problem is described. The deterministic control problem and the filtering problem are solved independently using two different hierarchical algorithms as well as for comparison by using the global single level method (of integrating the 52 x 52 Riccati equation The computation time and computer storage requirements of the three approaches are compared.

A three level costate prediction method for continuous dynamical systems

Abstract In this paper a continuous time version of a previous discrete systems optimisation algorithm is developed. The new algorithm uses prediction of costates within a three level structure to provide an efficient organisation of both the storage and the computation. The algorithm which applies to both linear and non linear interconnected dynamical systems has been proved to converge uniformly to the optimum. Two practical examples are given to illustrate the approach The first of a non linear synchronous machine and the other of a 22nd order river pollution system. In each case, the present approach appears to provide faster convergence and smaller storage than previous hierarchical and global methods.

Hierarchical optimisation of dynamical systems using multiprocessors

Abstract Two important dynamical optimisation problems are solved on a multi-processor system using a hierarchical structure. The first of these problems is concerned with the optimisation of a distributed parameter system and the second with a traffic control problem. In each case the computational efficiency of the multiprocessor calculation is compared with the corresponding hierarchical solution using a single computer. From these two examples, some of the difficulties which need to be resolved before on-line hierarchical control could be practically used, are briefly examined.

A note of the convergence of infeasible dynamical hierarchical controllers

In this note, a brief study is made of the convergence characteristics of infeasible dynamical hierarchical controllers. An. attempt is made to provide qualitative guidelines on the necessary degree of accuracy required for the resolution of the problems on each level in order for the overall optimal control to be achieved. It is shown that it is much more important to achieve a high degree of accuracy on the first level than on the second. Some experimental verification is provided for this assertion by studying the convergence characteristics of a non-linear dynamical system comprising two subsystems.