Near-optimal control using reduced-order models

Two theorems have been proved demonstrating that the tracking properties of low-order models obtained using the theory of partial realisations are unchanged under state or output feedback. It follows, therefore, that an optimal feedback law for the reduced-order model can be used for near-optimal control of the high-order system with similar tracking of the output as for the open-loop case.     

Reduction of linear systems by canonical forms

A new companion-type realisation of a rational transfer function is introduced. This form is then used for obtaining a reduced-order model. It is possible, using this approach, to simultaneously match time moments, Markov parameters and to retain desired poles, thus combining the methods of partial realisation (Padé approximation) and aggregation.     

Optimally aggregated models of high-order systems

A straightforward scheme for generating optimally aggregated models of high-order systems is presented. The simplicity of the scheme is a direct result of generalising the model forms under consideration. The interesting case of optimal projection along invariant subspaces is a special case. Finally, the notion of quasioptimal aggregated models is introduced, which reduces computation considerably.     

An efficient algorithm for transformation of state equations to canonical forms

An algorithm is presented which enables the transformation of the triple (A, B, C) of a linear multivariable system into the column or the row companion form without requiring any matrix inversion.     

Iterative approach to multivariable control

An iterative technique is proposed for the design of control inputs for linear multivariable systems. Using aggregation to reduce the problem size at each step, compensation can be accomplished in as few as N steps, where N is the controllability index of the system. For controllable systems, arbitrary pole placement is possible subject only to mild restrictions. Applications to deadbeat control and minimal-order observers are illustrated.     

Approximate aggregation for linear multivariable systems

Given a reduced order model of a high order system, the question of approximate aggregation is examined. An error analysis indicates that there is an optimal choice for the aggregation matrix. The method shows that reduced order models are related to Luenberger observers. A comparison with the method of singular perturbations is made.     

Transformation of state equations to the controllable canonical form

An algorithm is presented for the transformation of the state equations of a linear multivariable system to the controllable canonical form without requiring any matrix inversion.     

Aggregation matrices for a class of low-order models for large-scale systems

A simple technique for aggregation is established for model reduction by projection. This leads to a direct formula for deriving the aggregation matrix. It is shown that aggregation is a generalisation of projection, and the work of Aoki is related to that of Mitra, Davison and Chidambara.