Abstract
This paper focuses on the suboptimization of a class of multivariable discrete‐time bilinear systems consisting of interconnected bilinear subsystems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only. Conditions which ensure the controllability of the overall system are given as a previous requirement for optimization. Three transformations of variables are made on the system equations in order to implement the scheme on an equivalent linear system. This leads to an equivalent representation of the used quadratic performance index that involves the appearance of quadratic weighting terms related to both transformed input and state variables. In this way, a Riccati‐matrix sequence, allowing the synthesis of a standard feedback control law, is obtained. Finally, the proposed control scheme is tested on realistic examples.
Highlights
Dynamic bilinear systems have received great attention by researchers in the last decades, from the classical works of Anderson and Moore 1, Feldbaum 2, Tarn 3, or Tarn et al 4, to the recent works of Al-Baiyat 5, Kotta et al 6 or Garrido et al 7
This paper reports suboptimal optimization techniques which are applied to bilinear models
An equivalent feed-forward linear system with equivalent inputs, which are derived from products state-input, has been given
Summary
Dynamic bilinear systems have received great attention by researchers in the last decades, from the classical works of Anderson and Moore 1 , Feldbaum 2 , Tarn 3 , or Tarn et al 4 , to the recent works of Al-Baiyat 5 , Kotta et al 6 or Garrido et al 7. This paper reports suboptimal optimization techniques which are applied to bilinear models Such models can be considered as direct extensions to the linear continuous interconnected systems stated by the work of Ramakrishna and Viswanadham 27. As a previous requirement for optimization, controllability results for the overall systems performance are given by extending those ones given in 17, 18, 27–31. This is achieved through the above equivalent linear system with the use of centralized control methods. An explicit solution of Riccati type which is unusual for such an optimization criterion is found out as the suboptimal solution by using manipulations on the input/state variables of the problem statement 1, 32. Equations and results from the appendices are sometimes invoked in the main body of the paper order not to repeat mathematical material
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
