Parallel Algorithms for Optimal Control of Large Scale Linear Systems

Abstract

and to point out its various advantages, we have included many real control system examples such as: F-8 aircraft, L-l 0 11 fighter aircraft, fluid catalytic cracker, twelve plate absorption column, magnetic tape control system, power system composed of two interconnected areas, distillation column, steam power system, hydro power plant, chemical plants, gas absorber, supported beam control problem, induction motor drives (bilinear model), large space structure, optimal control of a paper making machine (bilinear model), satellite control problem, and synchronous machine connected to an infinite bus.The authors hope that this book will reduce some of barriers that exist in recognizing the power and usefulness of the synchronous parallel algorithms for optimal control of large scale linear and bilinear systems, and that it will help to broaden their implementation in practice. Also, we hope that this book will motivate some researchers to develop the corresponding asynchronous parallel algorithms and extend the presented results to nonlinear control systems.The authors are thankful for support and contributions from Professors V.

Joint queue-perturbed and weakly coupled power control for wireless backbone networks

“…Furthermore, multiple independent and active collocated radios do interfere significantly with each other due to the orthogonality violation of wireless links. This is the problem of weakly coupled wireless control systems (Gajic and Shen, 1993). Investigating the effects of singular perturbation phenomena (in which the rate of energy consumption and queue evolution differ) and weak coupling of multiple channels on power control in wireless network is the subject of this paper.…”

Optimal Control of Transmission Power Management in Wireless Backbone Mesh Networks

“…For N users at each WMR, the SPWC large-scale linear dynamic system is written as (Gajic & Shen, 1993;Mukaidani, 2009;Sagara et al, 2008) , respectively. The system matrices A, B, C and W are defined in the same way as discussed in our recent invesitigation (Olwal et al, 2009b).…”

“…The optimal solution to the given problem (10) with the conflict of interest and simultaneous decision making leads to the so called Nash strategies (Gajic & Shen, 1993) …”

“…It should be noted that the inversion of the partitioned matrices T ε εεε + RB P B in (25) will produce numerous terms and cause the DARRE approach to be computationally very involved, even though one is faced with the reduced-order numerical problem (Gajic & Shen, 1993). This problem is resolved by using bilinear transformation to transform the discrete-time Riccati equations (DARRE) into the continuous-time algebraic Riccati equation (CARRE) with equivalent co-relation.…”

“…This problem is resolved by using bilinear transformation to transform the discrete-time Riccati equations (DARRE) into the continuous-time algebraic Riccati equation (CARRE) with equivalent co-relation. The differential game Riccati matrices iε P satisfy the singularly-perturbed and weaklycoupled, continuous in time, algebraic Regulator Riccati equation (SWARREs) (Gajic & Shen, 1993;Sagara et al, 2008) …”