By Zoran Gajić PhD, Xuemin Shen BSc, MSc, PhD (auth.)
Parallel Algorithms for optimum keep watch over of enormous Scale Linear structures is a accomplished presentation for either linear and bilinear structures. The parallel algorithms offered during this ebook are acceptable to a much wider classification of functional platforms than these served through conventional equipment for big scale singularly perturbed and weakly coupled structures in line with the power-series growth tools. it truly is meant for scientists and improve graduate scholars in electric engineering and machine technology who care for parallel algorithms and regulate platforms, specifically huge scale structures. the cloth awarded is either complete and unique.
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Additional info for Parallel Algorithms for Optimal Control of Large Scale Linear Systems
Example text
27). 27) exists under the following assumption. jQ ( £ detectable. 29) The zero-order solution is 0 (£) close to the exact one. s will produce the 0 (£k+l) approximation of the required matrix P, which is why we are interested in finding equations for the error term and a convenient algorithm for their solutions. 31) have all cross-coupling tenns and all nonlinear tenns multiplied by a small parameter €, which suggests that a fixed point algorithm can be efficient for their solution. We will propose the following algorithm, similar to one obtained in (Gajic, 1986), for the nonparametrized case.
1 Case Study: Discrete Model of An F-8 Aircraft A linearized model of an F-8 aircraft is considered in (Elliott, 1977). 7 Small elements in the first two rows indicate two slow variables in contrary to relatively big elements in the third and forth rows corresponding to fast variables. The small perturbation parameter £ is chosen as £ = 1/30. This model is discretized in (Litkouhi. 1983) by using the sampling period T = 1. 008: of. 7 is satisfied. 5. 7 Recursive Methods for Weakly Coupled Linear Discrete Systems The main goal in the theory of weakly coupled control systems is to obtain the required solution in terms of reduced-order problems, namely subsystems.
86) Ai, i = 1, 2, 3, 4, and Qj, j = 1, 2, 3, are asswned to be continuous functions of £. Matrices PI and P3 are of dimensions n x n and m x m, respectively. Remaining matrices are of compatible dimensions. 92) Note that we did not set £ ... 0 in A~s and Qjs. 94) The invertibility of the matrix (I - A4) follows from the stability asswnption that I ,\ (A4) 1< 1. 96) Thus, we can get solutions for PI: P2, and P3 by solving one lower order continuous-time Lyapunov equation and lower order discrete-time Lyapunov equation.