By Zijad Aganovic, Zoran Gajic
This ebook is designed to be a accomplished remedy of linear easy methods to optimum keep watch over of bilinear platforms. The unified subject of this publication is using dynamic programming for you to simplify and decompose required computations for the optimum keep watch over of bilinear-quadratic platforms. there are many examples of bilinear keep an eye on structures that supply nice demanding situations to engineers, mathematicians and laptop scientists: those comprise nuclear reactors, missile intercept difficulties and mechanical brake platforms. The e-book additionally examines specified periods of bilinear-quadratic keep an eye on difficulties: particularly singularly perturbed and weakly coupled bilinear regulate structures. The usefulness of the offered the way to those forms of keep an eye on challenge is tested by way of numerous actual keep an eye on approach examples.
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Additional info for Linear Optimal Control of Bilinear Systems: with Applications to Singular Perturbations and Weak Coupling
The corresponding algorithm applied to the problem under consideration is given bellow. 45). 45) by setting e = O. , 1990). 71) or ]IEJ = The approximation P~)(e) = Pji(e) + eEJ~)(e), will produce O(e k+l) approximation of the required solution Pi. Thus, having obtained Pi with the accuracy of O (e k+l), we get the same accuracy for the optimal trajectories and the approximate optimal control law. 65) at each discrete-time instant in the interval of interest. There are several methods available in the literature for solving the algebraic Lyapunov equation.
22). The main problem that we are faced with in the presented method is the problem of finding the transition matrices O(t, to, e) and ~(t, to, e) of the corresponding time varying systems. One way to overcome this problem is to study the optimal open-loop control of singularly perturbed system in the discrete-time domain, where the analytic expressions for the corresponding transition matrices exist. In that direction the first step should be to develop SINGULARLY PERTURBED SYSTEMS 27 the discrete-time version of the results of (Hofer and Tibken, 1988).
8)-(b. 22) 46 SINGULARLY PERTURBED SYSTEMS with starting point chosen as E~ °) = O, E~°) = O, E(3O) : O. 22) converges to the exact solution of the error terms with the rate of convergence of O(e), that is (Gajic and Shen, 1993) = o¢), .... 24) After obtaining p(i+l) with the desired accuracy we go to the next iteration step with respect to i. Note that i iterations are the Newton method iterations so that one has to perform only 4-5 iterations with respect to i (the Newton method either converges in 4-5 iterations or does not converge at all).
Linear Optimal Control of Bilinear Systems: with Applications to Singular Perturbations and Weak Coupling by Zijad Aganovic, Zoran Gajic