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By Zijad Aganovic, Zoran Gajic
This e-book is designed to be a accomplished therapy of linear easy methods to optimum keep watch over of bilinear structures. The unified subject matter of this publication is using dynamic programming which will simplify and decompose required computations for the optimum keep watch over of bilinear-quadratic structures. there are various examples of bilinear regulate structures that supply nice demanding situations to engineers, mathematicians and machine scientists: those contain nuclear reactors, missile intercept difficulties and mechanical brake platforms. The e-book additionally examines targeted sessions of bilinear-quadratic keep an eye on difficulties: specifically singularly perturbed and weakly coupled bilinear keep an eye on platforms. The usefulness of the provided how you can those different types of keep watch over challenge is tested through a number of actual regulate procedure examples.
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Extra info for Linear Optimal Control of Bilinear Systems: with Applications to Singular Perturbations and Weak Coupling
Example text
2) O = lq~ql %T q2 , P = ePT cP3 where e is a small positive singular perturbation parameter indicating the separation of the state variables into slow and fast ones. It is known that the Newton method is convenient for the singularly perturbed systems whenever the first-order approximation (obtained by setting e = 0 in the partitioned equation (1)) is close to the exact one. In that case the Newton method is superior over the fixed-point type reduced-order parallel algorithm for solving this Riccati equation (Gajic and Shen, 1993), owing to its quadratic speed of convergence.
2) O = lq~ql %T q2 , P = ePT cP3 where e is a small positive singular perturbation parameter indicating the separation of the state variables into slow and fast ones. It is known that the Newton method is convenient for the singularly perturbed systems whenever the first-order approximation (obtained by setting e = 0 in the partitioned equation (1)) is close to the exact one. In that case the Newton method is superior over the fixed-point type reduced-order parallel algorithm for solving this Riccati equation (Gajic and Shen, 1993), owing to its quadratic speed of convergence.
The results are obtained in terms of the reduced-order problems (similarly to the singularly perturbed bilinear systems) for both the optimal open-loop and "closed-loop" control of weakly coupled bilinear systems. An extension of the presented methodology to the time varying weakly coupled bilinear systems can be done by paralleling the work presented in this chapter. Many real physical systems are naturally weakly coupled such as power systems, communication satellites, helicopters, chemical reactors, electrical networks, flexible space structures, mechanical systems in modal coordinates.