Abstract
The non-fragile guaranteed controller design problem for an interval system and a given cost function is discussed. A sufficient condition is established such that the closed-loop system stability and cost function is guaranteed to be no more than a certain upper bound with all admissible uncertainties as well as a controller gain perturbation uncertainty. A modified interval system described by matrix factorization will lead to less conservative conclusions. An effective linear matrix inequality (LMI) approach is developed to solve the addressed problem. Furthermore, a convex optimization problem is formulated to design the optimal non-fragile guaranteed cost controller which minimizes the upper bound of the closed-loop system cost. The effectiveness of this approach has been verified on a missile launched underwater attitude control system design. Simulation results on a real example are presented to validate the proposed design approach.
Highlights
A missile launched underwater is an essential naval device because it can be used in deep water and control large areas of sea
This paper considers the missile launched underwater model for an interval system, provides a non-fragile guaranteed cost controller design approach, and applies to a missile launched underwater control test, which is validated by a moving body’s control trajectory numerical simulation
The objective of this paper is to develop a procedure for determining a state feedback gain matrix Kwhich contains controller gain perturbation such that the control law u = Kx is a non-fragile guaranteed cost control of the system (1) and cost function (4)
Summary
A missile launched underwater is an essential naval device because it can be used in deep water and control large areas of sea. In order to avoid the instability of the control system, the most commonly used method of predicting the motion test data is to extrapolate trends of identifying hydrodynamic parameters This gives a basis for boundary prediction of the uncertain moving body and provides seaworthiness conditions to achieve the precision strikes purpose. In order for the design methods to be more useful, practical considerations need to be taken into account in the control design, for example, the inevitable model uncertainties, interval system, guaranteed cost control and even possible fragility. These issues will make the design more challenging. The LMI approach is used to study the design problem of non-fragile guaranteed cost controller of an interval system. Its application is given to illustrate the effectiveness and necessity for the control design
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