Observer‐based linear parameter‐varying control with guaranteed ‐gain and ‐type performance objectives

Abstract

SUMMARY Synthesis of an observer‐based linear parameter‐varying controller is considered for a general linear parameter‐varying plant. The parameter vector and its derivative are both assumed to take values in known bounded domains, whereas only the parameter vector is assumed to be measurable during online operation. The synthesis problem is considered for scriptL2‐gain and scriptH2‐type performance objectives. Potentially conservative parameter‐dependent linear matrix inequality conditions are derived for the solvability of these two problems. To facilitate the reduction of conservatism, the conditions are expressed in a way to have bilinear dependence on an arbitrary positive scalar. In addition to employing a suitable relaxation scheme to reduce these conditions into finitely many constraints, a line search hence needs to be performed over the positive scalar to obtain the best achievable performance with an observer‐based controller. The online implementation of the observer‐based controller is relatively simpler if compared with a controller of unrestricted structure. Moreover, the observer‐based controller will have no dependence on the parameter derivatives irrespective of the choices of the design variables. Copyright © 2013 John Wiley & Sons, Ltd.

Design of LPV-Based Sliding Mode Controller with Finite Time Convergence for a Morphing Aircraft

“…The explicit expressions of E, F 1 , F 2 , F 3 , W 1 , W 2 , and W 3 are given in Appendix C. Remark 1. By adopting the Kane modeling, only the position, velocity and acceleration of Λ and Δ appear in the dynamic modeling equation (9). They can be computed and manipulated more practically than the position, velocity, and acceleration of the center of mass or instantaneous inertia tensor and its derivative [17].…”

“…This shows another major superiority of the Kane method. Notice that we will apply our designed LPV-based controller on the original nonlinear equation 9, and the exact values of Λ ′ , Λ ″ and Δ′, Δ″ at every moment must be obtained so that we can substitute them into (9). Therefore, the motion trajectories of sweep angle and span need to be scheduled appropriately in advance.…”

“…While its controller synthesis methods are theoretically well-founded based on LMI, LPV control is confronted with an inevitable challenge: direct generation of these methods to LPV systems will result in infinitely many LMI constraints that have to be satisfied [9]. There are three most common approaches to fixing this problem.…”

Multi-objective LPV L2-gain control with game-theoretic synthesis

“…We may expect that the BRL-stemmed synthesis in conjunction with observer-based structure, e.g. in [26][27], can resolve this difficulty in the near future. For the present, the game-theoretic synthesis for the observer-based DGKF ∞ H -control can be extended into suppressing this difficulty.…”

Special issue on linear parameter varying systems

“…The paper by Köroğlu considers the problem of synthesising an observer‐based linear parameter‐varying controller for a general linear parameter‐varying plant. The synthesis problem is considered with respect to ‐gain and ‐type performance objectives.…”