New Approaches to H-Infinity Control II

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Author Index
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Robust H-Infinity Control of Uncertain Linear Systems via Parameter-Dependent Lyapunov Functions

Authors:

Carlos E. de Souza, Alexandre Trofino, José de Oliveira,

Volume: 1, Page 3194 Paper number 9505

Abstract:

This paper addresses the problems of robust H-infinity performance analysis and control synthesis for linear systems subject to uncertain real time-varying parameters. The uncertain parameters enter affinely in the matrices of the system state-space model and the admissible values of the parameters and their rates of variation are supposed to belong to a given polytope. New LMI based methods of robust H-infinity analysis and control design via state feedback are proposed using parameter-dependent Lyapunov functions.

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Constantly Scaled H-Infinity Control Problems For Pseudo Full Information Problems

Authors:

Toru Asai,

Volume: 1, Page 3200 Paper number 1825

Abstract:

This paper deals with the constantly scaled H-infinity control problem. In general, the solvability condition for this problem is non-convex. However, it is known that the state feedback (SF) and the full information (FI) problems can be reduced to convex problems. In this paper, we consider a class of problems including the SF and the FI problems as the special cases. The class is characterized by an additional assumption called a pseudo full information (PFI) condition. Assuming the PFI condition, we first derive a solvability condition. This condition involves fewer number of variables than the standard solutions for the constantly scaled H-infinity control problem. Based on this condition, we further give a convex sufficient condition for the solvability. The convex solvability condition for the SF and the FI problems can be regarded as the extreme cases of the derived sufficient condition. Moreover, we show that there exists a simple formula of a possible controller, if the PFI condition is assumed.

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H-Infinity Control And Frequency Analysis For Systems With Mixed Continuous-Time And Discrete-Time Measurements

Authors:

Olof Lindgärde, Bengt Lennartson,

Volume: 1, Page 3206 Paper number 1939

Abstract:

Feedback control using both continuous-time and discrete-time measurements is considered in this paper. A design method including both H-infinity-synthesis and frequency analysis is suggested. It includes a strategy for selecting weighting filters in the control design. The presented frequency analysis method is then a powerful tool in the design process.

CD001939.PDF (From Author)

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Hierarchical Optimization in the Presence of an Intelligent Adversary - an H_(infinity) Approach

Authors:

Muralidhar Ravuri, Chung-Yao Kao, Alexander Megretski,

Volume: 1, Page 3212 Paper number 1915

Abstract:

In this paper, we consider the H_(infinity) optimization problem for systems with a hierarchical structure. We propose an iterative algorithm to treat the problem. In each iteration of our algorithm, we need to solve a problem of H_(infinity) optimization feature, but with a much smaller dimension. We also show that the solution of the optimization problem in each iteration can be obtained by solving a set of Linear Matrix Inequalities (LMIs).

CD001915.PDF (From Author)

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H-Infinity Control of Unstable, Uncertain Systems Using Horowitz Bounds

Authors:

Carl-Magnus Fransson, Bengt Lennartson, Claes Breitholtz, Anders Bondeson, Yueqiang Liu,

Volume: 1, Page 3218 Paper number 2071

Abstract:

A constrained, two step optimization procedure based on H-inf loop shaping is suggested for highly unstable plants with large parametric uncertainties. With the proposed controller synthesis, optimality is inherited from the H-inf design, and robustness to uncertainties is guaranteed by use of Horowitz bounds. This implies that specifications can be made for the worst case of the sensitivity, the complementary sensitivity, and the controller sensitivity functions. The method is applied to a Tokamak fusion reactor for two different types of sensors, and in this example, optimization of one plant design parameter and one controller tuning parameter will illustrate the procedure. The results are validated by theory for performance limitations of unstable plants, as well as with a manual search over the two dimensional design and tuning parameter space.

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Robust And Non-Fragile H-Infinity Controller Design For Affine Parameter Uncertain Systems

Authors:

Sang Hyun Cho, Ki Tae Kim, Hong Bae Park,

Volume: 1, Page 3224 Paper number 1855

Abstract:

This paper describes the synthesis of robust and non-fragile H-infinity state feedback controllers for linear time varying systems with affine parameter uncertainties and static state feedback controller with polytopic uncertainty. The sufficient condition of controller existence, the design method of robust and non-fragile H-infinity static state feedback controller, and the region of controllers which satisfies non-fragility are presented. Also using some change of variables and Schur complements, the obtained condition can be rewritten as parameterized Linear Matrix Inequalities (PLMIs), that is, LMIs whose coefficients are functions of a parameter confined to a compact set. We show that the resulting controller guarantees the asymptotic stability and disturbance attenuation of the closed loop system in spite of controller gain variations within a resulted polytopic region.

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On Stable H_(infinity) Controller Parameterization Using Doubly Coprime Fractional Representation

Authors:

Youngjin Choi, Wan Kyun Chung, Youngil Youm,

Volume: 1, Page 3230 Paper number 2164

Abstract:

Suboptimal H_(infinity) controller is said to internally stabilize the closed loop transfer matrix. However, the stability of controller is not assured in conventional H_(infinity) control theory. Unstable controller can damage the whole system when the sensor fails or actuator saturates. The sufficient condition for the existence of stable H_(infinity) controller is suggested. This paper presents the stable n-dimensional H_(infinity) controller and its parameterization based on the suggested sufficient condition for the linear time invariant systems using doubly coprime factorization. The stability of H_(infinity) controller and closed-loop stability are guaranteed if the positive semi-definite solutions for the suggested three Riccati equations exist.

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