A Nash game approach to mixed H/sub 2//H/sub ∞/ control

Limebeer, D.J.N.; Anderson, Brian D. O.; Hendel, B.

doi:10.1109/9.273340

Cited by 300 publications

(199 citation statements)

References 22 publications

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“…However, the more complex nature of the mixed H 2 /H ∞ control problem calls for a somewhat different approach. In Limebeer et al [1992Limebeer et al [ , 1994 linear systems are considered and a novel approach for solving the problem is proposed by recognising that it can be described as a two-player, nonzero-sum differential game. Thus, solutions are found using a game This work has been conducted as part of the research project "Stability and Control of Power Networks with Energy Storage (STABLE-NET)" which is funded by the RCUK's Energy Programme (contract no: EP/L014343/1).…”

Section: Introductionmentioning

confidence: 99%

A Nash Game Approach to Mixed H2/H∞ Control for Input-Affine Nonlinear Systems

Mylvaganam

Astolfi

2016

IFAC-PapersOnLine

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With the aim of designing controllers to simultaneously ensure robustness and optimality properties, the mixed H 2 /H ∞ control problem is considered. A class of inputaffine nonlinear systems is considered and the problem is formulated as a nonzero-sum differential game, similar to what has been done earlier by Limebeer et al. for linear systems. A heuristic algorithm for obtaining solutions for the coupled algebraic Riccati equations which are characteristic of the linear quadratic problem is provided together with a systematic method for constructing approximate solutions for the general, nonlinear problem. A few numerical examples are provided.

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Section: Introductionmentioning

confidence: 99%

A Nash Game Approach to Mixed H2/H∞ Control for Input-Affine Nonlinear Systems

Mylvaganam

Astolfi

2016

IFAC-PapersOnLine

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“…The aim of the buffet control is to minimise the deck's buffet response using ideas from mixed H 2 /H ∞ optimal control theory; see Limebeer et al (1994) and the references therein. The H 2 optimal control serves to minimise the output (pitch and heave of bridge deck) variance under stochastic excitation, while H ∞ guarantees the buffet control still has certain robustness although less than the case of flutter control.…”

Section: Robust Flutter and Buffet Controller Designmentioning

confidence: 99%

Buffet loading, dynamic response and aerodynamic control of a suspension bridge in a turbulent wind

Zhao

Gouder

Graham

et al. 2016

Journal of Fluids and Structures

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This paper describes experiments relating to the buffet response and control of a section of a long-span suspension bridge deck elastically mounted as part of a wind tunnel experiment. The bridge section is subject to grid generated flow turbulence. Two grids are used -one is a standard biplanar grid, while the second is a new design that provides larger turbulence length scales. The buffet response results are compared with admittances calculated using unsteady, three-dimensional, lifting-surface theory that extends standard two-dimensional Sears' theory. The bridge deck heave and pitch responses are predicted with comparisons made with wind tunnel measurements. In order to suppress buffeting, and increase the deck's critical flutter speed, the deck model is fitted with controllable leading-and trailing-edge flaps. Two sets of passive controllers, which use the flap angles as the control inputs, are demonstrated and evaluated for their capability to suppress the buffet response of the deck and increase its critical flutter speed. The first set of controllers sense the deck's position (pitch angle and heave, or pitch angle alone), whilst the second set (which are mechanical controllers) sense the vertical velocity of the flap hinge points. The control system design problem is solved as a mixed H 2 /H ∞ optimisation problem. The wind tunnel experPreprint submitted to Fluids and Structures June 14, 2016 iments show that these control systems can reduce considerably the deck's buffet response, whilst simultaneously increasing its critical flutter speed.

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“…It has attracted much attention and has been widely applied to various fields, such as control theory (see [2,7,15,19], and reference therein), management science and economics [9], ecology [34], etc. Recent advances in stochastic LQ control problems have allowed us to expand the study on the Nash games for stochastic systems with state-and control-dependent noise (see [5,6,17,18]).…”

Section: Introductionmentioning

confidence: 99%

Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

Zhu

Zhang

Ning

2014

J. Oper. Res. Soc. China

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This paper investigates Nash games for a class of linear stochastic systems governed by Itô's differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon. First, stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic (LQ) control problems. Second, in order to obtain Nash equilibrium strategies, crosscoupled stochastic Riccati differential (algebraic) equations (CSRDEs and CSRAEs) are derived. Moreover, in order to demonstrate the validity of the obtained results, stochastic H 2 /H ? control with state-and control-dependent noise is discussed as an immediate application. Finally, a numerical example is provided.

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A Nash game approach to mixed H/sub 2//H/sub ∞/ control

Cited by 300 publications

References 22 publications

A Nash Game Approach to Mixed H2/H∞ Control for Input-Affine Nonlinear Systems

A Nash Game Approach to Mixed H2/H∞ Control for Input-Affine Nonlinear Systems

Buffet loading, dynamic response and aerodynamic control of a suspension bridge in a turbulent wind

Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

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