Mixed<tex>$H_2/H_infty$</tex>Design for a Decentralized Discrete Variable Structure Control With Application to Mobile Robots

Abstract

In this paper, a decentralized discrete variable structure control via mixed H2/H infinity design was developed. In the beginning, the H2-norm of output error and weighted control input was minimized to obtain a control such that smaller energy consumption with bounded tracking error was assured. In addition, a suitable selection of this weighted function (connected with frequency) could reduce the effect of disturbance on the control input. However, an output disturbance caused by the interactions among subsystems, modeling error, and external load deteriorated system performance or even brought about instability. In this situation, the H infinity-norm of weighted sensitivity between output disturbance and output error was minimized to attenuate the effect of output disturbance. Moreover, an appropriate selection of this weighted function (related to frequency) could reject the corresponding output disturbance. No solution of Diophantine equation was required; the computational advantage was especially dominated for low-order system. For further improving system performance, a switching control for every subsystem was designed. The proposed control (mixed H2/H infinity DDVSC) was a three-step design method. The stability of the overall system was verified by Lyapunov stability criterion. The simulations and experiments of mobile robot were carried out to evaluate the usefulness of the proposed method.

Characteristic model-based H 2/H ∞ robust adaptive control during the re-entry of hypersonic cruise vehicles

“…http://engine.scichina.com/doi/10.1007/s11432-014-5179-4 which further yields inequality (31). The H 2 performance is bounded by (32) with the upper bound of γ 2 being guaranteed by (33), which finishes the proof.…”

“…The mixed H 2 /H ∞ robust control problem has been discussed in numerous literatures concerning either the topic of cost-guaranteed filtering problem with state-error variance constraints [31], or the topic of robust controller design [32] even in a decentralized scheme [33]. When dealing with timevarying systems, gain-scheduled H 2 /H ∞ control has been proved efficient to engineering problems [34].…”

Internet traffic control with the H<inf>2</inf>/H<inf>&#x221E;</inf> controller

“…To solve the H 2 /H problem, there are different popular convex approaches such as the Riccati approach (e.g., [23]) which is relatively complex and the LMI (Linear Matrix Inequality) approach, (e.g., [24]) which reduces the complexity order of the problem. The H 2 /H controllers have been mostly applied in mechanical and mechatronic applications so far, e.g., for mobile robot tracking [25].…”

Modeling and μ -synthesis Based Robust Trajectory Tracking Control of a Wheeled Mobile Robot

“…These algorithms are mainly to deal with the issue of unknown parameters in the dynamics of WMR without clearly addressing the effect of external disturbances and other modeling uncertainties. Hwang used H 2 /H ∞ control method to attenuate the effect of output disturbances (Hwang and Han (2005); Hwang and Chang (2007)), but without addressing the effect of other model uncertainties. Solea and Park applied sliding mode control methods to the control of WMR systems with matched model uncertainties and external disturbances only (Solea et al (2010); Park et al (2009)).…”