State-space solutions to standard H2 and H∞ control problems

Doyle, John C.; Glover, K.; Khargonekar, Pramod P.; Francis, Bruce A.

doi:10.23919/acc.1988.4789992

Cited by 824 publications

(799 citation statements)

References 6 publications

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“…Case 1 Q = −I , S = 0, R = γ 2 I , the strict (Q, S, R) dissipativity reduces to H ∞ design (Doyle et al, 1989). The overall control design satisfies mixed NLQR-H ∞ performance.…”

Section: System Model and General Performance Criteria Analysismentioning

confidence: 99%

“…Dissipativity performance includes H ∞ performance, passivity, positive realness and sector-bounded constraint as special cases. Research addressing the problems of H ∞ and positive real control systems can be found in Zhou and Khargonekar (1988) Doyle, Glover, Khargonekar, and Francis (1989), Haddad and Bernstein (1991), Sun, Khargonekar, and Shim (1994), Safonov, Jonckheere, Verma, and Limebeer (1987) and Shim (1996). Control of uncertain linear systems with L 2 -bounded structured uncertainty satisfying H ∞ and passivity criteria has been tackled in Khargonekar, Petersen, and Zhou (1990) and Petersen (1987).…”

Section: Introductionmentioning

confidence: 99%

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Robust and resilient state-dependent control of continuous-time nonlinear systems with general performance criteria

Wang

Yaz

Long

2014

Systems Science & Control Engineering

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A novel state-dependent control approach for continuous-time nonlinear systems with general performance criteria is presented in this paper. This controller is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state-dependent linear matrix inequality at each time, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H ∞ and positive real control. The efficacy of the proposed technique is demonstrated by numerical simulations of the nonlinear control of the inverted pendulum on a cart system.

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“…Case 1 Q = −I , S = 0, R = γ 2 I , the strict (Q, S, R) dissipativity reduces to H ∞ design (Doyle et al, 1989). The overall control design satisfies mixed NLQR-H ∞ performance.…”

Section: System Model and General Performance Criteria Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust and resilient state-dependent control of continuous-time nonlinear systems with general performance criteria

Wang

Yaz

Long

2014

Systems Science & Control Engineering

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“…Pioneering works, despite success stories for applications, suffered from a lack of proofs of key mathematical properties useful for analyzing closed-loop systems: stability, robustness and performances including pole placement, H 2 or H ∞ attenuation; such properties were clearly established in the 80s for linear systems (see, for instance, the celebrated paper [14]). …”

Section: Decades 1985-2005: the Model-based Approachmentioning

confidence: 99%

Fuzzy control turns 50: 10 years later

Guerra

Sala

Tanaka

2015

Fuzzy Sets and Systems

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In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.

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“…This seems to be a result from the asymptotic approach to Butterworth configuration in LQG or H2 control scheme [1). When the control is heavily constrained, the corresponding closed-loop pole configuration is generally far from the Butterworth configuration and it causes less damping in oscillatory systems.…”

Section: Introductionmentioning

confidence: 99%

Derivative State Constrained Optimal H2 Control for Oscillatory Systems and its Application

et al. 2000

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The optimal H2 control of oscillatory systems via the constraints of the derivatives of state variables is discussed and applied to a physical system in this paper. It is shown that the derivative state constrained optimal H2 control can be reduced into the standard optimal H2 control problem with modified controlled output equations. The solution to the modified standard problem has salient features for controlling oscillatory systems that have been a tough subject in state space as well as in classical frequency domain controls.The results obtained in the paper suggest the directions how to select the constraining weights in the standard state space control designs of oscillatory systems.The application of this approach to the control of a two-inertia resonance system is shown to demonstrate the proposed schemes.

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State-space solutions to standard H₂ and H_∞ control problems

Cited by 824 publications

References 6 publications

Robust and resilient state-dependent control of continuous-time nonlinear systems with general performance criteria

Robust and resilient state-dependent control of continuous-time nonlinear systems with general performance criteria

Fuzzy control turns 50: 10 years later

Derivative State Constrained Optimal <i>H</i><sub>2</sub> Control for Oscillatory Systems and its Application

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