Design of strictly positive real systems using constant output feedback

Huang, Chi‐Hsiang; Ioannou, Pétros; Maroulas, John; Safonov, Michael G.

doi:10.1109/9.751352

“…where C s = S 1 C and ⌦ is defined as in Assumption 1E-(b), then (20) holds. PROOF Using C s = S 1 C the inequality (20) can be written (43) satisfies (20).…”

Section: Finding Lmentioning

confidence: 99%

“…Solving (34) for X 22 also requires Q, although this equation places no restriction on how Q > 0 is selected. However, we must choose an appropriate Q which guarantees the feasibility of the LMI in (18) by satisfying (20), as given by the following theorem.…”

Section: Finding Lmentioning

confidence: 99%

“…An X satisfying (23) specifies a P as in (22) that reduces (15) to a feasible LMI in L. This feasible LMI can then be easily solved using any widely available numerical LMI solver. Reference [20] gave the inequality (23) for a square system, suggesting that X be obtained by solving this LMI numerically. However, it was shown in Reference [23] that for a square system, the eigenvalues of N AM are the transmission zeros of the system and the annihilators N and M can be always be selected such that NM = I.…”

Section: Finding Lmentioning

confidence: 99%

See 1 more Smart Citation

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

Wiese

¹

,

Annaswamy

²

,

Muse

³

et al. 2015

AIAA Guidance, Navigation, and Control Conference

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This paper presents a new method of synthesizing an output feedback adaptive controller for a class of uncertain, non-square, multi-input multi-output systems that often occur in hypersonic vehicle models. The main challenge that needs to be addressed is the determination of a corresponding square and strictly positive real transfer function. This paper proposes a new procedure to synthesize two gain matrices that allows the realization of such a transfer function, thereby allowing a globally stable adaptive output feedback law to be generated.The unique features of this output feedback adaptive controller are a baseline controller that uses a Luenberger observer, a closed-loop reference model, manipulations of a bilinear matrix inequality, and the KalmanYakubovich Lemma. Using these features, a simple design procedure is proposed for the adaptive controller, and the corresponding stability property is established. The proposed adaptive controller is compared to the classical multi-input multi-output adaptive controller.A numerical example based on a 6 degree-of-freedom nonlinear, scramjet powered, blended wing-body generic hypersonic vehicle model is presented. The adaptive output feedback controller is applied to result in stable tracking of uncertainties that destabilize the baseline linear output feedback controller.

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“…Assumption 2f can be considered without loss of generality as the case of wide systems p < m holds by duality. The case of square systems has been given in Reference [20] and is discussed in Section IV.…”

Section: Control Problem Formulationmentioning

confidence: 99%

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

Wiese¹,

Annaswamy²,

Muse³

et al. 2015

Journal of Guidance, Control, and Dynamics

View full text Add to dashboard Cite

This paper presents a new method of synthesizing an output feedback adaptive controller for a class of uncertain, non-square, multi-input multi-output systems that often occur in hypersonic vehicle models. The main challenge that needs to be addressed is the determination of a corresponding square and strictly positive real transfer function. This paper proposes a new procedure to synthesize two gain matrices that allows the realization of such a transfer function, thereby allowing a globally stable adaptive output feedback law to be generated.The unique features of this output feedback adaptive controller are a baseline controller that uses a Luenberger observer, a closed-loop reference model, manipulations of a bilinear matrix inequality, and the KalmanYakubovich Lemma. Using these features, a simple design procedure is proposed for the adaptive controller, and the corresponding stability property is established. The proposed adaptive controller is compared to the classical multi-input multi-output adaptive controller.A numerical example based on a 6 degree-of-freedom nonlinear, scramjet powered, blended wing-body generic hypersonic vehicle model is presented. The adaptive output feedback controller is applied to result in stable tracking of uncertainties that destabilize the baseline linear output feedback controller.

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“…7 is positive real and passive. An interconnection containing a passive subsystem (linear or not) with a strictly proper, strictly positive real one, is always closed-loop stable [39][40][41][42]. Furthermore, based on Eqs.…”

Section: Second-order System Modulementioning

confidence: 99%

A Novel Trajectory Generation Method for Robot Control

Ning

¹

,

Kulvičius

²

,

Tamošiūnaitė

³

et al. 2012

J Intell Robot Syst

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This paper presents a novel trajectory generator based on Dynamic Movement Primitives (DMP). The key ideas from the original DMP formalism are extracted, reformulated and extended from a control theoretical viewpoint. This method can generate smooth trajectories, satisfy position-and velocity boundary conditions at start-and endpoint with high precision, and follow accurately geometrical paths as desired. Paths can be complex and processed as a whole, and smooth transitions can be generated automatically. Performance is analyzed for several cases and a comparison with a splinebased trajectory generation method is provided. Results are comparable and, thus, this novel trajectory generating technology appears to be a viable alternative to the existing solutions not

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Design of strictly positive real systems using constant output feedback

Cited by 144 publications

References 19 publications

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

Adaptive Output Feedback Based on Closed-Loop Reference Models for Hypersonic Vehicles

A Novel Trajectory Generation Method for Robot Control

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