Exponential stability region estimates for the State-Dependent Riccati Equation controllers

Chang, Insu; Chung, Soon‐Jo

doi:10.1109/cdc.2009.5400575

Cited by 17 publications

(23 citation statements)

References 23 publications

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“…Sontag [11] has shown that if a CLF is known for a nonlinear system that is affine in the control, then the CLF and the system equations can be used to find controllers that make the system asymptotically stable. Chang and Chung (2009) have recognized that SDRE stability usually only exists in a local region and at its best will be the ROA which is the expanded local region of stability. They have come up with a new strategy called contraction analysis to estimate the exponential stability region for the SDRE controlled system.…”

Section: Control Lyapunov Function (Clf) Based Approachmentioning

confidence: 99%

SDRE Control Stability Criteria and Convergence Issues: Where Are We Today Addressing Practitioners' Concerns?

Lam

Xin

Cloutier

2012

Infotech@Aerospace 2012

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This paper has three purposes: 1) to provide a survey on the State-Dependent Riccati Equation (SDRE) stability analysis methodologies developed to date; these stability analysis techniques produce either a guarantee or a high degree of confidence that the closed-loop system is asymptotically stable over a domain of interest, 2) to present an argument that practical rules of thumb can be just as important as theoretical stability proofs with regard to real world implementation, and 3) to justify support of the above argument using some forms of actual implementation. The paper neither favors any particular stability analysis technique nor introduces a new stability analysis framework. Rather it presents a view of stability reasoned judgment and practical justification for actual implementation. The reasoned judgment and justification are mainly based on the space access vehicle control and the satellite attitude control examples whose performance becomes unstable in the presence of high gain magnitude conditions. The fundamental argument of this new view (i.e., reasoned judgment and justification) is that for even linear and static gain controllers such as the Linear Quadratic Regulator (LQR), stability of the system depends on the operational domain under practical implementation with nonlinear limiters in the loop. Therefore, for a variable gain or nonlinear controller like the SDRE method, the task of determining a region of stability either practically or theoretically is much more difficult as compared to a linear LQRbased approach. The SDRE designs of a space access vehicle control, a helicopter flight control, and a satellite attitude control are presented with a set of practical rules defined and applied to it as a practical design benchmark problem on how to pass the SDRE stability concern gate. The paper concludes with the recommendation of some practical design rules of thumb for practitioners

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Section: Control Lyapunov Function (Clf) Based Approachmentioning

confidence: 99%

SDRE Control Stability Criteria and Convergence Issues: Where Are We Today Addressing Practitioners' Concerns?

Lam

Xin

Cloutier

2012

Infotech@Aerospace 2012

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“…28 Chang and Chung proposed a strategy based on contraction analysis to estimate the exponential stability region for SDRE controlled systems. 29 Furthermore, there are some review papers addressing the SDRE method. [30][31][32][33] For aerospace applications, most of spacecraft require position and attitude maneuver to complete space missions, such as rendezvousing, docking, debris removal, etc.…”

Section: Introductionmentioning

confidence: 99%

A Suboptimal Tracking Control Approach Based on the State-Dependent Riccati Equation Method

Kuo

Wu²

2016

j comput theor nanosci

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This paper presents a tracking control based on the SDRE method applied to a rigid spacecraft dynamics. In literature, the SDRE tracking control is performed by applying an integral servomechanism, which will enhance the complexity of systems due to the increasing number of state variables. The presented approach is extended from the linear quadratic tracking problems to the nonlinear quadratic-like tracking problems. By solving the algebraic Riccati equation and an auxiliary equation, the presented approach provides a suboptimal solution. A numerical example demonstrates the attitude and position tracking control of a rigid spacecraft, and the results show that the tracking errors approach to zeros as time increases.

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“…Note that computing the state transition matrix for different values of t 0 corresponds to perturbing the system at different times along the perching trajectory. The figure shows that the longitudinal state transition matrix comprises of bounded elements for Φ(t, 0), Φ(t, 10) and Φ(t, 17) but becomes unbounded in the case of Φ(t, 25). Note that since this system possesses time-varying dynamics, therefore the behavior of the system in response to perturbations hitting the system at different times, can be different.…”

Section: Iiib Aircraft Dynamicsmentioning

confidence: 99%

“…This linearization is distinct from the state-dependent coefficient factorization wherein the nonlinear equations are represented as linear structures with state-dependent coefficients (See Chang and Chung 25 for an example). This thus forms the motivation for having the controller structure shown in Figure 5 -a variable (symmetric) dihedral trajectory is applied that keeps the aircraft reasonably close to (but not exactly on) the reference perching trajectory; the elevator and the twist are controlled in the feedback paths to keep the aircraft more closer to the perching trajectory as well as reject wind disturbances that may hit the aircraft.…”

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confidence: 99%

Control Law Design for Perching an Agile MAV with Articulated Wings

Chakravarthy

Paranjape

Chung

2010

AIAA Atmospheric Flight Mechanics Conference

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This paper explores the use of variable wing dihedral and variable wing twist (in conjunction with a conventional horizontal elevator) to control an aircraft performing a perching maneuver. A choice of controller architecture wherein the dihedral is employed in the forward path and the elevator and twist are employed in the feedback path, is considered. The aircraft is modeled as a multivariable linear time-varying system. A specific perching trajectory is considered; and the open-loop aircraft is longitudinally unstable for a segment of this perching trajectory and lateral-directionally unstable for the entire perching trajectory. A multivariable time-varying controller is designed to efficiently stabilize the aircraft as well as reject longitudinal-lateral-directional wind disturbances, while closely tracking the reference perching trajectory.

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Exponential stability region estimates for the State-Dependent Riccati Equation controllers

Cited by 17 publications

References 23 publications

SDRE Control Stability Criteria and Convergence Issues: Where Are We Today Addressing Practitioners' Concerns?

SDRE Control Stability Criteria and Convergence Issues: Where Are We Today Addressing Practitioners' Concerns?

A Suboptimal Tracking Control Approach Based on the State-Dependent Riccati Equation Method

Control Law Design for Perching an Agile MAV with Articulated Wings

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