Robust Feedback Control for a Class of Uncertain MIMO Nonlinear Systems

Chen, Jian; Behal, Aman; Dawson, D.M.

doi:10.1109/tac.2008.916658

Cited by 52 publications

(55 citation statements)

References 12 publications

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“…Specifically, by applying a similar formulation to that of Xian et al (2004), which is a nonlinear proportional integral controller fused with integral of the sign of the error feedback, we were able to achieve asymptotic tracking as opposed to the UUB tracking result of Chen et al (2008). From this perspective, we might say that our work extends the results given in Xian et al (2004) to a broader class of nonlinear systems.…”

Section: Introductionmentioning

confidence: 75%

“…Similar to Chen et al (2008) and Costa et al (2003), we assume that D is available for control design. We would like to note that since the leading principal minors of g(X) are non-zero, g −1 (X) exists and the following expression can be obtained by pre-multiplying (3) with g −1 (X):…”

Section: Error System Developmentmentioning

confidence: 99%

“…In this work, under similar restrictions given in Chen et al (2008), we designed a new continuous robust controller for the class of nonlinear systems described by (2). Specifically, by applying a similar formulation to that of Xian et al (2004), which is a nonlinear proportional integral controller fused with integral of the sign of the error feedback, we were able to achieve asymptotic tracking as opposed to the UUB tracking result of Chen et al (2008).…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics

Bıdıklı

Tatlıcıoğlu

Zergeroğlu

et al. 2015

International Journal of Systems Science

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In this work, we present a novel continuous robust controller for a class of multi-input/multi-output nonlinear systems that contains unstructured uncertainties in their drift vectors and input matrices. The proposed controller compensates uncertainties in the system dynamics and achieves asymptotic tracking while requiring only the knowledge of the sign of the leading principal minors of the input gain matrix. A Lyapunov-based argument backed up with an integral inequality is applied to prove the asymptotic stability of the closed-loop system. Simulation results are presented to illustrate the viability of the proposed method.Keywords: nonlinear uncertain dynamical systems; multi-input/multi-output systems; robust control; Lyapunov methods Nomenclature x(t) System states x (i) (t) ith-order time derivative of x(t) H(·), h(·) Functional containing uncertain components G(·), g(·)Real-valued matrix with nonzero leading principal minors τ (t), τ 1 (t), τ 2 (t) Control inputs X(t) Combined state vector S(X) Symmetric positive definite matrix D Diagonal matrix with entries ±1 U(X) Unity upper triangular matriẋ τ (t) Time derivative of control input ϕ (X, x (n) ) Auxiliary function m Positive bounding constant m (X) Positive non-decreasing bounding function x r (t) Reference trajectory e 1 (t) Output tracking error e i (t) Auxiliary error signals for i = 2, . . ., n r(t) Filtered error signal a i, j Positive-valued coefficients generated via a Fibonacci number series I m m × m identity matrix 0 m × 1

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Section: Introductionmentioning

confidence: 75%

Section: Error System Developmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics

Bıdıklı

Tatlıcıoğlu

Zergeroğlu

et al. 2015

International Journal of Systems Science

View full text Add to dashboard Cite

show abstract

“…As a result of applying the above matrix decomposition to the models that are available in the literature, D came out to be an identity matrix. Despite this, the derivations given in this paper will be presented for the general case where it is assumed that D is available for control design (see Chen et al, 2008) for the precedence of this type assumption).…”

Section: Open-loop Operationmentioning

confidence: 99%

Robust dynamic positioning of surface vessels via multiple unidirectional tugboats

2016

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a b s t r a c tIn this paper, the problem of accurate positioning of an unactuated surface vessel by using multiple unidirectional tugboats is investigated. Specifically a robust controller that ensures asymptotic position tracking is designed. The control design procedure is implemented in two steps: Initially by locating opposing tugboats to specific configurations, the overall problem is transformed into a second order system with an uncertain non-symmetric input gain matrix. Then via a matrix decomposition, a novel robust controller methodology is proposed. The stability of the overall system is ensured via rigorous stability analysis where asymptotic position tracking is ensured. Numerical simulation results are presented to demonstrate the efficiency of the proposed controller.

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“…As a result of applying the above matrix decomposition to the models that are available in the literature, D came out to be an identity matrix. Despite this, the derivations given in this paper will be presented for the general case where it is assumed that D is available for control design (see [14] for the presendence of this type assumption).…”

Section: B Open-loop Operationmentioning

confidence: 99%

Robust control design for positioning of an unactuated surface vessel

Bıdıklı

Tatlıcıoğlu

Zergeroğlu

2015

2015 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Abstract-In this paper, a robust controller is designed to achieve accurate positioning of an unactuated surface vessel by using multiple unidirectional tugboats. After initially locating opposing tugboats to specific configurations, the control problem is transformed into a second order system with an uncertain non-symmetric input gain matrix. Upon applying a matrix decomposition, a robust controller is proposed. Detailed stability analysis ensured asymptotic tracking. Numerical simulation results demonstrate the efficiency of the proposed controller. I. INTRODUCTIONThe positioning of large surface vessels like barges, platforms and unactuated ships is considered as the marine example of the swarm robotic applications. Since these types of large vessels can not generate necessary position and orientation control effort due to their low speed operation, they are in need of assistance of multiple tugboats. As a result of this, this objective is realized via a group of tugboats that are strategically positioned along the vessel's hull. Manipulation with multiple tugboats can be seen as a feasible solution for these type of applications. However, the radio communication between all involved tugboats, especially in human manipulated tugboats, affects the control performance dramatically. Although, the communication performance is increased with advanced global positioning systems, control of these type of systems is still a challenging problem because of possible problems that may arise in communication system during manipulation. As a natural result of these, above mentioned marine control problem has attracted attention of the control community.In the last decade, different types of controller designs have been proposed for these type of applications. In [1], orientation tracking control of a unactuated vessel through the utilization of a swarm of vehicles operating in a decentralized fashion was achieved via presented robust control strategy. In order to design this robust controller, the influence of the other swarm vehicle was treated as a force disturbance into the model dynamics. In [2], an exact model knowledge position and orientation tracking controller was proposed for an unactuated surface vessel. In [3], an adaptive position

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Robust Feedback Control for a Class of Uncertain MIMO Nonlinear Systems

Cited by 52 publications

References 12 publications

An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics

An asymptotically stable robust controller formulation for a class of MIMO nonlinear systems with uncertain dynamics

Robust dynamic positioning of surface vessels via multiple unidirectional tugboats

Robust control design for positioning of an unactuated surface vessel

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