A Nonlinear Hybrid Life Support System: Dynamic Modeling, Control Design, and Safety Verification

Glavaski, S.; Subramanian, Dharmashankar; Ariyur, Kartik B.; Ghosh, Rajib; Lamba, Nitin; Papachristodoulou, Antonis

doi:10.1109/tcst.2007.899649

Cited by 14 publications

(9 citation statements)

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“…At the present time, the largest system that we could analyze was a polynomial hybrid system with 10 continuous states and 6 locations, for which the safety properties were assessed [34]. It is important to note that the computation of Lyapunov functions is polynomial-time for a fixed order system, however limitations are imposed because of the size of the associated semidefinite programmes.…”

Section: Discussionmentioning

confidence: 99%

Robust Stability Analysis of Nonlinear Hybrid Systems

Papachristodoulou

Prajna

2009

IEEE Trans. Automat. Contr.

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as (19), and compute the standard deviation of the values of the corresponding perturbed polynomial at the point ( 3 1 ; 3 2 ). We perform the test at ( (0:6; 0:6) and compare the results of both approaches in Table IV.There are several reasons showing that our approach is promising. First, we can see from Tables I and III that the number of variables in the conventional approach grows rapidly when the degrees of the monomial bases increase, while the number of variables in our approach grows linearly with respect to the number of subregions. Moreover, our approach attains the exact optimal value with less computational cost than the conventional SOS approach. Secondly, Table IV shows that the standard deviations of the perturbed polynomial from the proposed approach are less than that from the conventional approach, for all selected points. This implies that the optimal value of the proposed approach is less numerically sensitive than that of the conventional approach. Strictly speaking, the asymptotic exactness of our scheme is not guaranteed in the case of lowest-degree monomial bases. However, it is achieved apparently in this example. We expect that the asymptotic exactness can also be proved with the monomial bases of lowest degrees, and this is the direction of our further research. REFERENCES[1] A. Ben-Tal and A. Nemirovski, "Robust convex optimization," Math.Oper. Res., vol. 23, no. 4, pp. 769-805, 1998 Robust Stability Analysis of Nonlinear Hybrid Systems Antonis Papachristodoulou and Stephen PrajnaAbstract-We present a methodology for robust stability analysis of nonlinear hybrid systems, through the algorithmic construction of polynomial and piecewise polynomial Lyapunov-like functions using convex optimization and in particular the sum of squares decomposition of multivariate polynomials. Several improvements compared to previous approaches are discussed, such as treating in a unified way polynomial switching surfaces and robust stability analysis for nonlinear hybrid systems.Index Terms-Hybrid systems, linear matrix inequality, sum of squares, switched systems.

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Section: Discussionmentioning

confidence: 99%

Robust Stability Analysis of Nonlinear Hybrid Systems

Papachristodoulou

Prajna

2009

IEEE Trans. Automat. Contr.

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“…In order to demonstrate the practical relevance of the NARX-M-for-D (3), consider a nonlinear oscillator system as shown in Fig.1, where 0 3 c are the oscillator parameters to be designed to achieve a desired vibration isolation performance.   ut and   yt are the input and output of the system, respectively.…”

Section: Fig1 a Nonlinear Oscillatormentioning

confidence: 99%

“…where S R is a set of S -dimensional nonnegative integer vectors which contains the exponents of (4), the parameters of interest for the system design are 3 k and 3 c , and the OFRF can be obtained as:…”

Section: B the Ofrf Of The Narx-m-for-dmentioning

confidence: 99%

“…In (45),   iso ft is the damping force produced by the isolator in the system, 3  is the parameter of the isolator to be used for the system design, and According to the basic physical principle, the system in Fig.5 can be described as:…”

Section: B Case Studymentioning

confidence: 99%

“…N engineering practice, the design of a system is often concerned with the determination of the system parameters that can be used to achieve desired system responses under considered loadings or input excitations [1][2][3]. The frequency domain design of linear systems [4][5][6] based on the traditional concept of Frequency Response Function (FRF) has been widely applied in engineering system designs such as, e.g., the design of the dynamic properties of vibration absorbers [7], vehicle suspensions [8], and aero engine blades [9].…”

Section: Introductionmentioning

confidence: 99%

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