Model Reduction of Neutral Linear and Nonlinear Time-Invariant Time-Delay Systems With Discrete and Distributed Delays

Scarciotti, Giordano; Astolfi, Alessandro

doi:10.1109/tac.2015.2461093

Cited by 78 publications

(44 citation statements)

References 72 publications

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“…Hence, the present paper together with its linear version [32] generalize both the classical time-invariant moments (see e.g. [31], [36]) and the time-varying moments introduced in those papers.…”

Section: Remarkmentioning

confidence: 98%

Model order reduction for stochastic nonlinear systems

Scarciotti

Teel

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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Abstract-The problem of model reduction for stochastic nonlinear systems is addressed with the moment matching method. We characterize the steady-state of nonlinear stochastic systems exploiting a stochastic version of the center manifold theory. Exploiting the steady-state response we formulate the notion of moment for stochastic nonlinear systems and we solve the problem of model reduction proposing a family of nonlinear stochastic reduced order models. Moreover, we formulate also the notion of nonlinear stochastic reduced order model in the mean. The advantage of this last family of stochastic models is that the complexity of their determination is equal to the complexity of the determination of deterministic reduced order models. The relation between the two families of reduced order models is illustrated by means of a simple example based on an electrical circuit.

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Section: Remarkmentioning

confidence: 98%

Model order reduction for stochastic nonlinear systems

Scarciotti

Teel

2017

2017 IEEE 56th Annual Conference on Decision and Control (CDC)

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“…This interpretation of the notion of moment relies upon the center manifold theory and it has the advantage that it can be extended to nonlinear, possibly time-delay, systems Scarciotti and Astolfi [2016]. Theorem 8.…”

Section: Conclusion and Future Research Directionsmentioning

confidence: 99%

A geometric characterisation of persistently exciting signals generated by continuous-time autonomous systems

2016

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The persistence of excitation of signals generated by time-invariant, continuous-time, autonomous linear and nonlinear systems is studied. The notion of persistence of excitation is characterised as a rank condition which is reminiscent of a geometric condition used to study the controllability properties of a control system. The notions and tools introduced are illustrated by means of simple examples and of an application in system identification.

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“…The existing contributions are based on interpolation / moment matching and grounded in either the Krylov framework [30] or the data driven moment Loewner framework [37] (see also [42] for the generalization of moment matching to nonlinear systems). The adopted model reduction approach belongs to the first category (see Section 2 for an elaborate motivation).…”

Section: Introductionmentioning

confidence: 99%

“…These include approaches based on position balancing [20], a feedback interconnection interpretation of the system isolating the delay [47], a generalization of the dominant pole algorithm [40], moment matching [42] and the IRKA algorithm [44], and finally based on minimizing or bounding the H∞ norm of the approximation error [23]. Note that the latter is conceptually similar to fixed-order control design.…”

Section: Introductionmentioning

confidence: 99%

Reduced modelling and fixed‐order control of delay systems applied to a heat exchanger

Michiels

Hilhorst

Pipeleers

et al. 2017

IET Control Theory & Applications

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This paper presents an integrated approach for designing low-order multi-objective controllers for linear time-delay systems, combining recently developed methods for reduction of delay systems and fixed-order control design, respectively. First, as a benchmark problem for process control applications, a model of an experimental heat transfer setup is discussed in detail, which serves to motivate the adopted combination of model reduction and control technique. The former corresponds to a Krylov based reduction procedure, which is generalized to multiple-input-multiple-output systems with state, input and output delays, and allows the adaptive construction of an accurate low-order linear time-invariant approximation of the original linear time-delay system. Concerning the latter, a fixed-order controller is synthesized for the delay-free approximation, exploiting a recently proposed linear matrix inequality based framework for fixed-order controller design, and validated on the original linear time-delay system. In this way, the systematic overall design procedure, which is grounded in convex optimization, complements approaches based on directly optimizing stability and performance measures as a function of the controller parameters, which may lead to highly nonconvex and even non-smooth optimization problems. The successful design of a fixed-order multi-H 2 controller is validated on the benchmark problem, confirming the potential of the adopted approach for realistic industrial applications. IntroductionWe consider continuous-time models for control systems, described in terms of delay differential equations of the form(1) i = 1, . . . , my, where x(t) ∈ R n is the state, u i (t) ∈ R, i = 1, . . . , mu are the inputs, and y i (t) ∈ R, i = 1, . . . , my correspond to the outputs at time t. The quantities τ i , i = 1, . . . , mx, µ i , i = 1, . . . , mu and ν i , i = 1, . . . , my represent time-delays in the system's state, inputs and outputs, respectively, where the largest state delay is denoted by τmax = max i∈{1,...,mx} τ i . The inputs u i and outputs y i are grouped in vectors as follows:where we assume that the number of scalar inputs does not exceed the dimension of the system state, i.e., mu ≤ n. Without loss of generality, the input u and output y are subdivided asto distinguish between exogenous inputs u 1 and control inputs u 2 on the one hand, and regulated outputs y 1 and measured outputs y 2 on the other hand. The targeted class of delay systems described by (1) results from the physics based modeling of complex interconnections of components, where time-delay elements naturally appear in modeling propagation phenomena. The latter are due to the fact that the transfer of material, energy and information is mostly not instantaneous. For this class of systems, the experimental heat-transfer setup described in Section 3 serves as a benchmark problem for the control design. An analogous model has been derived in [25] for a greenhouse. More applications include chemical reactors [26], plate...

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Model Reduction of Neutral Linear and Nonlinear Time-Invariant Time-Delay Systems With Discrete and Distributed Delays

Cited by 78 publications

References 72 publications

Model order reduction for stochastic nonlinear systems

Model order reduction for stochastic nonlinear systems

A geometric characterisation of persistently exciting signals generated by continuous-time autonomous systems

Reduced modelling and fixed‐order control of delay systems applied to a heat exchanger

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