Publications
80 results found
Scarciotti G, Astolfi A, Jiang Z-P, 2016, Constrained optimal reduced-order models from input/output data, IEEE 55th Annual Conference on Decision and Control (CDC), Publisher: IEEE
Model reduction by moment matching does notpreserve, in a systematic way, the transient response of thesystem to be reduced, thus limiting the use of this modelreduction technique in control problems. With the final goalof designing reduced-order models which can effectively beused (not just for analysis but also) for control purposes, wedetermine, using a data-driven approach, an estimate of themoments and of the transient response of an unknown system.We compute the unique, up to a change of coordinates, reducedordermodel which possesses the estimated transient and,simultaneously, achieves moment matching at the prescribedinterpolation points. The error between the output of the systemand the output of the reduced-order model is minimized andwe show that the resulting system is a constrained optimal (ina sense to be specified) reduced-order model. The results of thepaper are illustrated by means of a simple numerical example.
Scarciotti G, Astolfi A, 2016, Model reduction for hybrid systems with state-dependent jumps, 10th IFAC Symposium on Nonlinear Control Systems, Publisher: Elsevier, Pages: 850-855, ISSN: 1474-6670
In this paper we present a model reduction technique based on moment matchingfor a class of hybrid systems with state-dependent jumps. The problem of characterizing thesteady-state for this class of systems is studied and a result which allows to described the steadystateresponse of hybrid systems through the use of a hybrid mapping is given. Then a familyof hybrid reduced order models which achieve moment matching and are easily parameterizableis provided. The special case of periodic input signals is analyzed and conditions for applyingthe technique are given for this class. A numerical simulation illustrates the results.
Padoan A, Scarciotti G, Astolfi A, 2016, A geometric characterisation of persistently exciting signals generated byautonomous systems, 10th IFAC Symposium on Nonlinear Control Systems, Publisher: Elsevier, Pages: 826-831, ISSN: 1474-6670
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 ischaracterised as a rank condition which is reminiscent of a geometric condition used to study thecontrollability properties of a control system. The notions and tools introduced are illustratedby means of simple examples and of an application in system identification.
Scarciotti G, Astolfi A, 2016, Moment-based discontinuous phasor transform and its application tothe steady-state analysis of inverters and wireless power transfersystems, IEEE Transactions on Power Electronics, Vol: 31, Pages: 8448-8460, ISSN: 0885-8993
Power electronic devices are inherently discontinuous systems. Square waves, produced by interconnected transistors, are commonly used to control inverters. This paper proposes a novel phasor transform, based on the theory of moments, which allows to analyze the steady-state behavior of discontinuous power electronic devices in closed-form, i.e. without approximations. In the first part of the paper it is shown that the phasors of an electric circuit are the moments on the imaginary axis of the linear system describing the circuit. Exploiting this observation, in the second part of the paper, we focus on the analysis of circuits powered by discontinuous sources. The new “discontinuous phasor transform” is defined and the v-i characteristics for inductors, capacitors and resistors are described in terms of this new phasor transform. Since the new quantities maintain their physical meaning, the instantaneous power and average power can be computed in the phasor domain. The analytic potential of the new tool is illustrated studying the steady-state response of power inverters and of wireless power transfer systems with non-ideal switches.
Scarciotti G, Astolfi A, 2016, A note on the electrical equivalent of the moment theory, 2016 American Control Conference (ACC), Publisher: IEEE, Pages: 7462-7465
In this short note the relation between the moments of a linear system and the phasors of an electric circuit is discussed. We show that the phasors are a special case of moments and we prove that the components of the solution of a Sylvester equation are the phasors of the currents of the system. We point out several directions in which the phasor theory can be extended using recent generalizations of the moment theory, which can benefit the analysis of circuits and power electronics.
Scarciotti G, 2016, Low computational complexity model reduction of power systems with preservation of physical characteristics, IEEE Transactions on Power Systems, Vol: 32, Pages: 743-752, ISSN: 1558-0679
A data-driven algorithm recently proposed to solvethe problem of model reduction by moment matching is extendedto multi-input, multi-output systems. The algorithm isexploited for the model reduction of large-scale interconnectedpower systems and it offers, simultaneously, a low computationalcomplexity approximation of the moments and the possibilityto easily enforce constraints on the reduced order model. Thisadvantage is used to preserve selected slow and poorly dampedmodes. The preservation of these modes has been shown to beimportant from a physical point of view and in obtaining anoverall good approximation. The problem of the choice of the socalledtangential directions is also analyzed. The algorithm andthe resulting reduced order model are validated with the studyof the dynamic response of the NETS-NYPS benchmark system(68-Bus, 16-Machine, 5-Area) to multiple fault scenarios.
Scarciotti G, Astolfi A, 2016, Moments at "discontinuous signals" with applications: model reduction for hybrid systems and phasor transform for switching circuits, 22nd International Symposium on Mathematical Theory of Networks and Systems
We provide an overview of the theory and applicationsof the notion of moment at “discontinuous interpolationsignals”, i.e. the moments of a system for input signals thatdo not satisfy a differential equation. After introducing thetheoretical framework, which makes use of an integral matrixequation in place of a Sylvester equation, we discuss someapplications: the model reduction problem for linear systems atdiscontinuous signals, the model reduction problem for hybridsystems and the discontinuous phasor transform for the analysisof circuits powered by discontinuous sources.
Scarciotti G, Astolfi A, 2015, Model reduction for nonlinear systems and nonlinear time-delay systems from input/output data, 2015 54th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 7298-7303, ISSN: 0743-1546
Scarciotti G, 2015, Model reduction by moment matching for linear singular systems, 2015 54th IEEE Conference on Decision and Control (CDC), Pages: 7310-7315, ISSN: 0743-1546
Scarciotti G, Astolfi A, 2015, Model reduction for linear systems and linear time-delay systems from input/output data, 2015 European Control Conference (ECC), Publisher: IEEE, Pages: 334-339
An algorithm for the estimation of the moments of linear systems and linear time-delay systems from input/output data is proposed. The estimate, which converges to the moments of the system, is exploited to construct a family of reduced order models. These models asymptotically match the moments of the unknown system to be reduced. The computational complexity of the algorithm is analyzed and the use of the algorithm is illustrated by a benchmark example.
Scarciotti G, 2015, Model reduction of power systems with preservation of slow and poorly damped modes, IEEE PES General Meeting 2015, Publisher: IEEE, Pages: 1-5, ISSN: 1944-9925
In this paper a recently proposed variation of the Krylov subspace method for model reduction is applied to power systems. The technique allows to easily enforce constraints on the reduced order model. Herein this is used to preserve the slow and poorly damped modes of the systems in the reduced order model. We analyze the role that these modes have in obtaining a good approximation and we show that the order of the reduced model can be decreased if the 'right' modes are preserved. We validate the theory on the 68-Bus, 16-Machine, 5-Area benchmark system (NETS-NYPS).
Scarciotti G, Astolfi A, 2015, Model reduction by matching the steady-state response of explicit signal generators, IEEE Transactions on Automatic Control, Vol: 99, ISSN: 1558-2523
Scarciotti G, Astolfi A, 2015, Model reduction of neutral linear and nonlinear time-invariant time-delay systems with discrete and distributed delays, IEEE Transactions on Automatic Control, Vol: 99, ISSN: 1558-2523
The problem of model reduction by moment matching for linear and nonlinear differential time-delay systems is studied. The class of models considered includes neutral differential time-delay systems with discrete-delays and distributeddelays. The description of moment is revisited by means of a Sylvester-like equation for linear time-delay systems and by means of the center manifold theory for nonlinear time-delay systems. In addition the moments at infinity are characterized for both linear and nonlinear time-delay systems. Parameterized families of models achieving moment matching are given. The parameters can be exploited to derive delay-free reduced order models or time-delay reduced order models with additional properties, e.g. interpolation at an arbitrary large number of points. Finally, the problem of obtaining a reduced order model of an unstable system is discussed and solved.
Scarciotti G, Praly L, Astolfi A, 2015, Invariance-like theorems and “lim inf” convergence properties, IEEE Transactions on Automatic Control, Vol: 61, Pages: 648-661, ISSN: 1558-2523
Several theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish “lim inf” convergence results are presented in a unified framework. These properties are useful to “describe” the oscillatory behavior of the solutions of dynamical systems. The theorems resemble “lim inf” Matrosov and Small-gain theorems and are based on a “lim inf” Barbalat's Lemma. Additional technical assumptions to have “lim” convergence are given: the “lim inf”/“lim” relation is discussed in-depth and the role of some of the assumptions is illustrated by means of examples.
Scarciotti G, Astolfi A, 2015, Characterization of the moments of a linear system driven by explicit signal generators, American Control Conference, Publisher: IEEE, Pages: 589-594, ISSN: 0743-1619
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- Citations: 18
Scarciotti G, Astolfi A, 2014, Model reduction by moment matching for nonlinear time-delay systems, Pages: 3642-3647
Scarciotti G, Astolfi A, 2014, Approximate finite-horizon optimal control for input-affine nonlinear systems with input constraints, Journal of Control and Decision, Vol: 1, Pages: 149-165, ISSN: 2330-7706
The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval (possibly unknown) minimising a cost functional, while satisfying hard constraints on the input. In this framework, the minimum-time optimal control problem and some related problems are of interest for both theory and applications. For linear systems, the solution of the problem often relies upon the use of bang-bang control signals. For nonlinear systems, the “shape” of the optimal input is in general not known. The control input can be found solving a Hamilton–Jacobi–Bellman (HJB) partial differential equation (PDE): it typically consists of a combination of bang-bang controls and singular arcs. In this paper, a methodology to approximate the solution of the HJB PDE is proposed. This approximation yields a dynamic state feedback law. The theory is illustrated by means of two examples: the minimum-time optimal control problem for an industrial wastewater treatment plant and the Goddard problem, i.e. a maximum-range optimal control problem.
Scarciotti G, Astollfi A, 2014, Model Reduction by Moment Matching for Linear Time-Delay Systems, 19th World Congress of the International-Federation-of-Automatic-Control (IFAC), Publisher: ELSEVIER SCIENCE BV, Pages: 9462-9467, ISSN: 2405-8963
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- Citations: 1
Scarciotti G, Astolfi A, 2013, Approximate finite-horizon optimal control for input-affine nonlinear systems with input constraints, Pages: 199-204, ISSN: 1474-6670
The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval (possibly unknown) minimizing a cost functional, while satisfying hard constraints on the input. For linear systems the solution of the problem often relies upon the use of bang-bang control signals. For nonlinear systems the "shape" of the optimal input is in general not known. The control input can be found solving an Hamilton-Jacobi-Bellman (HJB) partial differential equation (pde): it typically consists of a combination of bang-bang arcs and singular arcs. In the paper a methodology to approximate the solution of the HJB pde arising in the finite-horizon optimal control problem with input constraints is proposed. This approximation yields a dynamic state feedback law. The theory is illustrated by means of an example: the minimum time optimal control problem for an industrial wastewater treatment plant. © IFAC.
Scarciotti G, Praly L, Astolfi A, 2013, A small-gain-like theorem for large-scale systems, 52nd IEEE Annual Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 6593-6596, ISSN: 0743-1546
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- Citations: 1
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