Publications
685 results found
He W, Soriano-Rangel CA, Ortega R, et al., 2018, DC-DC Buck-Boost Converters With Unknown CPL: An Adaptive PBC, American Control Conference, Publisher: IEEE, Pages: 6749-6754, ISSN: 0743-1619
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- Citations: 4
Sassano M, Astolfi A, 2017, Is any SISO controllable and observable system dynamically passifiable and/or L-2-stabilizable?, IEEE 56th Annual Conference on Decision and Control (CDC), Publisher: IEEE, ISSN: 0743-1546
Padoan A, Scarciotti G, Astolfi A, 2017, A geometric characterization of the persistence of excitation condition for the solutions of autonomous systems, IEEE Transactions on Automatic Control, Vol: 62, Pages: 5666-5677, ISSN: 0018-9286
The persistence of excitation of signals generated by time-invariant, autonomous, linear, and nonlinear systems is studied using a geometric approach. A rank condition is shown to be equivalent, under certain assumptions, to the persistence of excitation of the solutions of the class of systems considered, both in the discrete-time and in the continuous-time settings. The rank condition is geometric in nature and can be checked a priori, i.e. without knowing explicitly the solutions of the system, for almost periodic systems. The significance of the ideas and tools presented is illustrated by means of simple examples. Applications to model reduction from input-output data and stability analysis of skew-symmetric systems are also discussed.
Di Franco P, Scarciotti G, Astolfi A, 2017, A note on the stability of nonlinear differential-algebraic systems, 20th IFAC World Congress, Publisher: Elsevier, Pages: 7421-7426, ISSN: 1474-6670
The problem of the stability analysis for nonlinear differential-algebraic systems is addressed using tools from classical control theory Exploiting Lyapunov Direct Method we provide linear matrix inequalities to establish stability properties of this class of systems. In addition, interpreting the differential-algebraic system as the feedback interconnection of a dynamical system and an algebraic system, a sufficient stability condition has been derived using the small-gain theorem. The proposed techniques are illustrated by means of simple examples.
Jiang J, Evangelou SA, Torquil MR, et al., 2017, Robust H-infinity control for autonomous scooters, IFAC papers online, Vol: 50, Pages: 297-302, ISSN: 1474-6670
This paper studies the trajectory tracking problem for the nonlinear model of a scooter and presents a robust H∞ controller based on measurements of the tracking errors, the roll angle, the yaw angle and the steering angle. The study first introduces the full nonlinear model developed in Autosim which has 12 degrees of freedom. This is far more complex than a simple bicycle model and provides a good description of the scooter. Then a robust H∞ controller based on the linearization of the nonlinear model is designed. Finally, the effectiveness of the controller is verified by means of two case studies.
Scarciotti G, Astolfi A, 2017, Nonlinear Model Reduction by Moment Matching, Foundations and Trends in Systems and Control, Vol: 4, Pages: 224-409, ISSN: 2325-6818
Mathematical models are at the core of modern science and technology. An accurate description of behaviors, systems and processes often requires the use of complex models which are difficult to analyze and control. To facilitate analysis of and design for complex systems, model reduction theory and tools allow determining “simpler” models which preserve some of the features of the underlying complex description. A large variety of techniques, which can be distinguished depending on the features which are preserved in the reduction process, has been proposed to achieve this goal. One such a method is the moment matching approach.This monograph focuses on the problem of model reduction by moment matching for nonlinear systems. The central idea of the method is the preservation, for a prescribed class of inputs and under some technical assumptions, of the steady-state output response of the system to be reduced. We present the moment matching approach from this vantage point, covering the problems of model reduction for nonlinear systems, nonlinear time-delay systems, data-driven model reduction for nonlinear systems and model reduction for “discontinuous” input signals. Throughout the monograph linear systems, with their simple structure and strong properties, are used as a paradigm to facilitate understanding of the theory and provide foundation of the terminology and notation. The text is enriched by several numerical examples, physically motivated examples and with connections to well-established notions and tools, such as the phasor transform.
Mylvaganam T, Sassano M, Astolfi A, 2017, A differential game approach to multi-agent collision avoidance, IEEE Transactions on Automatic Control, Vol: 62, Pages: 4229-4235, ISSN: 0018-9286
A multi-agent system consisting of N agents is considered. The problem of steering each agent from its initial position to a desired goal while avoiding collisions with obstacles and other agents is studied. This problem, referred to as the multi-agent collision avoidance problem, is formulated as a differential game. Dynamic feedback strategies that approximate the feedback Nash equilibrium solutions of the differential game are constructed and it is shown that, provided certain assumptions are satisfied, these guarantee that the agents reach their targets while avoiding collisions.
Padoan A, Astolfi A, 2017, Eigenvalues and Poles of a Nonlinear System: a Geometric Approach, 56th IEEE Conference on Decision and Control, Publisher: IEEE
Scarciotti G, Teel AR, Astolfi A, 2017, Model reduction for linear differential inclusions: robustness and time-variance, 2017 American Control Conference, Publisher: IEEE, ISSN: 2378-5861
This paper deals with the problem of modelreduction by moment matching for linear differential inclusions.The problem is formally formulated and the notions of moment-set, perturbed moment trajectory, approximate reduced ordermodel and robust reduced order model are introduced. Twosets of results are presented. The first part of the paper dealswith robustness of the reduced order models with respect toinput perturbations. Exploiting this result an enhanced modelreduction scheme for linear differential equations is presented.In the second part of the paper we focus on the problem ofmodel reduction by moment matching for time-varying systemsdriven by time-varying signal generators. Finally, these two setsof results are used to solve the problem of model reductionfor linear differential inclusions. The results are illustrated bymeans of numerical examples.
Padoan A, Astolfi A, 2017, Moments of random variables: a system-theoretic interpretation, 2017 American Control Conference (ACC), Publisher: IEEE
Moments of continuous random variables with aprobability density function which can be represented as theimpulse response of a linear time-invariant system are studied.Under some assumptions, the moments of the random variableare characterised in terms of the solution of a Sylvester equationand of the steady-state output response of an interconnectedsystem. This allows to interpret well-known notions and resultsof probability theory and statistics in the language of systemtheory, including the notion of moment generating function, thesum of independent random variables and the notion of mixturedistribution.
Padoan A, Astolfi A, 2017, Model reduction by moment matching at isolated singularities for linear systems: a complex analytic approach, 20th IFAC 2017 World Congress, Publisher: Elsevier
The model reduction problem by moment matching for continuous-time, single-input, single-output, linear, time-invariant systems is studied at isolated singularities (in particular, at poles). The notion of moment at a pole of the transfer function is defined. Exploiting this notion a one-to-one correspondence between moments at a pole of the transfer function and the “limit solution” of a family of Sylvester equations is established. Finally, a family of reduced order models is defined. A simple example illustrates the theory.
Mylvaganam T, Astolfi A, 2017, Zero finding via feedback stabilisation, IFAC 2017 World Congress, Publisher: Elsevier, Pages: 8133-8138, ISSN: 1474-6670
Two iterative algorithms for solving systems of linear and nonlinear equations are proposed. For linear problems the algorithm is based on a control theoretic approach and it is guaranteed to yield a converging sequence for any initial condition provided a solution exists. Systems of nonlinear equations are then considered and a generalised algorithm, again taking inspiration from control theory, is proposed. Local convergence is guaranteed in the nonlinear setting. Both the linear and the nonlinear algorithms are demonstrated on a series of numerical examples.
Scarciotti G, Astolfi A, 2017, Data-driven model reduction by moment matching for linear and nonlinear systems, Automatica, Vol: 79, Pages: 340-351, ISSN: 0005-1098
Theory and methods to obtain reduced order models by moment matching from input/output data are presented. Algorithms for the estimation of the moments of linear and nonlinear systems are proposed. The estimates are exploited to construct families of reduced order models. These models asymptotically match the moments of the unknown system to be reduced. Conditions to enforce additional properties, e.g. matching with prescribed eigenvalues, upon the reduced order model are provided and discussed. The computational complexity of the algorithms is analyzed and their use is illustrated by two examples: we compute converging reduced order models for a linear system describing the model of a building and we provide, exploiting an approximation of the moment, a nonlinear planar reduced order model for a nonlinear DC-to-DC converter.
Jiang J, Astolfi A, 2017, Shared-control for a rear-wheel drive car: dynamic environments and disturbance rejection, IEEE Transactions on Human-Machine Systems, Vol: 47, Pages: 723-734, ISSN: 2168-2291
This paper studies the shared-control problem for the kinematic model of a group of rear-wheel drive cars in a (possibly) dynamic (i.e., time-varying) environment. The design of the shared-controller is based on measurements of distances to obstacles, angle differences, and the human input. The shared-controller is used to guarantee the safety of the car when the driver behaves “dangerously.” Formal properties of the closed-loop system with the shared-controller are presented through a Lyapunov-like analysis. In addition, we consider uncertainties in the dynamics and prove that the shared-controller is able to help the driver drive the car safely even in the presence of disturbances. Finally, the effectiveness of the controller is verified by two case studies: traffic at a junction and at a roundabout.
Scarciotti G, Astolfi A, 2017, A Review on Model Reduction by Moment Matching for Nonlinear Systems, Feedback Stabilization of Controlled Dynamical Systems, Editors: Petit, Publisher: Springer International Publishing, Pages: 29-52
Jiang J, Astolfi A, 2017, Robust shared-control for rear-wheel drive cars, Trends in Control and Decision-Making for Human-Robot Collaboration Systems, Pages: 15-40, ISBN: 9783319405322
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- Citations: 2
Padoan A, Scarciotti G, Astolfi A, 2016, A geometric characterisation of the persistence of excitation condition for sequences generated by discrete-time autonomous systems, IEEE 55th Annual Conference on Decision and Control (CDC), Publisher: IEEE
The persistence of excitation condition for sequencesgenerated by time-invariant, discrete-time, autonomouslinear and nonlinear systems is studied. A rank conditionis shown to be equivalent to the persistence of excitationof sequences generated by the class of systems considered,consistently with the results established by the authors for thecontinuous-time case. The condition is geometric in nature andcan be checked a priori for a Poisson stable system, that is,without knowing explicitly the state trajectories of the system.The significance of the ideas and tools presented is illustratedby means of simple examples.
Ascencio P, Astolfi A, Parisini T, 2016, Backstepping PDE-based adaptive observer for a single particle model of lithium-ion batteries, 55th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 5623-5628, ISSN: 0743-1546
This article deals with the observer design problem for the simultaneous estimation of the solid Lithium concentration and of the diffusion parameter for a Single Particle Model of Lithium-Ion Batteries. The design is based on the Backstepping PDE methodology, including a modified Volterra transformation to compensate for the diffusivity uncertainty. The resulting coupled/uncoupled Kernel-PDE and Ordinary Differential Equation (ODE) are recast, via a Sum-of-Squares decomposition, in terms of a convex optimization problem and solved by semidefinite programming, allowing, at each fixed time, an efficient computation of the state and parameter observer gains. In addition, based on the Moment approach, a novel scheme of inversion of the nonlinear output mapping of the Single Particle Model is presented. The effectiveness of this approach is illustrated by numerical simulations.
Mylvaganam T, Astolfi A, 2016, Dynamic Algorithms for Solving Coupled Algebraic Riccati Equations Arising in Mixed H2/H∞ Control for Scalar Linear Systems, IEEE Conference on Decision & Control, Publisher: IEEE, ISSN: 0743-1546
The problem of mixed H2/H∞ control canbe formulated as a two-player nonzero-sum differentialgame as done by Limebeer et al. in the 1990s. For linearsystems the problem is characterised by two coupled algebraicRiccati equations. Solutions for such algebraic Riccatiequations are not straight-forward to obtain, particularly forinfinite-horizon problems. In this paper two algorithms forobtaining solutions for the coupled algebraic Riccati equationsassociated with the mixed H2/H∞ control problemfor scalar, linear systems is provided along with illustrativenumerical examples.
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.
Mylvaganam T, Astolfi A, 2016, A Nash Game Approach to Mixed H2/H∞ Control for Input-Affine Nonlinear Systems, Nonlinear Control System Symposium (NOLCOS), Publisher: Elsevier, Pages: 1024-1029, ISSN: 1474-6670
With the aim of designing controllers to simultaneously ensure robustness and optimality properties, the mixed H2/H∞ control problem is considered. A class of input-affine nonlinear systems is considered and the problem is formulated as a nonzero-sum differential game, similar to what has been done in the 1990s by Limebeer et al. for linear systems. A heuristic algorithm for obtaining solutions for the coupled algebraic Riccati equations which are characteristic of the linear quadratic problem is provided together with a systematic method for constructing approximate solutions for the general, nonlinear problem. A few numerical examples are provided.
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.
Chang H, Moog C, Astolfi A, 2016, Occurrence of HIV eradication for preexposure prophylaxis treatment with a deterministic HIV model, IET Systems Biology, Vol: 10, Pages: 237-243, ISSN: 1751-8857
The authors examine the human immunodeficiency virus (HIV) eradication in this study using a mathematical model and analyse the occurrence of virus eradication during the early stage of infection. To this end they use a deterministic HIV-infection model, modify it to describe the pharmacological dynamics of antiretroviral HIV drugs, and consider the clinical experimental results of preexposure prophylaxis HIV treatment. They also use numerical simulation to model the experimental scenario, thereby supporting the clinical results with a model-based explanation. The study results indicate that the protocol employed in the experiment can eradicate HIV in infected patients at the early stage of the infection.
Mylvaganam T, Astolfi A, 2016, Towards a systematic solution for differential games with limited communication, 2016 American Control Conference (ACC), Publisher: American Automatic Control Council, Pages: 3814-3819, ISSN: 2378-5861
The main aim of this work is to develop a systematic approach for dealing with differential games with limited communication. To this end a differential game with limited communication is considered. The communication topology is described by a directed graph. The main components characterising the differential game with limited communication are identified before the resulting game is formally defined. Sufficient conditions to solve the problem are identified both in the general nonlinear case and in the linear-quadratic case. A numerical example illustrating the theoretical approach and results is presented. Finally, several directions for further developments are identified.
Padoan A, Astolfi A, 2016, Nonlinear system identification for continuous-time autonomous systems via functional equations methods, 2016 American Control Conference (ACC), Publisher: IEEE, Pages: 1814-1819
The problem of identifying an autonomous nonlinear system, that is, the problem of finding a state-space description of a given sequence generated by sampling the output of an unknown autonomous nonlinear system, is studied. A theoretical framework which combines the use of the Schroder functional equation with realization-theoretic techniques is developed.
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.
Bauso D, Mylvaganam T, Astolfi A, 2016, Crowd-averse robust mean-field games: approximation via state space extension, IEEE Transactions on Automatic Control, Vol: 61, Pages: 1882-1894, ISSN: 0018-9286
We consider a population of dynamic agents, also referred to as players. The state of each player evolves according to a linear stochastic differential equation driven by a Brownian motion and under the influence of a control and an adversarial disturbance. Every player minimizes a cost functional which involves quadratic terms on state and control plus a cross-coupling mean-field term measuring the congestion resulting from the collective behavior, which motivates the term “crowd-averse.” Motivations for this model are analyzed and discussed in three main contexts: a stock market application, a production engineering example, and a dynamic demand management problem in power systems. For the problem in its abstract formulation, we illustrate the paradigm of robust mean-field games. Main contributions involve first the formulation of the problem as a robust mean-field game; second, the development of a new approximate solution approach based on the extension of the state space; third, a relaxation method to minimize the approximation error. Further results are provided for the scalar case, for which we establish performance bounds, and analyze stochastic stability of both the microscopic and the macroscopic dynamics.
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.
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