Publications
685 results found
Padoan A, Astolfi A, 2019, Moments of random variables: a systems-theoretic interpretation, IEEE Transactions on Automatic Control, Vol: 64, Pages: 4407-4422, ISSN: 0018-9286
Moments of continuous random variables admitting a probability density function are studied. We show that, under certain assumptions, the moments of a random variable can be characterised in terms of a Sylvester equation and of the steady-state output response of a specific interconnected system. This allows to interpret well-known notions and results of probability theory and statistics in the language of systems theory, including the sum of independent random variables, the notion of mixture distribution and results from renewal theory. The theory developed is based on tools from the center manifold theory, the theory of the steady-state response of nonlinear systems, and the theory of output regulation. Our formalism is illustrated by means of several examples and can be easily adapted to the case of discrete and of multivariate random variables.
Breschi V, Formentin S, Scarciotti G, et al., 2019, Simulation-driven fixed-order controller tuning via moment matching, 2019 European Control Conference, Publisher: IEEE, Pages: 2307-2312
We propose a controller tuning method basedon the data-driven model reduction by moment matchingtheory. By selecting a reference closed-loop transfer function,a moment matching data-driven model reduction algorithm isused to synthesize a fixed-order controller, via the identificationof a model of the inverse transfer function of the controller,i.e.the transfer function from the controlled input of thesystem to the mismatch error signal. The controller is finallyobtained by inverting this transfer function. The fixed-ordercontroller is guaranteed to match the steady-state behaviorof the ideal controller at certain pre-selected frequencies. Theeffectiveness of the resulting design method is assessed on acontrol problem for the48-th order model of the Los AngelesUniversity Hospital building.
Faedo N, Scarciotti G, Astolfi A, et al., 2019, Moment-based constrained optimal control of an array of wave energy converters, 2019 American Control Conference, Publisher: IEEE, Pages: 4797-4802, ISSN: 2378-5861
The roadmap to a successful commercialisation ofwave energy inherently incorporates the concept of anarrayorfarmof Wave Energy Converters (WECs). These interactinghydrodynamic structures require an optimised process that canensure the maximum extraction of time-averaged energy fromocean waves, while respecting the physical limitations of eachdevice and actuator characteristics. Recently, a novel optimalcontrol framework based on the concept ofmoment, for asingle WEC device, has been introduced in [1]. Such a strategyoffers an energy-maximising computationally efficient solutionthat can systematically incorporate state and input constraints.This paper presents the mathematical extension of the optimalcontrol framework of [1] to the case where an array of WECsis considered, providing an efficient solution that exploits thehydrodynamic interaction between devices to maximise the totalabsorbed energy.
Di Franco P, Scarciotti G, Astolfi A, 2019, A disturbance attenuation approach for the control of differential-algebraic systems, 2018 IEEE Conference on Decision and Control (CDC), Publisher: IEEE
Inthispapertheproblemofcontrollingdifferential-algebraic systems with index-1 is addressed. Theproposed technique is based on the interpretation of differential-algebraic systems as the feedback interconnection of a differ-ential system and an algebraic system. In this framework, thealgebraic variable can be treated as an external disturbanceacting on the differential system. A direct consequence of thisapproach is that the control problem reduces to a classicaldisturbance attenuation problem with internal stability. We alsoshow that the application of the proposed theory to the linearcase yields classical results. Finally, an example inspired by anair suspension system in a truck illustrates the technique.
Jiang J, Astolfi A, 2019, Under-Actuated Back-Stepping: An Introduction, 57th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 5910-5915, ISSN: 0743-1546
Chen K, Astolfi A, 2019, I&I adaptive control for systems with varying parameters, 57th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 2205-2210, ISSN: 0743-1546
This paper combines the so-called congelation of variables method with adaptive immersion and invariance (I&I) to adaptively control systems with varying parameters. A dynamic scaling estimator without overparameterization is proposed. This does not require solving partial differential equations and removes other restrictive assumptions in the classical I&I estimator design. A controller that guarantees input-to-state stability of the closed-loop system is then used. The joint estimator-controller design guarantees global stability of the adaptive closed-loop system, convergence of the plant state and global boundedness of the estimator state. A design example for the position/force control of a series elastic actuator is discussed. This exploits the idea that bounded nonlinearities in the system dynamics can be viewed as time-varying parameters. Simulation results show a well-damped transient response and illustrate the theoretical results.
Sassano M, Astolfi A, 2019, A local separation principle via dynamic approximate feedback and observer linearization for a class of nonlinear systems, IEEE Transactions on Automatic Control, Vol: 64, Pages: 111-126, ISSN: 0018-9286
A separation principle for a class of nonlinear systems inspired by the techniques of feedback linearization and observer design with linear error dynamics is discussed. The output feedback construction combines strategies for approximate feedback linearization and observer design, which are of interest per se, yielding a dynamic control law that ensures a linear, spectrally assignable, behavior from the certainty equivalence input mismatch to the extended state of the system and the observer. The first ingredient, namely the approximate feedback linearization strategy, can be applied, under mild conditions, also to nonlinear systems that are linearly uncontrollable-or that do not possess a well-defined relative degree in the case of a given output function-yet providing a chain of integrators of length equal to the dimension of the state in the transformed coordinates. Interestingly, a systematically designed nonlinear inner loop enables the use of linear design techniques, e.g., pole placement. The observer design, on the other hand, employs an additional dynamic extension that allows us to assign the local dynamic behavior of the error dynamics independently from its zeros, differently from the classic high-gain observer design. The paper is concluded by presenting several numerical simulations, including an output tracking control problem for the Ball and Beam model that does not possess a well-defined relative degree.
Sassano M, Mylvaganam T, Astolfi A, 2019, An algebraic approach to dynamic optimisation of nonlinear systems: a survey and some new results, Journal of Control and Decision, Vol: 6, Pages: 1-29, ISSN: 2330-7706
Dynamic optimisation, with a particular focus on optimal control and nonzero-sum differential games, is considered. For nonlinear systems solutions sought via the dynamic programming strategy are inevitably characterised by partial differential equations (PDEs) which are often difficult to solve. A detailed overview of a control design framework which enables the systematic construction of approximate solutions for optimal control problems and differential games without requiring the explicit solution of any PDE is provided along with a novel design of a nonlinear control gain aimed at improving the ‘level of approximation’ achieved. Multi-agent systems are considered as a possible application of the theory.
Di Franco P, Scarciotti G, Astolfi A, 2019, Stabilization of differential-algebraic systems with Lipschitz nonlinearities via feedback decomposition, 18th European Control Conference (ECC), Publisher: IEEE, Pages: 1154-1158
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- Citations: 2
Tahirovic A, Astolfi A, 2019, Optimal Control for Continuous-time Nonlinear Systems based on a Linear-like Policy Iteration, 58th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 5238-5243, ISSN: 0743-1546
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- Citations: 3
Jiang J, Astolfi A, Parisini T, 2019, Traffic Wave Damping: A Shared Control Approach, American Control Conference (ACC), Publisher: IEEE, Pages: 4860-4865, ISSN: 0743-1619
Sassano M, Astolfi A, 2019, Optimal control of MIMO input-quadratic nonlinear systems, 58th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 3328-3333, ISSN: 0743-1546
Simard JD, Astolfi A, 2019, An Interconnection-Based Interpretation of the Loewner Matrices, 58th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 7788-7793, ISSN: 0743-1546
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- Citations: 7
Machado JE, Ortega R, Astolfi A, et al., 2019, Active Damping of a DC Network with a Constant Power Load: An Adaptive Observer-based Design, 18th European Control Conference (ECC), Publisher: IEEE, Pages: 411-416
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- Citations: 2
Faedo N, Scarciotti G, Astolfi A, et al., 2018, Energy-maximising control of wave energy converters using a moment-domain representation, Control Engineering Practice, Vol: 81, Pages: 85-96, ISSN: 0967-0661
Wave Energy Converters (WECs) have to be controlled to ensure maximum energy extraction from waves while considering, at the same time, physical constraints on the motion of the real device and actuator characteristics. Since the control objective for WECs deviates significantly from the traditional reference “tracking” problem in classical control, the specification of an optimal control law, that optimises energy absorption under different sea-states, is non-trivial. Different approaches based on optimal control methodologies have been proposed for this energy-maximising objective, with considerable diversity on the optimisation formulation. Recently, a novel mathematical tool to compute the steady-state response of a system has been proposed: the moment-based phasor transform. This mathematical framework is inspired by the theory of model reduction by moment-matching and considers both continuous and discontinuous inputs, depicting an efficient and closed-form method to compute such a steady-state behaviour. This study approaches the design of an energy-maximising optimal controller for a single WEC device by employing the moment-based phasor transform, describing a pioneering application of this novel moment-matching mathematical scheme to an optimal control problem. Under this framework, the energy-maximising optimal control formulation is shown to be a strictly concave quadratic program, allowing the application of well-known efficient real-time algorithms.
Franco E, Rodriguez y Baena F, Astolfi A, 2018, Robust balancing control of flexible inverted-pendulum systems, Mechanism and Machine Theory, Vol: 130, Pages: 539-551, ISSN: 0094-114X
This work studies the balancing control problem for flexible inverted-pendulum systems and investigates the relationship between system parameters and robustness to disturbances. To this end, a new energy-shaping controller with adaptive disturbance-compensation for a class of underactuated mechanical systems is presented. Additionally, a method for the identification of key system parameters that affect the robustness of the closed-loop system is outlined. The proposed approach is applied to the flexible pendulum-on-cart system and a simulation study is conducted to demonstrate its effectiveness. Finally, the control problem for a classical pendulum-on-cart system with elastic joint is discussed to highlight the similarities with its flexible-link counterpart.
Mylvaganam T, Ortega R, Machado J, et al., 2018, Dynamic zero finding for algebraic equations, European Control Conference, Publisher: IEEE, Pages: 1244-1249
In a variety of contexts, for example the solution of differential games and the control of power systems, the design of feedback control laws requires the solution of nonlinear algebraic equations: obtaining such solutions is often not trivial. Motivated by such situations we consider systems of nonlinear algebraic equations and propose a method for obtaining their solutions. In particular, a dynamical system is introduced and (locally) stabilizing control laws which ensure that elements of the state converge to a solution of the algebraic equations are given. Illustrative numerical examples are provided. In addition it is shown that the proposed method is applicable to determine the equilibria of electrical networks with constant power loads.
Chen K, Astolfi A, 2018, Adaptive control of linear systems with time-varying parameters, American Control Conference, Publisher: IEEE, Pages: 80-85, ISSN: 0743-1619
A new method for the adaptive control of linear systems with time-varying parameters is proposed. The method does not require any restriction on the rates of parameter variations. For linear systems in parametric strict-feedback form a state feedback adaptive backstepping controller with nonlinear damping terms is proposed and stability properties are proved. For systems in observable canonical form an ISS Kreisselmeier filter and an adaptive observer backstepping controller with an additional linear damping term are proposed: these guarantee asymptotic output regulation and bounded states. Simulation results show that the proposed controllers have superior performance over the standard controllers in the presence of varying parameters.
Ascencio P, Astolfi A, Parisini T, 2018, Backstepping PDE design: a convex optimization approach, IEEE Transactions on Automatic Control, Vol: 63, Pages: 1943-1958, ISSN: 0018-9286
Backstepping design for boundary linear PDE is formulated as a convex optimization problem. Some classes of parabolic PDEs and a first-order hyperbolic PDE are studied, with particular attention to non-strict feedback structures. Based on the compactness of the Volterra and Fredholm-type operators involved, their Kernels are approximated via polynomial functions. The resulting Kernel-PDEs are optimized using Sum-of-Squares (SOS) decomposition and solved via semidefinite programming, with sufficient precision to guarantee the stability of the system in the L2-norm. This formulation allows optimizing extra degrees of freedom where the Kernel-PDEs are included as constraints. Uniqueness and invertibility of the Fredholm-type transformation are proved for polynomial Kernels in the space of continuous functions. The effectiveness and limitations of the approach proposed are illustrated by numerical solutions of some Kernel-PDEs.
Padoan A, Astolfi A, 2018, The Dimension Estimation Problem for Nonlinear Systems, European Control Conference (ECC), Publisher: IEEE, Pages: 184-189
Jiang J, Astolfi A, 2018, Shared-Control for the Lateral Motion of Vehicles, European Control Conference (ECC), Publisher: IEEE, Pages: 225-230
Jiang J, Astolfi A, 2018, Lateral Control of an Autonomous Vehicle, IEEE Transactions on Intelligent Vehicles, Vol: 3, Pages: 228-237, ISSN: 2379-8858
The asymptotic stabilization problem for a class of nonlinear under-actuated systems is studied and solved. Its solution, together with the back-stepping and the forwarding control design methods, is exploited in the control of the nonlinear lateral dynamics of a vehicle. Even though the theoretical studies of the lateral control of autonomous vehicles are traditionally applied to lane keeping cases, the results can be applied to broader range of areas, such as lane changing cases. The comparison between the performances of the closed-loop systems with the given controller and a typical human driver is given and demonstrates the speediness and the effectiveness of the feedback controller.
He W, Soriano-Rangel CA, Ortega R, et al., 2018, Energy shaping control for buck-boost converters with unknown constant power load, CONTROL ENGINEERING PRACTICE, Vol: 74, Pages: 33-43, ISSN: 0967-0661
We develop in this paper an adaptive passivity-based controller for output voltage regulation of DC–DC buck–boost converter with an unknown constant power load. This control problem is theoretically challenging since the average model of the converter is a bilinear second order system that, due to the presence of the constant power load, is non-minimum phase with respect to both states. A solution to the problem was recently reported in Wei et al. (2017), however, the resulting control law is extremely complicated to be of practical interest. The purpose of this paper is to present a new, significantly simpler, controller that can be easily implemented in applications. The key modifications introduced in the new design are the use of a change of coordinates and a partial linearization that transform the system into a cascade form, to which an adaptive energy-shaping controller is applied. Another advantage of the proposed controller, besides its simplicity, is that it is amenable for the addition of an outer-loop PI that improves its transient and disturbance rejection performances. Simulations and experimental results are provided to assess the improved performance of the proposed controller.
Astolfi A, 2018, Some Closing Statements, EUROPEAN JOURNAL OF CONTROL, Vol: 40, Pages: 88-88, ISSN: 0947-3580
Di Franco P, Scarciotti G, Astolfi A, 2018, Discretization schemes for constraint stabilization in nonlinear differential-algebraic systems, 2018 European Control Conference, Publisher: IEEE
In this paper the problem of simulation ofdifferential-algebraic systems is addressed. In modelling me-chanical systems the use of redundant coordinates and con-straints results in differential-algebraic equations, the integra-tion of which can lead to numerical instabilities, such as theso-called drift phenomenon. In [1] the authors have proposeda globally convergent conceptual continuous-time algorithmfor the integration of constrained mechanical systems whichensures the existence of solutions and global attractivity of thesolution manifold. The objective of this paper is to study thenumerical implementation of the algorithm presented in [1]. Inaddition, the stability properties of the constrained system inthe manifold are studied in both the continuous and discretetime cases. The proposed technique is illustrated by means ofa simple example.
Jiang J, Astolfi A, 2018, A lateral control assistant for the dynamic model of vehicles subject to state constraints, 56th IEEE Conference on Decision and Control, Publisher: IEEE
An assistant control scheme for the dynamic model of a car to help the driver track a given reference or to keep the car in a given lane while making sure that all the system states satisfy pre-defined constraints is given. The assistant control algorithm is based on a hysteresis switch and the formal properties of the closed-loop system are studied via a Lyapunov-like analysis. Simulation results showing the effectiveness of the driving assistance system are presented.
Di Franco P, Scarciotti G, Astolfi A, 2018, On the stability of constrained mechanical systems, 56th IEEE Conference on Decision and Control, Publisher: IEEE
The problem of the stability analysis for constrained mechanical systems is addressed using tools from classical geometric control theory, such as the notion of zero dynamics. For the special case of linear constrained mechanical systems we show that stability is equivalent to a detectability property. The proposed techniques are illustrated by means of simple examples.
Padoan A, Astolfi, 2018, Model reduction by moment matching at isolated singularitiesfor linear systems: a geometric approach, 56th IEEE Conference on Decision and Control, Publisher: IEEE
The model reduction problem for continuous-time, linear, time-invariant systems is studied at isolated singularities of the transfer function. The moments at a pole of the transfer function are shown to be uniquely specified by the solutions of certain Sylvester equations exploiting two distinct approaches based on complex analysis and on geometric control theory. This allows to determine reduced order models which preserve given poles and match the corresponding moments. An in-depth analysis of the assumptions underlying this approach is provided in a companion paper. The applicability of the approaches developed is demonstrated with simple academic examples.
Di Franco P, Scarciotti G, Astolfi A, 2018, A globally stable convergent algorithm for the integration of constrained mechanical systems, 2018 American Control Conference, Publisher: IEEE
In this paper the problem of simulation of con-strained mechanical systems is addressed. In modeling multi-body mechanical systems, the Lagrange formulation producesa redundant set of differential-algebraic equations, the integra-tion of which can lead to several difficulties, for example thedrift of the “constraint violation”. One of the most popularapproaches to alleviate this issue is the so-called Baumgarte’smethod that relies on a linear feedback mechanism. Thismethod can however lead to numerical instabilities whenapplied to nonlinear (mechanical) systems. The objective ofthis study is to propose a new method that ensures existenceof solutions and makes the constraint manifold asymptoticallyattractive. The proposed technique is illustrated by means of asimple example.
Astolfi A, 2018, A New Beginning Within a Solid Tradition, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 63, Pages: 1-2, ISSN: 0018-9286
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