Publications
685 results found
Sassano M, Mylvaganam T, Astolfi A, 2021, (Cyclo-passive) Port-Controlled Hamiltonian dynamics in LQ differentialgames, American Control Conference, Publisher: IEEE
It is shown that the state/costate dynamics arising in a certain class of linear quadratic differential games can be interpreted as the interconnection of (cyclo-passive) Port-Controlled Hamiltonian systems. This property relies on the fact that the (virtual) energy functions associated to each player depend only on the interplay between the inputs of the players, as opposed to the system’s matrix or the individual cost functionals. Finally, it is shown that an arbitrarily accurate approximation of an open-loop Nash equilibrium strategy, obtained from the trajectories of the state/costate system, can be robustified by externally stabilizing the stable eigenspace of the underlying state/costate system.
Astolfi A, Scarciotti G, Simard J, et al., 2021, Model reduction by moment matching: beyond linearity a review of the last 10 years, 2020 59th IEEE Conference on Decision and Control (CDC), Publisher: IEEE
We present a review of some recent contributions to the theory and application of nonlinear model order reduction by moment matching. The tutorial paper is organized in four parts: 1) Moments of Nonlinear Systems; 2) Playing with Moments: Time-Delay, Hybrid, Stochastic, Data-Driven and Beyond; 3) The Loewner Framework; 4) Applications to Optimal Control and Wave Energy Conversion.
Xiang X, Gu Y, Chen K, et al., 2021, On the dynamics of inherent balancing of modular multilevel DC-AC-DC converters, IEEE Transactions on Power Electronics, Vol: 36, Pages: 34-40, ISSN: 0885-8993
Modular multilevel dc–ac–dc converters (MMDACs) serve as an enabler for dc distribution systems. The modular multilevel structure enables flexible voltage transforms, but raises issues over balancing of the submodule (SM) capacitor voltages. This letter focuses on the dynamics of inherent balancing of MMDACs under circulant modulation. We provide an invariance-like result using a variant of Barbalat's Lemma and prove that the SM capacitor voltages converge to the kernel of the circulant switching matrix, which is the intersection of the invariant sets for each switching state. We further interpret the balancing dynamics as a permuted linear time-invariant system and prove that the envelop of the balancing trajectories is governed by the eigenvalues of the permuted state-transition matrix. This result extends previous full-rank criterion for inherent balancing in a steady state and provides new insight into the dynamic behavior of MMDACs.
Franco E, Brown T, Astolfi A, et al., 2021, Adaptive energy shaping control of robotic needle insertion, Mechanism and Machine Theory, Vol: 155, ISSN: 0094-114X
This work studies the control of a pneumatic actuator for needle insertion in soft tissue without using axial rotation or additional needle supports. Employing a simplified rigid-link model description of an axial-symmetric tip needle supported at the base, two energy shaping controllers are proposed. The friction forces of the pneumatic actuator are compensated adaptively and the stability conditions for the closed-loop equilibrium are discussed. The controllers are compared by means of simulations and experiments on two different silicone rubber phantoms. The results indicate that the proposed controllers effectively compensate the actuator's friction, which is comparable to the insertion forces for the chosen pneumatic actuators. The first controller only depends on the actuator's position thus it achieves the prescribed insertion depth but results in a larger tip rotation and corresponding deflection. The second controller also accounts for the rotation of the needle tip on the bending plane, which can consequently be reduced by over 70% for this specific system. This is achieved by modulating the actuator force and, in case of harder phantoms, by automatically limiting the insertion depth.
Hernandez-Vargas EA, Giordano G, Sontag E, et al., 2021, Second special section on systems and control research efforts against COVID-19 and future pandemics, ANNUAL REVIEWS IN CONTROL, Vol: 51, Pages: 424-425, ISSN: 1367-5788
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- Citations: 3
Simard JD, Astolfi A, 2021, Loewner Functions and Model Order Reduction for Nonlinear Input-Affine Descriptor Systems, 60th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 6887-6894, ISSN: 0743-1546
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- Citations: 3
Chen K, Astolfi A, 2021, Identification-based Adaptive Control for Systems with Time-varying Parameters, 60th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 1083-1088, ISSN: 0743-1546
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- Citations: 1
Hernandez-Vargas EA, Giordano G, Sontag E, et al., 2021, Third special section on systems and control research efforts against COVID-19 and future pandemics, ANNUAL REVIEWS IN CONTROL, Vol: 52, Pages: 446-447, ISSN: 1367-5788
Dastjerdi AA, Astolfi A, Hosseinnia SH, 2020, A Frequency-Domain Stability Method for Reset Systems, Pages: 5785-5791, ISSN: 0743-1546
The potential of reset controllers to enhance the performance of control systems has been extensively demonstrated in the literature. However, similarly to other non-linear controllers, the stability analysis for these controllers is complex and relies on parametric models of the systems which may hinder the applicability of these controllers in industry. The well-known Hß method tries to solve this significant issue. However, assessing the Hß condition in the frequency-domain is complex, especially for high dimensional plants. In addition, it cannot be used to assess UBIBS stability of reset control systems in the case of reseting to non-zero values. These problems have been solved in this paper for the first order reset elements, and an easy-to-use frequency approach for assessing stability of reset control systems is proposed. The effectiveness of the proposed approach is demonstrated through a practical example.
Sassano M, Astolfi A, 2020, Combining pontryagin's principle and dynamic programming for linear and nonlinear systems, IEEE Transactions on Automatic Control, Vol: 65, Pages: 5312-5327, ISSN: 0018-9286
To study optimal control and disturbance attenuation problems, two prominent-and somewhat alternative-strategies have emerged in the last century: dynamic programming (DP) and Pontryagin's minimum principle (PMP). The former characterizes the solution by shaping the dynamics in a closed loop (a priori unknown) via the selection of a feedback input, at the price, however, of the solution to (typically daunting) partial differential equations. The latter, instead, provides (extended) dynamics that must be satisfied by the optimal process, for which boundary conditions (a priori unknown) should be determined. The results discussed in this article combine the two approaches by matching the corresponding trajectories, i.e., combining the underlying sources of information: knowledge of the complete initial condition from DP and of the optimal dynamics from PMP. The proposed approach provides insights for linear as well as nonlinear systems. In the case of linear systems, the derived conditions lead to matrix algebraic equations, similar to the classic algebraic Riccati equations (AREs), although with coefficients defined as polynomial functions of the input gain matrix, with the property that the coefficient of the quadratic term of such equation is sign definite, even if the corresponding coefficient of the original ARE is sign indefinite, as it is typically the case in the H ∞ control problem. This feature is particularly appealing from the computational point of view, since it permits the use of standard minimization techniques for convex functions, such as the gradient algorithm. In the presence of nonlinear dynamics, the strategy leads to algebraic equations that allow us to (locally) construct the optimal feedback by considering the behavior of the closed-loop dynamics at a single point in the state space.
Sassano M, Astolfi A, 2020, Model matching and passivation of MIMO linear systems via dynamic output feedback and feedforward, IEEE Transactions on Automatic Control, Vol: 65, Pages: 4016-4030, ISSN: 0018-9286
A model matching and passivating control architecture for multi-input/multi-output linear systems, comprising dynamic feedback and feedforward, is proposed. The approach-essentially without any restriction on the relative degree and the zeros of the underlying system and by relying only on input/output measurements-provides a closed-loop system, the transfer matrix of which matches any desired matrix of rational functions. An alternative implementation of the above design allows to achieve an arbitrary approximation accuracy of a desired transfer matrix while also preserving structural properties-in particular observability-of the overall interconnected system. Such a construction can be then specialized to provide input/output decoupling or a system that is passive from a novel control input to a modified output. The result is achieved by arbitrarily assigning the relative degree and location of the poles and zeros on the complex plane of the interconnected system in a systematic way. It is also shown that similar ideas can be employed to enforce a desired, arbitrarily small, L 2 -gain from an unknown disturbance input to a modified output, while preserving the corresponding gain from the control input to the same output. The article is concluded with applications and further discussions on the results.
Sassano M, Astolfi A, 2020, Optimality and passivity of input-quadratic nonlinear systems, IEEE Transactions on Automatic Control, Vol: 65, Pages: 3229-3240, ISSN: 0018-9286
The infinite-horizon optimal control problem with stability in the presence of single-input, inputquadratic nonlinear systems is addressed and tackled inthis paper. In addition, it is shown that similar ideas canbe extended to study the property of passivity of the underlying input-quadratic system from a given output. Theconstructive design of the optimal solution revolves aroundthe interesting fact that the property of optimality of theclosed-loop underlying system is shown to be locally equivalent to the property that an input-affine system possessesan L2-gain less than one from a virtual disturbance signal.The global version of the statement requires a technicalcondition on the graph of the storage function of the latterauxiliary plant, hence leads to the new notion of graphicalstorage function. Finally, the theory is corroborated by theapplication to the optimal control of the movable plane positioning in micro-mechanical systems (MEMS) actuators.
Padoan A, Astolfi A, 2020, Singularities and moments of nonlinear systems, IEEE Transactions on Automatic Control, Vol: 65, Pages: 3647-3654, ISSN: 0018-9286
The notions of eigenvalue, pole and moment at a pole of a continuous-time, nonlinear, time-invariant system are studied. Eigenvalues and poles are first characterized in terms of invariant subspaces. Tools from geometric control theory are used to define nonlinear enhancements of these notions and to study their relationship with the solution of certain partial differential equations, cascade decompositions and steady-state impulse responses. The theory is illustrated by means of worked-out examples and its significance is demonstrated by solving the model reduction problem by moment matching at poles for nonlinear systems.
Chen K, Astolfi A, 2020, Adaptive control for nonlinear systems with time-varying parameters and control coefficient, IFAC World Congress 2020, Publisher: Elsevier, Pages: 3829-3834, ISSN: 2405-8963
This paper exploits the so-called congelation of variables method to design an adaptive controller for nonlinear systems with time-varying parameters. Two motivating examples describing scalar systems are discussed to illustrate the flexibility of the congelation of variables method to deal with the cases in which the time-varying parameters are coupled with the state and with the input, respectively. Interpretations from a passivity perspective are also provided. Then design procedures are derived for general nonlinear systems in parametric strict-feedback form, and it is shown that the state of the underlying system converges to the origin and all signals of the closed-loop system remain bounded. Simulations show that, in the presence of parameter variations, the performance of the proposed controller is superior to that of the classical adaptive controller designed for time-invariant systems.
Franco E, Rodriguez y Baena F, Astolfi A, 2020, Robust dynamic state feedback for underactuated systems with linearly parameterized disturbances, International Journal of Robust and Nonlinear Control, Vol: 30, Pages: 4112-4128, ISSN: 1049-8923
This article investigates the control problem for underactuated port‐controlled Hamiltonian systems with multiple linearly parameterized additive disturbances including matched, unmatched, constant, and state‐dependent components. The notion of algebraic solution of the matching equations is employed to design an extension of the interconnection and damping assignment passivity‐based control methodology that does not rely on the solution of partial differential equations. The result is a dynamic state‐feedback that includes a disturbance compensation term, where the unknown parameters are estimated adaptively. A simplified implementation of the proposed approach for underactuated mechanical systems is detailed. The effectiveness of the controller is demonstrated with numerical simulations for the magnetic‐levitated‐ball system and for the ball‐on‐beam system.
Di Francor P, Scarciotti G, Astolfi A, 2020, Stability of nonlinear differential-algebraic systems via additive identity, IEEE/CAA Journal of Automatica Sinica, Vol: 7, Pages: 929-941, ISSN: 2329-9266
The stability analysis for nonlinear differential-algebraic systems is addressed using tools from classical control theory. Sufficient stability conditions relying on matrix inequalities are established via Lyapunov Direct Method. In addition, a novel interpretation of differential-algebraic systems as feedback interconnection of a purely differential system and an algebraic system allows reducing the stability analysis to a small-gain-like condition. The study of stability properties for constrained mechanical systems, for a class of Lipschitz differential-algebraic systems and for an academic example is used to illustrate the theory.
Ortega R, Aranovskiy S, Pyrkin AA, et al., 2020, New results on parameter estimation via dynamic regressor extension and mixing: continuous and discrete-time cases, IEEE Transactions on Automatic Control, Vol: 66, Pages: 2265-2272, ISSN: 0018-9286
We present some new results on the dynamic regressor extension and mixing parameter estimators for linear regression models recently proposed in the literature. This technique has proven instrumental in the solution of several open problems in system identification and adaptive control. The new results include the following, first, a unified treatment of the continuous and the discrete-time cases; second, the proposal of two new extended regressor matrices, one which guarantees a quantifiable transient performance improvement, and the other exponential convergence under conditions that are strictly weaker than regressor persistence of excitation; and, third, an alternative estimator ensuring convergence in finite-time whose adaptation gain, in contrast with the existing one, does not converge to zero. Simulations that illustrate our results are also presented.
Scarciotti G, Jiang Z-P, Astolfi A, 2020, Data-driven constrained optimal model reduction, European Journal of Control, Vol: 53, Pages: 68-78, ISSN: 0947-3580
Model reduction by moment matching can be interpreted as the problem of finding a reduced-order model which possesses the same steady-state output response of a given full-order system for a prescribed class of input signals. Little information regarding the transient behavior of the system is systematically preserved, limiting the use of reduced-order models in control applications. In this paper we formulate and solve the problem of constrained optimal model reduction. Using a data-driven approach we determine an estimate of the moments and of the transient response of a possibly unknown system. Consequently we determine a reduced-order model which matches the estimated moments at the prescribed interpolation signals and, simultaneously, possesses the estimated transient. We show that the resulting system is a solution of the constrained optimal model reduction problem. Detailed results are obtained when the optimality criterion is formulated with the time-domain ℓ1, ℓ2, ℓ∞ norms and with the frequency-domain norm. The paper is illustrated by two examples: the reduction of the model of the vibrations of a building and the reduction of the Eady model (an atmospheric storm track model).
Di Franco P, Scarciotti G, Astolfi A, 2020, A globally stable algorithm for the integration of high-index differential-algebraic systems, IEEE Transactions on Automatic Control, Vol: 65, Pages: 2107-2122, ISSN: 0018-9286
The problem of constraint stabilization and numerical integration for differential-algebraic systems is addressed using Lyapunov theory. It is observed that the application of stabilization methods which rely on a linear feedback mechanism to nonlinear systems may result in trajectories with finite escape time. To overcome this problem we propose a method based on a nonlinear stabilization mechanism which guarantees the global existence and convergence of the solutions. Discretization schemes, which preserve the properties of the method, are also presented. The results are illustrated by means of the numerical integration of a slider-crank mechanism.
Ortega R, Yi B, Guadalupe Romero J, et al., 2020, Orbital stabilization of nonlinear systems via the immersion and invariance technique, International Journal of Robust and Nonlinear Control, Vol: 30, Pages: 1850-1871, ISSN: 1049-8923
Immersion and invariance is a technique for the design of stabilizing and adaptive controllers and state observers for nonlinear systems. In all these applications the problem considered is the stabilization of equilibrium points. Motivated by some modern applications, we show that the technique can also be used to solve the problem of orbital stabilization, where the final objective is to generate periodic solutions that are attractive. The feasibility of our result is illustrated by means of some classical mechanical engineering and power electronics examples.
Franco E, Garriga Casanovas A, Rodriguez y Baena F, et al., 2020, Model based adaptive control for a soft robotic manipulator, 58th IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 1019-1024
The application of model based adaptive control to an underactuated system representative of a class of soft continuummanipulators is investigated. To this end, a rigid-linkmodel with elastic joints is employed and an energy shaping controller is designed. Additionally, model uncertainties and external disturbances, both matched and unmatched, are compensated with an adaptive algorithm. This results in a control law that only depends on the orientation and on the angular velocity of the distal link and it is therefore independent of the number of links. Finally, stability conditions are discussed and the effectiveness of the controller is verified via simulations.
Chen K, Astolfi A, 2020, Output-feedback I&I adaptive control for linear systems with time-varying parameters, 58th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 1965-1970, ISSN: 0743-1546
This paper combines the so-called congelation of variables method with the adaptive immersion and invariance (I&I) approach to control linear single-input-single-output systems with time-varying parameters via output feedback. The system is first reparameterized using a pair of reduced-order filters and the reparameterization error dynamics show that the input is coupled with a time-varying perturbation. By exploiting the input-to-state stability (ISS) of the inverse dynamics, which is regarded as a counterpart in the time-varying setting of the classical minimum-phase property, the coupling between the input and the time-varying perturbation is transformed into a coupling between the output and another time-varying perturbation that can be dominated in the controller design stage. A pair of high-gain filters are then implemented so that the reparameterization error dynamics are ISS. Finally, output regulation is achieved by strengthened damping design, which invokes a small-gain-like argument from a Lyapunov perspective.
Jones A, Astolfi A, 2020, On the Solution of Optimal Control Problems using Parameterized State-Dependent Riccati Equations, 59th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 1098-1103, ISSN: 0743-1546
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- Citations: 6
Dastjerdi AA, Astolfi A, HosseinNia SH, 2020, A Frequency-Domain Stability Method for Reset Systems, 59th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 5785-5791, ISSN: 0743-1546
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- Citations: 7
Simard JD, Astolfi A, 2020, Loewner Functions for Linear Time-Varying Systems with Applications to Model Reduction, 21st IFAC World Congress on Automatic Control - Meeting Societal Challenges, Publisher: ELSEVIER, Pages: 5623-5628, ISSN: 2405-8963
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- Citations: 6
Chen K, Astolfi A, 2020, On the Active Nodes of Network Systems, 59th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 5561-5566, ISSN: 0743-1546
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- Citations: 3
Hernandez-Vargas EA, Giordano G, Sontag E, et al., 2020, First special section on systems and control research efforts against COVID-19 and future pandemics, ANNUAL REVIEWS IN CONTROL, Vol: 50, Pages: 343-344, ISSN: 1367-5788
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- Citations: 5
Simard JD, Astolfi A, 2020, Online Estimation of the Loewner Matrices, 59th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 3425-3430, ISSN: 0743-1546
Chen K, Astolfi A, 2019, Output-feedback adaptive control for systems with time-varying parameters, 8th International-Federation-of-Automatic-Control (IFAC) Symposium on Mechatronic Systems (MECHATRONICS) / 11th International-Federation-of-Automatic-Control (IFAC) Symposium on Nonlinear Control Systems (NOLCOS), Publisher: Elsevier, Pages: 586-591, ISSN: 2405-8963
This paper investigates the output-feedback adaptive control problem, exploiting the so-called congelation of variables method, to achieve output regulation for systems with time-varying parameters. To overcome the coupling between the input and the time-varying parameters, a strong minimum-phase property, i.e. input-to-state stability (ISS) of the inverse dynamics, is assumed. This property allows replacing the original coupling with a new coupling between the output and the varying parameters, which can be dominated via backstepping. A set of high-gain Kreisselmeier filters is then designed to guarantee that the state estimation error dynamics are also ISS. Finally, implementing the backstepping controller with a strengthened nonlinear damping term guarantees that all trajectories of the closed-loop system are bounded and that the output converges to zero asymptotically.
Faedo N, Garcia-Violini D, Scarciotti G, et al., 2019, Robust Moment-Based Energy-Maximising Optimal Control of Wave Energy Converters, 2019 IEEE 58th Conference on Decision and Control (CDC), Publisher: IEEE
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