Publications
685 results found
Giannari AG, Astolfi A, 2024, Nonlinear control of neurodegenerative diseases. A case study on optical illusion networks disrupted by diabetic retinopathy, Neurocomputing, Vol: 569, ISSN: 0925-2312
We present an efficient computational framework for the design of optimal drug delivery control strategies that can successfully treat a family of neurodegenerative diseases that originate from channelopathies and synaptopathies. To this end, we extend our previously introduced scalable and adaptable modelling framework that models heterogeneous Hodgkin–Huxley (HH) neuronal networks to account for the modular organisation of the neurons in the brain, e.g. interconnecting sub-networks of heterogeneous neurons. Based on this framework, we introduce a novel design of lateral inhibition networks to successfully reproduce 2D optical illusions that are known to occur in the human retina. We model the dynamic behaviour of Diabetic Retinopathy (DR), a neurodegenerative disease that progressively hinders the inherent ability of patients to distinguish optical illusions. We implement nonlinear control on accurate models of diabetic lateral inhibition neuronal networks to recover their functionality and investigate the effects of virtual drug administration. We utilise the healthy and diabetic optical illusions generated by these networks as a ‘computational’ phenotype to design therapies based on an adaptive terminal error iterative learning controller (TE-ILC). Therefore, we provide a comprehensive computational framework that is able to imitate the dynamics of healthy and diseased neuronal networks and we propose an adaptive nonlinear control strategy based on the error between output images that correspond to healthy and diseased conditions.
Gao J, Chaudhuri B, Astolfi A, 2024, An optimization-based method for transient stability assessment, IEEE Conference on Decision and Control, Publisher: IEEE, ISSN: 2576-2370
The paper proposes an optimization-based method for the transient stability assessment of lossy multi-machine power systems. To achieve this objective, a global control Lyapunov function candidate including an auxiliary state is introduced. On this basis, a new excitation control law is proposed. This control law is well-defined provided that an ‘index’ matrix remains non-singular along the closed-loop trajectories. Such a matrix plays a key role in the formulation of an optimization problem, which allows calculating the so-called critical value associated to the introduced Lyapunov function. This permits a direct assessment of transient stability property of the considered post-fault power system. To illustrate the effectiveness of such an optimization-based method, a case study on the model of a three-machine system is presented.
Sassano M, Astolfi A, 2024, On the Role of Convexity/Concavity in Vector Fields, Flows, and Stability/Stabilizability, IEEE Transactions on Automatic Control, Vol: 69, Pages: 32-42, ISSN: 0018-9286
It is shown that strong convexity/concavity of a component of the vector field, as a function of the state variables, induces the same property on the corresponding component of the flow, as a function of the initial condition. Such an inherited property is then instrumental, for instance, for establishing several instability theorems, the proofs of which rely precisely on consequences of convexity/concavity of the flow with respect to the initial condition. Furthermore, the property of convexity/concavity permits the construction of a canonical Chetaev function to certify instability without explicitly resorting to the computation of the flow. Finally, necessary conditions for continuous stabilizability are derived, hence putting the properties of convexity/concavity of the vector field in relation to the well-known Brockett's theorem.
Simard JD, Astolfi A, 2024, On the construction and parameterization of interpolants in the Loewner framework, Automatica, Vol: 159, ISSN: 0005-1098
We develop a general method for the construction of interpolants in the Loewner framework for nonlinear differential–algebraic systems. The approach involves building a family of systems preserving the properties of Loewner equivalence and matching of tangential data functions. It is shown that under mild conditions this family of systems parameterizes all interpolants of sufficiently large dimension matching the tangential data while possessing tangential generalized controllability and observability functions with full column and row rank Jacobians. As a result, this family of systems provides all possible degrees of freedom that an interpolant can have. The results are also discussed in the linear setting and, when taken in combination with existing results, provide a broader framework for the construction of linear interpolating systems.
Scarciotti G, Astolfi A, 2024, Interconnection-based model order reduction - a survey, European Journal of Control, Vol: 75, ISSN: 0947-3580
In this survey we present in an organic, complete, and accessible style the interconnection framework for model order reduction. While this framework originally started as a revisitation of the moment matching method, in the last 15 years it has expanded to provide solutions to the model order reduction problem for general classes of systems, such as nonlinear, time-delay, stochastic, and hybrid, and to give insight on topics as diverse as circuit analysis and optimal control. The main theme of the paper is the characterization of “interconnection behaviors” as primary properties to be maintained by the reduction process. The survey is enriched by historical notes on the development of the interconnection framework.
Tarantino L, Sassano M, Galeani S, et al., 2024, Finite-Horizon Optimal Control for Linear and Nonlinear Systems Relying on Constant Optimal Costate, IEEE Transactions on Automatic Control, Pages: 1-15, ISSN: 0018-9286
Tahirovic A, Astolfi A, 2023, Linear-like policy iteration based optimal control for continuous-time nonlinear systems, IEEE Transactions on Automatic Control, Vol: 68, Pages: 5837-5849, ISSN: 0018-9286
We propose a novel strategy to construct optimal controllers for continuous-time nonlinear systems by means of linear-like techniques, provided that the optimal value function is differentiable and quadratic-like . This assumption covers a wide range of cases and holds locally around an equilibrium under mild assumptions. The proposed strategy does not require solving the Hamilton-Jacobi-Bellman equation, that is a nonlinear partial differential equation, which is known to be hard or impossible to solve. Instead, the Hamilton-Jacobi-Bellman equation is replaced with an easy-solvable state-dependent Lyapunov matrix equation. We exploit a linear-like factorization of the underlying nonlinear system and a policy-iteration algorithm to yield a linear-like policy-iteration for nonlinear systems. The proposed control strategy solves optimal nonlinear control problems in an asymptotically exact, yet still linear-like manner. We prove optimality of the resulting solution and illustrate the results via four examples.
Moreschini A, Bin M, Astolfi A, et al., 2023, On ϱ-passivity, Pages: 8556-8561
We discuss passivity beyond continuous-time systems by highlighting several inconsistencies of the definition currently in use, for instance when applied to discrete-time systems, and by motivating the need for a new and more consistent notion. Hence, we propose a new definition, ϱ-passivity, that addresses the raised issues and that, as a result, is naturally applicable to a larger class of systems including discrete-time systems with non-zero relative degree. We show that, in line with the classical definition, ϱ-passivity is preserved under parallel and negative-feedback interconnection. These are preliminary results aimed at bridging passivity between different time domains, and taking the first step towards a more comprehensive and consistent passivity theory.
Chen K, Astolfi A, Parisini T, 2023, Active Nodes for Passivity and Finite-Gain Stability of Non-autonomous Networks, Pages: 3812-3817
This paper studies the role of a class of node systems with adjustable damping coefficients in the node dissipation inequalities, called the active nodes, for achieving passivity and finite-gain stability of network systems with external inputs and outputs. The paper first discusses the relation between the active nodes with passivity-type dissipation inequalities and those with L2-stability-type dissipation inequalities, especially focusing on how to transform one type into the other. Then, the paper proceeds to discuss the graph-theoretic condition on the locations of active nodes to achieve network passivity or finite-gain stability. Thereafter, a method for network reduction by exploiting active nodes is presented. Finally, a human-in-the-loop stabilization problem is solved for a network system by exploiting the results developed in the paper.
Casagrande D, Abdalla HMA, Astolfi A, 2023, A Note on the Realization of Nonlinear ODEs in Optimal Control Problems, Pages: 7468-7473
When in the differential equation describing the behaviour of a dynamical system the time derivative of the input is involved, a naive realization may mislead the application of the Pontryagin Maximum Principle for the solution of optimal control problems. We show that a suitable procedure to eliminate the time derivative of the input leads to a realization that provides more information on the existence and on the form of the solution.
Moreschini A, Simard JD, Astolfi A, 2023, Model Reduction for Linear Port-Hamiltonian Systems in the Loewner Framework, Pages: 9493-9498
The problem of model order reduction with assignment and preservation of port-Hamiltonian structure in the reduced order model is tackled in the Loewner framework. Given a set of right-tangential interpolation data, the (subset of) left-tangential interpolation data that allow for the construction of an interpolant possessing port-Hamiltonian structure is characterized. Conditions under which an interpolant retains the underlying port-Hamiltonian structure of the system generating the data are given by requiring a particular structure of the generalized observability matrix.
Franco E, Astolfi A, 2023, Energy shaping control of a class of underactuated mechanical systems with high-order actuator dynamics, European Journal of Control, Vol: 72, Pages: 1-13, ISSN: 0947-3580
In this work we present some new results on energy shaping control for underactuated mechanical systems with high-order actuator dynamics. To this end, we propose an extension of the Interconnection and damping assignment Passivity based control methodology to account for actuator dynamics. This brings the following new results: i) a potential and kinetic energy shaping and damping assignment procedure that yields two alternative controllers; ii) a potential energy shaping and damping assignment procedure for a narrower class of underactuated mechanical systems. The proposed approach is illustrated with numerical simulations on three examples: an Acrobot system with a series elastic actuator; a soft continuum manipulator actuated by electroactive polymers; a two-mass-spring system actuated by a DC motor.
Sassano M, Mylvaganam T, Astolfi A, 2023, Model-based policy iterations for nonlinear systems via controlled Hamiltonian dynamics, IEEE Transactions on Automatic Control, Vol: 68, Pages: 2683-2698, ISSN: 0018-9286
The infinite-horizon optimal control problem for nonlinear systems is studied. In the context of model-based, iterative learning strategies we propose an alternative definition and construction of the temporal difference error arising in Policy Iteration strategies. In such architectures the error is computed via the evolution of the Hamiltonian function (or, possibly, of its integral) along the trajectories of the closed-loop system. Herein the temporal difference error is instead obtained via two subsequent steps: first the dynamics of the underlying costate variable in the Hamiltonian system is steered by means of a (virtual) control input in such a way that the stable invariant manifold becomes externally attractive. Then, the distance-from-invariance of the manifold, induced by approximate solutions, yields a natural candidate measure for the policy evaluation step. The policy improvement phase is then performed by means of standard gradient descent methodsthat allows to correctly update the weights of the underlying functional approximator. The above architecture then yields an iterative (episodic) learning scheme based on a scalar, constant reward at each iteration, the value of which is insensitive to the length of the episode, as in the originalspirit of Reinforcement Learning strategies for discrete-time systems. Finally, the theory is validated by means of a numerical simulation involving an automatic flight control problem.
Dastjerdi AA, Astolfi A, HosseinNia SH, 2023, Frequency-domain stability methods for reset control systems, AUTOMATICA, Vol: 148, ISSN: 0005-1098
Gao J, Chaudhuri B, Astolfi A, 2023, Lyapunov-based transient stability analysis, IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 5099-5104, ISSN: 2576-2370
The paper presents an analytical control solution to the problem of transient stabilization of lossy multi-machine power systems. Firstly, a new form of control Lyapunov function candidates with a flexible potential-energy-like term is proposed. This is achieved mainly by introducing an auxiliary state that contributes to the derivation of a cross-term. Based on the Lyapunov function candidates, a new control law ensuring asymptotic stability of the desired closed-loop operating equilibrium is proposed. Finally, a case study on the model of a two-machine system to illustrate the effectiveness of the proposed control solution is presented.
Simard JD, Moreschini A, Astolfi A, 2023, Moment Matching for Nonlinear Systems of Second-Order Equations, Pages: 4978-4983, ISSN: 0743-1546
In this paper we consider the problem of constructing nonlinear systems of second-order equations that achieve moment matching. In particular, necessary and sufficient conditions are given for which a system of second-order equations achieves moment matching, and a family of systems of second-order equations achieving moment matching is directly constructed by extracting it, via particular choices of the free mappings, from a parameterization of all systems achieving moment matching. The results are specialized for the scenario in which the signal generator is a linear system. Finally, the results of the paper are demonstrated by constructing reduced order models of a two link robotic manipulator in the second-order equation form.
Mao M, Astolfi A, 2023, Optimal Dynamic Economic Dispatch for Microgrid Using Pontryagin's Minimum Principle, ISSN: 1944-9925
This paper proposes an innovative solution for the day-ahead optimal dynamic economic dispatch problem based on Pontryagin's Minimum Principle (PMP). The PMP is used to compute the optimal power outputs for a system with two online generating units over a 24 h period by minimizing the total cost and satisfying the associated equality and inequality constraints. Numerical simulations are conducted on a case study: the results show that the proposed day-ahead optimal dynamic economic dispatch solution satisfies the constraints of the supply-demand balance and the capacity and output threshold in real time, and the proposed PMP solution is very competitive compared with reported representative methods in yielding low fuel costs along with short execution time.
Chen K, Astolfi A, 2023, Active Nodes of Network Systems with Sum-type Dissipation Inequalities, IEEE Transactions on Automatic Control, ISSN: 0018-9286
This paper studies a small-gain-like analysis and control synthesis tool for large-scale interconnected dynamical systems (networks). By exploiting the structure of the interconnection one can derive (or enforce it via control synthesis) an algebraic condition (the small-gain-like condition) to allow the construction of a network storage function with a network dissipation inequality in a desired form (the small-gain-like property), which can be further used for establishing convergence or stability properties. Small-gain-like conditions, for systems with quadratic, general-form nonlinear, and parametrized supply rates, respectively, are derived and interpreted using the underlying graph. This allows enforcing such a condition via the design of a class of controlled nodes, called active nodes, provided their locations satisfy a graph-based condition. The paper then proceeds to discuss control synthesis methods using the notion of active nodes, including the placement, the parameter computation, and the adaptation of the active nodes. Finally an example of public-health-related control for interconnected settlements, to demonstrate the implementation of the active-node-based scheme, is presented.
Bhattacharjee D, Astolfi A, 2023, Closed-Loop Model Reduction by Moment Matching for Linear Systems, Pages: 4954-4959, ISSN: 0743-1546
We study the model reduction by moment matching problem for linear systems in a closed-loop configuration. First we show that the moments of a linear system can be expressed in a form that is independent of the structure of the signal generator. Then we define a class of reduced-order models that can replicate the steady-state response of the original system from input-output data. Finally, we demonstrate the applicability of the results using two simple numerical examples.
Tarantino L, Astolfi A, Sassano M, 2023, On the Effect of the Presence of an Opponent in a Class of LQ Differential Games, Pages: 6000-6005, ISSN: 0743-1546
The aim of this paper is to assess the effect of the presence of an opponent in a class of finite-horizon differential games described by scalar linear differential equations and quadratic cost functionals in which the state is penalized only at the terminal time. The contribution of the other player is quantitatively characterized by comparing the solutions of the underlying Riccati differential equations for the optimal control (in the absence of the opponent) and of the differential game. In the case of open-loop Nash equilibria, this effect can be characterized in closed form, since an analytic expression for the solutions of the coupled asymmetric differential Riccati equations can be computed. For feedback Nash equilibria a closed-form solution to the related coupled symmetric differential Riccati equations cannot be determined. Therefore an estimate of the solution is provided by relying on a functional approximation approach, allowing to characterize the effect of the presence of an opponent also in this setting.
Lee JG, Astolfi A, 2023, Realization from Moments: The Linear Case, Pages: 1486-1491, ISSN: 0743-1546
By exploiting the time-domain notion of moments we recover a time-domain counterpart of the fact that a certain number of steady-state responses is sufficient to realize a linear system. This may pave the way to a realization theory for nonlinear systems based on their steady-state responses.
Moreschini A, Simard JD, Astolfi A, 2023, Model Reduction in the Loewner Framework for Second-Order Network Systems On Graphs, Pages: 6713-6718, ISSN: 0743-1546
This paper studies the model reduction problem in the Loewner framework for second-order network systems evolving on graphs. The selection of particular sets of tangential interpolation data allows constructing reduced order models which interpolate the underlying network system while preserving the second-order structure of the system. The conditions that the tangential interpolation data must satisfy are established on the basis of the block structure of the Loewner matrices. We use this result to link the Loewner matrices to the cluster matrix gained by partitioning the graph associated with the underlying model. Finally, we provide an illustrative example to validate the obtained results.
Chen K, Astolfi A, 2023, On the Adaptive Tracking Problem of Time -Varying Systems using the Congelation for Variables Method, 12th IFAC Symposium on Nonlinear Control Systems (NOLCOS), Publisher: ELSEVIER, Pages: 13-18, ISSN: 2405-8963
Simard JD, Moreschini A, Astolfi A, 2023, Parameterization of All Moment Matching Interpolants, European Control Conference (ECC), Publisher: IEEE
Franco E, Astolfi A, 2022, Energy shaping control of underactuated mechanical systems with fluidic actuation, International Journal of Robust and Nonlinear Control, Vol: 32, Pages: 10011-10028, ISSN: 1049-8923
Energy shaping is a remarkably effective control strategy which can be applied to a wide range of systems, including underactuated mechanical systems. However, research in this area has generally neglected actuator dynamics. While this is often appropriate, it might result in degraded performance in the case of fluidic actuation. In this work we present some new results on energy shaping control for underactuated mechanical systems for which the control action is mediated by a pressurized ideal fluid. In particular, we introduce an extended multi-step energy shaping and damping-assignment controller design procedure that builds upon the Interconnection-and-damping-assignment Passivity-based-control methodology in a modular fashion to account for the pressure dynamics of the fluid. Stability conditions are assessed with a Lyapunov approach, the effect of disturbances is discussed, and the case of redundant actuators is illustrated. The proposed approach is demonstrated with numerical simulations for a modified version of the classical ball-on-beam example, which employs two identical cylinders, either hydraulic or pneumatic, to actuate the beam.
Sassano M, Mylvaganam T, Astolfi A, 2022, On the analysis of open-loop Nash equilibria admitting a feedbacksynthesis in nonlinear differential games, Automatica, Vol: 142, Pages: 1-8, ISSN: 0005-1098
Open-loop Nash equilibrium strategies for differential games described by nonlinear, input-affine, systems and cost functionals that are quadratic with respect to the control input are studied. First it is shown that the computation of such strategies hinges upon the solution of a system of nonlinear, time-varying, partial differential equations (PDEs) obtained by building on arguments borrowed from Pontryagin’s Minimum Principle and combined with Dynamic Programming considerations. Then, by relying on a state/costate interpretation of the above characterization, a feedback synthesis of the underlying open-loop strategy is obtained by solving linear first-order PDEs that ensure invariance of certain submanifolds in the state-space of the extended state/costate dynamics. These PDEs are the nonlinear counterpart of the well-known asymmetric Algebraic Riccati Equations arising in the study of linear quadratic Nash games.
Giannari AG, Astolfi A, 2022, Model design for networks of heterogeneous Hodgkin-Huxley neurons, Neurocomputing, Vol: 496, Pages: 147-157, ISSN: 0925-2312
We present a novel modular, scalable and adaptable modelling framework to accurately model neuronal networks composed of neurons with different dynamic properties and distinct firing patterns based on a control-inspired feedback structure. We consider three important classes of neurons: inhibitory Fast spiking neurons, excitatory regular spiking with adaptations neurons, and excitatory intrinsic bursting neurons. We also take into consideration two basic means of neuronal interconnection: electrical and chemical synapses. By separating the neuronal dynamics from the network dynamics, we have developed a fully flexible feedback structure that can be further augmented to incorporate additional types of neurons and/or synapses. We use an augmented version of the Hodgkin–Huxley model to describe the individual neuron dynamics and graph theory to define the network structure. We provide simulation results for small fundamental neuron motifs as well as bigger neuronal networks and we verify the accuracy, flexibility and scalability of the proposed method. Therefore, we provide the basis for a comprehensive modelling framework that is able to imitate the dynamics of individual neurons and neuronal networks and is able to replicate basic normal brain function. The structure of the proposed framework is ideal for applications of control and optimization methods both for modelling the effect of pharmacological substances as well as for modelling diseased neuron and network conditions.
Li A, Astolfi A, Liu M, 2022, Attitude regulation with bounded control in the presence of large disturbances with bounded moving average, IEEE/CAA Journal of Automatica Sinica, Vol: 9, Pages: 834-846, ISSN: 2329-9266
The attitude regulation problem with bounded control for a class of satellites in the presence of large disturbances, with bounded moving average, is solved using a Lyapunov-like design. The analysis and design approaches are introduced in the case in which the underlying system is an integrator and are then applied to the satellite attitude regulation problem. The performance of the resulting closed-loop systems are studied in detail and it is shown that trajectories are ultimately bounded despite the effect of the persistent disturbance. Simulation results on a model of a small satellite subject to large, but bounded in moving average, disturbances are presented.
Tziovani L, Hadjidemetriou L, Kolios P, et al., 2022, Energy management and control of photovoltaic and storage systems in active distribution grids, IEEE Transactions on Power Systems, Vol: 37, Pages: 1956-1968, ISSN: 0885-8950
The evolution of power distribution grids from passive to active systems creates reliability and efficiency challenges to the distribution system operators. In this paper, an energy management and control scheme for managing the operation of an active distribution grid with prosumers is proposed. A multi-objective optimization model to minimize (i) the prosumers electricity cost and (ii) the cost of the grid energy losses, while guaranteeing safe and reliable grid operation is formulated. This is done by determining the active and reactive power set-points of the photovoltaic and storage systems integrated in the grid buildings. The resulting optimization model is non-convex, thus a convex second-order cone program is developed by appropriately relaxing the non-convex constraints which yields optimal results in most operating conditions. The convexified model is further utilized to develop an algorithm that yields feasible solutions to the non-convex problem under any operating conditions. Moreover, a second novel algorithm to find the operating point that provides fairness between the prosumers and the grid costs is proposed. Simulation results demonstrate the effectiveness and superiority of the proposed scheme in managing an industrial distribution grid compared to a self-consumption approach.
Bobtsov A, Yi B, Ortega R, et al., 2022, Generation of new exciting regressors for consistent on-line estimation of unknown constant parameters, IEEE Transactions on Automatic Control, Vol: 67, Pages: 4746-4753, ISSN: 0018-9286
The problem of estimating constant parameters from a standard vector linear regression equation in the absence of sufficient excitation in the regressor is addressed. The first step to solve the problem consists in transforming this equation into a set of scalar ones using the well-known dynamic regressor extension and mixing technique. Then a novel procedure to generate new scalar exciting regressors is proposed. The superior performance of a classical gradient estimator using this new regressor, instead of the original one, is illustrated with comprehensive simulations.
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