## Publications

42 results found

Sassano M, Mylvaganam T, Astolfi A, 2022, Model-based Policy Iterations for nonlinear systems via controlled Hamiltonian dynamics, *IEEE Transactions on Automatic Control*, ISSN: 0018-9286

Sassano M, Mylvaganam T, Astolfi A, 2022, On the analysis of open-loop Nash equilibria admitting a feedbacksynthesis in nonlinear differential games, *Automatica*, 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.

Nortmann B, Mylvaganam T, 2022, Data-driven cost representation for optimal control and its relevance toa class of asymmetric linear quadratic dynamic games, 2022 European Control Conference, Publisher: IEEE

Motivated by the fact that optimal performance criteria are often not known a priori, we present an approach to represent quadratic objective functions in the context of optimal control directly using finite, open-loop, non-optimaldata trajectories of the state, input and a performance variable. Combined with a data-based representation of linear time-invariant systems this allows us to solve linear quadratic regulator problems with unknown dynamics and unknown cost matrices via data-dependent convex programmes. We show that this result is relevant to a specific class of linear quadratic games, in which one player is missing information regarding the control objectives of the other players and/or the system dynamics. The applicability of the presented results is highlighted via an example concerning human-robot interaction.

Bai H, Mylvaganam T, Scarciotti G, 2022, Model reduction for quadratic-bilinear systems using nonlinear moments, European Control Conference 2022, Publisher: IEEE

We propose a steady-state based moment matchingmethod for model reduction of quadratic-bilinear systems.Considering a large-scale quadratic-bilinear system possessing astable equilibrium at the origin, the goal of this paper is to designa reduced order model which maintains certain properties of theoriginal system. More precisely, it is required that the reducedorder model also possesses a stable equilibrium at the originand, further, it may be desirable that its relative degree matchesthat of the original system. We use the notion of nonlinearmoments and exploit a formal power expansion to solve thisproblem. Two different families of reduced order models areprovided in this paper and their use is demonstrated on anillustrative numerical example.

Cappello D, Mylvaganam T, 2021, Distributed differential games for control of multi-agent systems, *IEEE Transactions on Control of Network Systems*, ISSN: 2325-5870

Motivated by the challenges arising in thefield of multi-agent systems (MAS) control, we consider linear heterogenous MAS subject to local communication andinvestigate the problem of designing distributed controllersfor such systems. We provide a game theoretic frameworkfor systematically designing distributed controllers, takinginto account individual objectives of the agents and theirpossibly incomplete knowledge of the MAS. Linear statefeedback control laws are obtained via the introduction of adistributed differential game, namely the combination of local non-cooperative differential games, which are solved ina decentralised fashion. Conditions for stability of the MASare provided for the special cases of acyclic and stronglyconnected communication graph topologies. These resultsare then exploited to provide stability conditions for general graph topologies. The proposed framework is demonstrated on a tracking synchronisation problem associatedwith the design of a distributed secondary voltage controller for microgrids and on a numerical example.

Sassano M, Mylvaganam T, Astolfi A, 2021, Optimal control for nonlinear systems driven by a known exogenous signal, *IEEE Transactions on Automatic Control*, ISSN: 0018-9286

We consider optimal control problems forcontinuous-time systems with time-dependent dynamics,in which the time-dependence arises from the presence of aknown exogenous signal. The problem has been elegantlysolved in the case of linear input-affine systems, for whichit has been shown that the solution has a remarkablestructure: it is given by the sum of two contributions; a statefeedback, which coincides with the unperturbed optimalcontrol law, and a purely feedforward term in charge ofcompensating the effect of the exogenous signal. The objective of this note is to extend the above result to nonlinearinput-affine systems. It is shown that, while some of therelevant features of the linear case indeed rely heavily onlinearity and are not preserved in the nonlinear setting, several structural claims can be proved also in the nonlinearcase.

Sassano M, Mylvaganam T, Astolfi A, 2021, Infinite-horizon optimal control problems for nonlinear systems, IEEE Conference on Decision and Control (CDC 2021), Publisher: IEEE

Infinite-horizon optimal control problems for non-linear systems are studied and discussed. First, we thoroughlyrevisit the formulation of the underlying dynamic optimisation problem together with the classical results providing itssolution. Then, we consider two alternative methods to con-struct solutions (or approximations there of) of such problems, developed in recent years, that provide theoretical insights as well as computational benefits. While the considered methods are mostly based on tools borrowed from the theories of Dynamic Programming and Pontryagin’s Minimum Principles, or a combination of the two, the proposed control design strategies yield innovative, systematic and constructive methods to provide exact or approximate solutions of nonlinear optimal control problems. Interestingly, similar ideas can be extended also to linear and nonlinear differential games, namely dynamic optimisation problems involving several decision-makers. Due their advantages in terms of computational complexity, the considered methods have found several applications. An example ofthis is provided, through the consideration of the multi-agent collision avoidance problem, for which both simulations and experimental results are provided.

Mylvaganam T, Sassano M, Astolfi A, 2021, Nonlinear optimal control of a ballast-stabilized floating wind turbine viaexternally stabilised Hamiltonian dynamics, IEEE Conference on Decision and Control, Publisher: IEEE

We consider the problem of controlling a ballast-stabilized offshore wind turbine. We formulate an optimal control problem with the objective of maximising the power generation while minimising structural fatigue of the wind turbine. Due to the nonlinear nature of the model, obtaining a solution to the above control task poses a severe challenge.Recalling that solutions of the optimal control problem are characterised by a certain (unstable) invariant manifold of the underlying Hamiltonian system, we demonstrate that nonlinear control strategies which approximate the solution of the optimalcontrol problem can be constructed through the introduction of an externally stabilised Hamiltonian system. This observation enables the construction of an algorithm to compute (with rel-atively low computational complexity) an approximate solution of the optimal control problem, without ignoring nonlinearities in the control design. This approach has several benefits, asdemonstrated via simulations on a ballast-stabilized offshore wind turbine.

Cappello D, Garcin S, Mao Z,
et al., 2021, A hybrid controller for multi-agent collision avoidance via a differential game formulation, *IEEE Transactions on Control Systems Technology*, Vol: 29, Pages: 1750-1757, ISSN: 1063-6536

We consider the multi-agent collision avoidance problemfor a team of wheeled mobile robots. Recently, a local solutionto this problem, based on a game theoretic formulation, has beenprovided and validated via numerical simulations. Due to itslocal nature the result is not well-suited for online application.In this paper we propose a novel hybrid implementation of thecontrol inputs that yields a control strategy suited for the onlinenavigation of mobile robots. Moreover, subject to a certain dwelltime condition, the resulting trajectories are globally convergent.The control design is demonstrated both via simulations andexperiments.

Cappello D, Mylvaganam T, 2021, Approximate Nash equilibrium solutions of linear quadratic differential games, 21st IFAC World Congress, 2020, Publisher: IFAC Secretariat, Pages: 6685-6690, ISSN: 2405-8963

It is well known that finding Nash equilibrium solutions of nonzero-sum differential games is a challenging task. Focusing on a class of linear quadratic differential games, we consider three notions of approximate feedback Nash equilibrium solutions and provide a characterisation of these in terms of matrix inequalities which constitute quadratic feasibility problems. These feasibility problems are then recast first as bilinear feasibility problems and finally as rank constrained optimisation problems, i.e. a class of static problems frequently encountered in control theory.

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.

Wrzos-Kaminska M, Mylvaganam T, Pettersen KY, et al., 2020, Collision avoidance using mixed H2/H∞ control for an articulated intervention-AUV, European Control Conference, Publisher: IEEE, Pages: 881-888

In this paper we consider the problem of mixedH2/H∞control to combine optimal and robust control for a dou-ble integrator system with nonlinear performance variables, andwe apply this to control an articulated intervention autonomousunderwater vehicle (AIAUV). The AIAUV has an articulatedbody like a snake robot, is equipped with thrusters, and canbe used as a free-floating underwater manipulator. The objectiveis to control the joints of the AIAUV to desired setpoints withoutcausing collisions between links or with obstacles in the envi-ronment. The mixedH2/H∞problem is viewed as a differentialgame, and a set of matrix equations is solved in order to constructan approximate solution to the problem for a system describedby double integrator dynamics and with nonlinear performancevariables. A feedback linearising controller is derived to obtainthe double integrator dynamics for the joints of the AIAUV, andthe solution found for the mixedH2/H∞control problem isapplied to the resulting system. Simulations demonstrate thatcollisions between links of the manipulator are successfullyavoided also in the presence of parameter uncertainties whileregulating the joints to the desired setpoints, and the methodcan easily be extended to include collision avoidance with staticand dynamic obstacles in the environment.

Nortmann B, Mylvaganam T, 2020, Data-Driven Control of Linear Time-Varying Systems, 59th IEEE Conference on Decision and Control

An identification-free control design strategy fordiscrete-time linear time-varying systems with unknown dynamics is introduced. The closed-loop system (under statefeedback) is parametrised with data-dependent matrices obtained from an ensemble of input-state trajectories collectedoffline. This data-driven system representation is used to classifycontrol laws yielding trajectories which satisfy a certain boundand to solve the linear quadratic regulator problem - both usingdata-dependent linear matrix inequalities only. The results areillustrated by means of a numerical example.

Cappello D, Mylvaganam T, 2020, A game theoretic framework for distributed control of multi-agent systems with acyclic communication topologies, 58th IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 1-6

A multi-agent system consisting of hetero-geneous agents, described by nonlinear dynamics andwith inter-agent communication characterised by a directedacyclic graph, is considered in this paper. A frameworkfor designing distributed control strategies obtained viathe combination oflocal non-cooperative differential gamesis provided. The resulting dynamic (local) state-feedbackcontrol laws can be computed offline and in a decentralisedmanner. Conditions for ensuring stability of the overallclosed-loop system are provided, before the proposed gametheoretic framework is applied to a formation control problem.

Mylvaganam T, Sassano M, 2020, Disturbance attenuation by measurement feedback in nonlinear systems via immersion and algebraic conditions, *IEEE Transactions on Automatic Control*, Vol: 65, Pages: 854-860, ISSN: 0018-9286

In this paper we consider the problem ofdis-turbance attenuation with internal stabilityfor nonlinear,input-affine systems via measurement feedback. The solu-tion to the above problem has been provided, three decadesago, in terms of the solution to a system of coupled non-linear, first-order partial differential equations (PDEs). Asa consequence, despite the rather elegant characterizationof the solution, the presence of PDEs renders the controldesign synthesis almost infeasible in practice. Therefore, tocircumvent such a computational bottle-neck, in this paperwe provide a novel characterization of the exact solution tothe problem that does not hinge upon theexplicitcompu-tation of the solution to any PDE. The result is achieved byconsidering theimmersionof the nonlinear dynamics intoan extended system for which locally positive definite func-tions solving the required PDEs may be directly provided inclosed-formby relying only on the solutions to Riccati-like,state-dependent, algebraic matrix equations.

Mylvaganam T, Possieri C, Sassano M, 2019, Global stabilization of nonlinear systems via hybrid implementation of dynamic continuous-time local controllers, *Automatica*, Vol: 106, Pages: 401-405, ISSN: 0005-1098

Given a continuous-time system and a dynamic control law such that the closed-loop system satisfies standard Lyapunov conditions for local asymptotic stability, we propose a hybrid implementation of the continuous-time control law. We demonstrate that subject to certain “relaxed” conditions, the hybrid implementation yields global asymptotic stability properties. These conditions can be further specialized to yield local/regional asymptotic stability with an enlarged basin of attraction with respect to the original control law. Two illustrative numerical examples are provided to demonstrate the main results.

Cappello D, Mylvaganam T, 2019, Distributed control of multi-agent systems via linear quadratic differential games with partial information, 57th IEEE Conference on Decision and Control, Publisher: Institute of Electrical and Electronics Engineers, ISSN: 0191-2216

A multi-agent system consisting of linear het-erogeneous agents is considered in this paper. Distributedcontrol laws for each agent are designed through theformulation of linear quadratic differential games withpartial information. Exact and approximate solutions for thedifferential games are provided before the problem of for-mation control with limited communication is considered.A numerical example is provided to illustrate the theory.

Scarciotti G, Mylvaganam T, 2019, Approximate infinite-horizon optimal control for stochastic systems, 57th IEEE Conference on Decision and Control (CDC), Publisher: IEEE

The policy of an optimal control problem fornonlinear stochastic systems can be characterized by a second-order partial differential equation for which solutions are notreadily available. In this paper we provide a systematic methodfor obtaining approximate solutions for the infinite-horizonoptimal control problem in the stochastic framework. Themethod is demonstrated on an illustrative numerical examplein which the control effort is not weighted, showing that thetechnique is able to deal with one of the most striking featuresof stochastic optimal control.

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.

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.

Cristofaro A, Mylvaganam T, Bauso D, 2018, A two-point boundary value formulation of a class of multi-population mean-field games, IEEE Conference on Control Technology and Applications, Publisher: IEEE

We consider a multi-agent system consisting ofseveral populations. The interaction between large populationsof agents seeking to regulate their state on the basis of thedistribution of the neighboring populations is studied. Examplesof such interactions can typically be found in social networksand opinion dynamics, where heterogeneous agents or clustersare present and decisions are influenced by individual objectivesas well as by global factors. In this paper, such a problemis posed as a multi-population mean-field game, for whichsolutions depend on two partial differential equations, namelythe Hamilton-Jacobi-Bellman equation and the Fokker-Planck-Kolmogorov equation. The case in which the distributions ofagents are sums of polynomials and the value functions arequadratic polynomials is considered. It is shown that for thisclass of problems, which can be considered as approximations ofmore general problems, a set of ordinary differential equations,with two-point boundary value conditions, can be solved inplace of the more complicated partial differential equationscharacterizing the solution of the multi-population mean-fieldgame.

Mylvaganam T, Sassano M, 2018, Autonomous collision avoidance for wheeled mobile robots using a differential game approach, *European Journal of Control*, Vol: 40, Pages: 53-61, ISSN: 0947-3580

A multi-agent system consisting of N wheeled mobile robots is considered. The robots are modeled by unicycle dynamics and the multi-agent collision avoidance problem, which lies in steering each robot from its initial position to a desired target position while avoiding collisions with obstacles and other agents is considered. The problem is solved in two steps. First, exploiting a differential game formulation, collision-free trajectories are generated for virtual agents satisfying single-integrator dynamics. Second, the previous step is used to construct dynamic feedback strategies for the wheeled mobile robots satisfying unicycle dynamics which ensure each of the robots reaches its target without collisions occurring. A numerical study of the proposed methodology is provided through a series of simulations.

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.

Mylvaganam T, 2017, A Game Theoretic Approach to Distributed Control of Homogeneous Multi-Agent Systems, 56th IEEE Conference on Decision and Control, Publisher: IEEE

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.

Mylvaganam T, Sassano M, 2017, Approximate optimal control via measurement feedback for a class of nonlinear systems, 20th IFAC World Congress, Publisher: IFAC Secretariat, Pages: 15391-15396, ISSN: 2405-8963

The approximate optimal control problem via measurement feedback for input-affine nonlinear systems is considered in this paper. In particular, a systematic method is provided for constructing stabilising output feedbacks that approximate - with the optimality loss explicitly quantifiable - the solution of the optimal control problem by requiring only the solution of algebraic equations. In fact, the combination of a classical state estimate with an additional dynamic extension permits the construction of a dynamic control law, without involving the solution of any partial differential equation or inequality. Moreover, provided a given sufficient condition is satisfied, the dynamic control law is guaranteed to be (locally) stabilising. A numerical example illustrating the method is provided.

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.

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.

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.

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.

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