Publications
53 results found
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.
Mylvaganam T, Astolfi A, 2015, Control of Microgrids Using a Differential Game Theoretic Framework, Conference on Decision and Control
Mylvaganam T, Astolfi A, 2015, A differential game approach to formation control for a team of agents with one leader, American Control Conference
Mylvaganam T, Sassano M, Astolfi A, 2015, Constructive epsilon-nash equilibria for nonzero-sum differential games, IEEE Transactions on Automatic Control, Vol: 60, Pages: 950-965, ISSN: 0018-9286
In this paper, a class of infinite-horizon, nonzero-sum differential games and their Nash equilibria are studied and the notion of ε α -Nash equilibrium strategies is introduced. Dynamic strategies satisfying partial differential inequalities in place of the Hamilton-Jacobi-Isaacs partial differential equations associated with the differential games are constructed. These strategies constitute (local) ε α -Nash equilibrium strategies for the differential game. The proposed methods are illustrated on a differential game for which the Nash equilibrium strategies are known and on a Lotka-Volterra model, with two competing species. Simulations indicate that both dynamic strategies yield better performance than the strategies resulting from the solution of the linear-quadratic approximation of the problem.
Mylvaganam T, Bauso D, Astolfi A, 2014, Mean-field games and two-point boundary value problems, Conference on Decision and Control
Bauso D, Mylvaganam T, Astolfi A, 2014, Transient stability of a power grid via robust mean-field games, Pages: 9-14
The transient stability of a power grid characterized by regional aggregations is studied via robust mean-field games. The model involves a set of coupled Hamilton-Jacobi-Bellman-Isaacs equations and Fokker-Planck-Kolmogorov equations. The former describe the behavior of each single machine, while the latter model the population behavior in aggregate form. The model sheds light on a multi-scale phenomenon including a fast synchronization within the same population and slow inter-cluster oscillations between geographically sparse grids.
Mylvaganam T, Astolfi A, 2014, Approximate solutions to a class of nonlinear Stackelberg differential games, Conference on Decision and Control
Bauso D, Mylvaganam T, Astolfi A, 2014, A Two-Point Boundary Value Formulation of a Mean-Field Crowd-Averse Game, IFAC World Congress
Bauso D, Mylvaganam T, Astolfi A, 2014, Approximate solutions for crowd-averse robust mean-field games, 13th European Control Conference (ECC), Publisher: IEEE, Pages: 1217-1222
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- Citations: 4
Mylvaganam T, Astolfi A, 2014, Approximate Optimal Monitoring, 13th European Control Conference (ECC), Publisher: IEEE, Pages: 1199-1204
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- Citations: 10
Mylvaganam T, Sassano M, Astolfi A, 2014, A Constructive Differential Game Approach to Collision Avoidance in Multi-Agent Systems, American Control Conference, Publisher: IEEE, Pages: 311-316, ISSN: 0743-1619
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- Citations: 15
Mylvaganam T, Sassano M, Astolfi A, 2013, Approximate Solutions to a Class of Nonlinear Differential Games Using a Shared Dynamic Extension, European Control Conference (ECC), Publisher: IEEE, Pages: 710-715
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- Citations: 3
Mylvaganam T, Fobelets K, Jaimoukha I, 2012, Optimal Design of Nanowire Array Based Thermocouple, 9th European Conference on Thermoelectrics (ECT), Publisher: AMER INST PHYSICS, Pages: 17-20, ISSN: 0094-243X
Mylvaganam T, Astolfi A, 2012, Approximate Optimal Monitoring: Preliminary Results, American Control Conference (ACC), Publisher: IEEE COMPUTER SOC, Pages: 4745-4750, ISSN: 0743-1619
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- Citations: 9
Mylvaganam T, Sassano M, Astolfi A, 2012, Approximate Solutions to a Class of Nonlinear Differential Games, 51st IEEE Annual Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 6489-6494, ISSN: 0743-1546
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- Citations: 4
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