Publications
46 results found
Kalise D, Saluzzi L, Sergey D, 2023, Data-driven tensor train gradient cross approximation for Hamilton-Jacobi-Bellman equations, SIAM Journal on Scientific Computing, Vol: 45, Pages: A2153-A2184, ISSN: 1064-8275
A gradient-enhanced functional tensor train cross approximation method for the resolution of the Hamilton–Jacobi–Bellman (HJB) equations associated with optimal feedback control of nonlinear dynamics is presented. The procedure uses samples of both the solution of the HJB equation and its gradient to obtain a tensor train approximation of the value function. The collection of the data for the algorithm is based on two possible techniques: Pontryagin Maximum Principle and State-Dependent Riccati Equations. Several numerical tests are presented in low and high dimension showing the effectiveness of the proposed method and its robustness with respect to inexact data evaluations, provided by the gradient information. The resulting tensor train approximation paves the way towards fast synthesis of the control signal in real-time applications.
Wells CA, Kalise D, Nichols NK, et al., 2023, The role of airspeed variability in fixed-time, fuel-optimal aircraft trajectory planning, Optimization and Engineering, Vol: 24, Pages: 1057-1087, ISSN: 1389-4420
With the advent of improved aircraft situational awareness and the need for airlines to reduce their fuel consumption and environmental impact whilst adhering to strict timetables, fixed-time, fuel-optimal routing is vital. Here, the aircraft trajectory planning problem is addressed using optimal control theory. Two variants of a finite horizon optimal control formulation for fuel burn minimization are developed, subject to arrival constraints, an aerodynamic fuel-burn model, and a data-driven wind field. In the first variant, the control variable is expressed as a set of position-dependent aircraft headings, with the optimal control problem solved through a reduced gradient approach at a range of fixed airspeeds. The fuel optimal result is taken as the lowest fuel use recorded. In the second variant, both heading angle and airspeed are controlled. Results from three months of simulated flight routes between London and New York show that permitting optimised en-route airspeed variations leads to fuel savings of 0.5% on an average day (and up to 4% on certain days), compared with fixed airspeed flights. We conclude that significant fuel savings are possible if airspeeds are allowed to vary en route to take optimal advantage of the wind field.
Alla A, Kalise D, Simoncini V, 2023, State-dependent Riccati equation feedback stabilization for nonlinear PDEs, Advances in Computational Mathematics, Vol: 49, ISSN: 1019-7168
The synthesis of suboptimal feedback laws for controlling nonlinear dynamics arising from semi-discretized PDEs is studied. An approach based on the State-dependent Riccati Equation (SDRE) is presented for 2 and ∞ control problems. Depending on the nonlinearity and the dimension of the resulting problem, offline, online, and hybrid offline-online alternatives to the SDRE synthesis are proposed. The hybrid offline-online SDRE method reduces to the sequential solution of Lyapunov equations, effectively enabling the computation of suboptimal feedback controls for two-dimensional PDEs. Numerical tests for the Sine-Gordon, degenerate Zeldovich, and viscous Burgers’ PDEs are presented, providing a thorough experimental assessment of the proposed methodology.
Kalise D, Sharma A, Tretyakov M, 2023, Consensus based optimization via jump-diffusion stochastic differential equations, Mathematical Models and Methods in Applied Sciences (M3AS), Vol: 33, Pages: 289-339, ISSN: 0218-2025
We introduce a new consensus-based optimization (CBO) method where an interacting particle system is driven by jump-diffusion stochastic differential equations (SDEs). We study well-posedness of the particle system as well as of its mean-field limit. The major contributions of this paper are proofs of convergence of the interacting particle system towards the mean-field limit and convergence of a discretized particle system towards the continuous-time dynamics in the mean-square sense. We also prove convergence of the mean-field jump-diffusion SDEs towards global minimizer for a large class of objective functions. We demonstrate improved performance of the proposed CBO method over earlier CBO methods in numerical simulations on benchmark objective functions.
King AJ, Portugal SJ, Strömbom D, et al., 2023, Biologically inspired herding of animal groups by robots, Methods in Ecology and Evolution, Vol: 14, Pages: 479-486, ISSN: 2041-210X
A single sheepdog can bring together and manoeuvre hundreds of sheep from one location to another. Engineers and ecologists are fascinated by this sheepdog herding because of the potential it provides for ‘bio-herding’: a biologically inspired herding of animal groups by robots. Although many herding algorithms have been proposed, most are studied via simulation.There are a variety of ecological problems where management of wild animal groups is currently impossible, dangerous and/or costly for humans to manage directly, and which may benefit from bio-herding solutions.Unmanned aerial vehicles (UAVs) now deliver significant benefits to the economy and society. Here, we suggest the use of UAVs for bio-herding. Given their mobility and speed, UAVs can be used in a wide range of environments and interact with animal groups at sea, over the land and in the air.We present a potential roadmap for achieving bio-herding using a pair of UAVs. In our framework, one UAV performs ‘surveillance’ of animal groups, informing the movement of a second UAV that herds them. We highlight the promise and flexibility of a paired UAV approach while emphasising its practical and ethical challenges. We start by describing the types of experiments and data required to understand individual and collective responses to UAVs. Next, we describe how to develop appropriate herding algorithms. Finally, we describe the integration of bio-herding algorithms into software and hardware architecture.
Albi G, Bicego S, Kalise D, 2022, Supervised learning for kinetic consensus control, 25th International Symposium on Mathematical Theory of Networks and Systems, Publisher: Elsevier BV, Pages: 103-108, ISSN: 2405-8963
In this paper, how to successfully and efficiently condition a target population of agents towards consensus is discussed. To overcome the curse of dimensionality, the mean field formulation of the consensus control problem is considered. Although such formulation is designed to be independent of the number of agents, it is feasible to solve only for moderate intrinsic dimensions of the agents space. For this reason, the solution is approached by means of a Boltzmann procedure, i.e. quasi-invariant limit of controlled binary interactions as approximation of the mean field PDE. The need for an efficient solver for the binary interaction control problem motivates the use of a supervised learning approach to encode a binary feedback map to be sampled at a very high rate. A gradient augmented feedforward neural network for the Value function of the binary control problem is considered and compared with direct approximation of the feedback law.
Borovykh A, Kalise D, Laignelet A, et al., 2022, Data-driven initialization of deep learning solvers for Hamilton-Jacobi-Bellman PDEs, IFAC-PapersOnLine, Vol: 55, Pages: 168-173, ISSN: 2405-8963
A deep learning approach for the approximation of the Hamilton-Jacobi-Bellman partial differential equation (HJB PDE) associated to the Nonlinear Quadratic Regulator (NLQR) problem. A state-dependent Riccati equation control law is first used to generate a gradient-augmented synthetic dataset for supervised learning. The resulting model becomes a warm start for the minimization of a loss function based on the residual of the HJB PDE. The combination of supervised learning and residual minimization avoids spurious solutions and mitigate the data inefficiency of a supervised learning-only approach. Numerical tests validate the different advantages of the proposed methodology.
Dolgov S, Kalise D, Saluzzi L, 2022, Optimizing semilinear representations for State-dependent Riccati Equation-based feedback control, 25th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Publisher: ELSEVIER, Pages: 510-515, ISSN: 2405-8963
An optimized variant of the State Dependent Riccati Equations (SDREs) approach for nonlinear optimal feedback stabilization is presented. The proposed method is based on the construction of equivalent semilinear representations associated to the dynamics and their affine combination. The optimal combination is chosen to minimize the discrepancy between the SDRE control and the optimal feedback law stemming from the solution of the corresponding Hamilton Jacobi Bellman (HJB) equation. Numerical experiments assess effectiveness of the method in terms of stability of the closed-loop with near-to-optimal performance.
Carrillo JA, Kalise D, Rossi F, et al., 2022, Controlling swarms toward flocks and mills, SIAM Journal on Control and Optimization, Vol: 60, Pages: 1863-1891, ISSN: 0363-0129
Self-organization and control around flocks and mills is studied for second-order swarming systems involving self-propulsion and potential terms. It is shown that through the action of constrained control, it is possible to control any initial configuration to a flock or a mill. The proof builds on an appropriate combination of several arguments: the LaSalle invariance principle and Lyapunov-like decreasing functionals, control linearization techniques, and quasi-static deformations. A stability analysis of the second-order system guides the design of feedback laws for the stabilization to flock and mills, which are also assessed computationally.
Albi G, Herty M, Kalise D, et al., 2022, Moment-driven predictive control of mean-field collective dynamics, SIAM Journal on Control and Optimization, Vol: 60, ISSN: 0363-0129
The synthesis of control laws for interacting agent-based dynamics and their mean-field limit is studied. A linearization-based approach is used for the computation of sub-optimal feedback laws obtained from the solution of differential matrix Riccati equations. Quantification of dynamic performance of such control laws leads to theoretical estimates on suitable linearizationpoints of the nonlinear dynamics. Subsequently, the feedback laws are embedded into nonlinear model predictive control framework where the control is updated adaptively in time according to dynamic information on moments of linear mean-field dynamics. The performance and robustness ofthe proposed methodology is assessed through different numerical experiments in collective dynamics.
Dutta R, Gomes S, Kalise D, et al., 2021, Using mobility data in the design of optimal lockdown strategies for the COVID-19 pandemic, PLoS Computational Biology, Vol: 17, ISSN: 1553-734X
A mathematical model for the COVID-19 pandemic spread, which integratesage-structured Susceptible-Exposed-Infected-Recovered-Deceased dynamics with realmobile phone data accounting for the population mobility, is presented. The dynamicalmodel adjustment is performed via Approximate Bayesian Computation. Optimallockdown and exit strategies are determined based on nonlinear model predictivecontrol, constrained to public-health and socio-economic factors. Through an extensivecomputational validation of the methodology, it is shown that it is possible to computerobust exit strategies with realistic reduced mobility values to inform public policymaking, and we exemplify the applicability of the methodology using datasets fromEngland and France.
Edalatzadeh MS, Kalise D, Morris KA, et al., 2021, Optimal actuator design for the Euler-Bernoulli vibration model based on LQR performance and shape calculus, IEEE Control Systems Letters, Vol: 6, Pages: 1334-1339, ISSN: 2475-1456
A method for optimal actuator design in vibration control is presented. The optimal actuator, parametrized as a characteristic function, is found by means of the topological derivative of the LQR cost. An abstract framework is proposed based on the theory for infinite-dimensional optimization of both the actuator shape and the associated control problem. A numerical realization of the optimality condition is developed for the actuator shape using a level-set method for topological derivatives. A numerical example illustrating the design of actuator for Euler-Bernoulli beam model is provided.
Albi G, Bicego S, Kalise D, 2021, Gradient-augmented supervised learning of optimal feedback laws using state-dependent Riccati equations, IEEE Control Systems Letters, Vol: 6, Pages: 836-841, ISSN: 2475-1456
A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solvers. The training phase is enriched by the use of gradient information in the loss function, which is weighted through the use of hyperparameters. High-dimensional nonlinear stabilization tests demonstrate that real-time sequential large-scale Algebraic Riccati Equation solvers can be substituted by a suitably trained feedforward neural network.
Wells CA, Williams PD, Nichols NK, et al., 2021, Reducing transatlantic flight emissions by fuel-optimised routing, ENVIRONMENTAL RESEARCH LETTERS, Vol: 16, ISSN: 1748-9326
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- Citations: 13
Dolgov S, Kalise D, Kunisch KK, 2021, TENSOR DECOMPOSITION METHODS FOR HIGH-DIMENSIONAL HAMILTON-JACOBI-BELLMAN EQUATIONS, SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol: 43, Pages: A1625-A1650, ISSN: 1064-8275
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- Citations: 18
Azmi B, Kalise D, Kunisch K, 2021, Optimal Feedback Law Recovery by Gradient-Augmented Sparse Polynomial Regression, JOURNAL OF MACHINE LEARNING RESEARCH, Vol: 22, ISSN: 1532-4435
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- Citations: 11
Kalise D, Kunisch K, Rao Z, 2020, Sparse and switching infinite horizon optimal controls with mixed-norm penalizations, ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, Vol: 26, ISSN: 1292-8119
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- Citations: 4
Kalise D, Kundu S, Kunisch K, 2020, Robust Feedback Control of Nonlinear PDEs by Numerical Approximation of High-Dimensional Hamilton-Jacobi-Isaacs Equations, SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, Vol: 19, Pages: 1496-1524, ISSN: 1536-0040
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- Citations: 10
Choi Y-P, Kalise D, Peszek J, et al., 2019, A Collisionless Singular Cucker-Smale Model with Decentralized Formation Control, SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, Vol: 18, Pages: 1954-1981, ISSN: 1536-0040
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- Citations: 37
Kalise Balza DF, Kunisch K, Sturm K, 2018, Optimal actuator design based on shape calculus, Mathematical Models and Methods in Applied Sciences, ISSN: 1793-6314
Bailo R, Bongini M, Carrillo JA, et al., 2018, Optimal consensus control of the Cucker-Smale model, IFAC-PapersOnLine, Vol: 51, Pages: 1-6, ISSN: 2405-8963
We study the numerical realisation of optimal consensus control laws for agent-based models. For a nonlinear multi-agent system of Cucker-Smale type, consensus control is cast as a dynamic optimisation problem for which we derive first-order necessary optimality conditions. In the case of a smooth penalisation of the control energy, the optimality system is numerically approximated via a gradient-descent method. For sparsity promoting, non-smooth l1-norm control penalisations, the optimal controllers are realised by means of heuristic methods. For an increasing number of agents, we discuss the approximation of the consensus control problem by following a mean-field modelling approach.
Herty M, Kalise D, 2018, Suboptimal nonlinear feedback control laws for collective dynamics, International Conference in Control and Automation ICCA 2018, Publisher: IEEE, Pages: 556-561, ISSN: 1948-3449
We present feedback control methodologies for the stabilization of nonlinear collective dynamics. The proposed controllers circumvent the curse of dimensionality associated to dynamic programming of large-scale nonlinear dynamics by means of different structural assumptions on the nonlinearity and the associated Hamilton-Jacobi-Bellman equation. We explore a power series expansion method, and a state-dependent Riccati equation approach. The proposed designs are studied for a relaxed optimal power flow model, and for binary interactions arising in opinion and consensus dynamics.
Albi G, Kalise D, 2018, (Sub)Optimal feedback control of mean field multi-population dynamics, IFAC-PapersOnLine, Vol: 51, Pages: 86-91, ISSN: 2405-8963
We study a multiscale approach for the control of agent-based, two-population models. The control variable acts over one population of leaders, which influence the population of followers via the coupling generated by their interaction. We cast a quadratic optimal control problem for the large-scale microscale model, which is approximated via a Boltzmann approach. By sampling solutions of the optimal control problem associated to binary two-population dynamics, we generate sub-optimal control laws for the kinetic limit of the multi-population model. We present numerical experiments related to opinion dynamics assessing the performance of the proposed control design.
Briceno-Arias LM, Kalise D, Silva FJ, 2018, Proximal Methods for Stationary Mean Field Games with Local Couplings, SIAM Journal on Control and Optimization, Vol: 56, Pages: 801-836, ISSN: 0363-0129
Kalise D, Kunisch K, 2018, POLYNOMIAL APPROXIMATION OF HIGH-DIMENSIONAL HAMILTON JACOBI BELLMAN EQUATIONS AND APPLICATIONS TO FEEDBACK CONTROL OF SEMILINEAR PARABOLIC PDES, SIAM JOURNAL ON SCIENTIFIC COMPUTING, Vol: 40, Pages: A629-A652, ISSN: 1064-8275
Albi G, Choi Y-P, Fornasier M, et al., 2017, Mean Field Control Hierarchy, APPLIED MATHEMATICS AND OPTIMIZATION, Vol: 76, Pages: 93-135, ISSN: 0095-4616
Kalise D, Kunisch K, Rao Z, 2017, Infinite Horizon Sparse Optimal Control, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Vol: 172, Pages: 481-517, ISSN: 0022-3239
Albi G, Fornasier M, Kalise D, 2017, A Boltzmann approach to mean-field sparse feedback control, IFAC PAPERSONLINE, Vol: 50, Pages: 2898-2903, ISSN: 2405-8963
Tonon D, Aronna MS, Kalise D, 2017, Optimal Control: Novel Directions and Applications Preface, OPTIMAL CONTROL: NOVEL DIRECTIONS AND APPLICATIONS, Editors: Tonon, Aronna, Kalise, Publisher: SPRINGER-VERLAG BERLIN, Pages: VII-VIII, ISBN: 978-3-319-60770-2
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- Citations: 1
Fuentes E, Kalise D, Kennel RM, 2016, Smoothened Quasi-Time-Optimal Control for the Torsional Torque in a Two-Mass System, IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, Vol: 63, Pages: 3954-3963, ISSN: 0278-0046
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