Skip to main content

Research Repository

Advanced Search

All Outputs (11)

Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations (2021)
Journal Article
Dolgov, S., Kalise, D., & Kunisch, K. (2021). Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations. SIAM Journal on Scientific Computing, 43(3), A1625-A1650. https://doi.org/10.1137/19m1305136

A tensor decomposition approach for the solution of high-dimensional, fully nonlin-ear Hamilton-Jacobi-Bellman equations arising in optimal feedback control of nonlinear dynamics is presented. The method combines a tensor train approximation for the... Read More about Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations.

Reducing transatlantic flight emissions by fuel-optimised routing (2021)
Journal Article
Wells, C. A., Williams, P. D., Nichols, N. K., Kalise, D., & Poll, I. (2021). Reducing transatlantic flight emissions by fuel-optimised routing. Environmental Research Letters, 16(2), Article 025002. https://doi.org/10.1088/1748-9326/abce82

© 2021 The Author(s). After decades of limited situational awareness for aircraft flying in the mid-North Atlantic, full satellite coverage will soon be available. This opens up the possibility of altering flight routes to exploit the wind field full... Read More about Reducing transatlantic flight emissions by fuel-optimised routing.

Optimal feedback law recovery by gradient-augmented sparse polynomial regression (2021)
Journal Article
Azmi, B., Kalise, D., & Kunisch, K. (2021). Optimal feedback law recovery by gradient-augmented sparse polynomial regression. Journal of Machine Learning Research, 22, 1-32

A sparse regression approach for the computation of high-dimensional optimal feedback laws arising in deterministic nonlinear control is proposed. The approach exploits the control-theoretical link between Hamilton-Jacobi-Bellman PDEs characterizing... Read More about Optimal feedback law recovery by gradient-augmented sparse polynomial regression.

Sparse and switching infinite horizon optimal controls with mixed-norm penalizations (2020)
Journal Article
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, 26, https://doi.org/10.1051/cocv/2019038

© 2020 EDP Sciences, SMAI. A class of infinite horizon optimal control problems involving mixed quasi-norms of Lp-type cost functionals for the controls is discussed. These functionals enhance sparsity and switching properties of the optimal controls... Read More about Sparse and switching infinite horizon optimal controls with mixed-norm penalizations.

Robust feedback control of nonlinear PDEs by numerical approximation of high-dimensional Hamilton-Jacobi-Isaacs equations (2020)
Journal Article
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, 19(2), 1496-1524. https://doi.org/10.1137/19M1262139

Copyright © by SIAM. We propose an approach for the synthesis of robust and optimal feedback controllers for nonlinear PDEs. Our approach considers the approximation of infinite-dimensional control systems by a pseudospectral collocation method, lead... Read More about Robust feedback control of nonlinear PDEs by numerical approximation of high-dimensional Hamilton-Jacobi-Isaacs equations.

A collisionless singular cucker-smale model with decentralized formation control (2019)
Journal Article
Peters, A. A., Choi, Y., Kalise, D., & Peszek, J. (2019). A collisionless singular cucker-smale model with decentralized formation control. SIAM Journal on Applied Dynamical Systems, 18(4), 1954-1981. https://doi.org/10.1137/19M1241799

We address the design of decentralized feedback control laws inducing consensus and prescribed spatial patterns over a singular interacting particle system of Cucker-Smale type. The control design consists of a feedback term regulating the distance b... Read More about A collisionless singular cucker-smale model with decentralized formation control.

On the implementation of a primal-dual algorithm for second order time-dependent Mean Field Games with local couplings (2019)
Journal Article
Briceño-Arias, L., Kalise, D., Kobeissi, Z., Laurière, M., Mateos González, Á., & Silva, F. (2019). On the implementation of a primal-dual algorithm for second order time-dependent Mean Field Games with local couplings. ESAIM. Proceedings and surveys, 65, 330-348. https://doi.org/10.1051/proc/201965330

We study a numerical approximation of a time-dependent Mean Field Game (MFG) system with local couplings. The discretization we consider stems from a variational approach described in [14] for the stationary problem and leads to the finite difference... Read More about On the implementation of a primal-dual algorithm for second order time-dependent Mean Field Games with local couplings.

Polynomial approximation of high-dimensional Hamilton–Jacobi–Bellman equations and applications to feedback control of semilinear parabolic PDES (2018)
Journal Article
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, 40(2), A629-A652. https://doi.org/10.1137/17M1116635

© 2018 Society for Industrial and Applied Mathematics. A procedure for the numerical approximation of high-dimensional Hamilton–Jacobi–Bellman (HJB) equations associated to optimal feedback control problems for semilinear parabolic equations is propo... Read More about Polynomial approximation of high-dimensional Hamilton–Jacobi–Bellman equations and applications to feedback control of semilinear parabolic PDES.

Infinite Horizon Sparse Optimal Control (2016)
Journal Article
Kalise, D., Kunisch, K., & Rao, Z. (2017). Infinite Horizon Sparse Optimal Control. Journal of Optimization Theory and Applications, 172(2), 481-517. https://doi.org/10.1007/s10957-016-1016-9

A class of infinite horizon optimal control problems involving nonsmooth cost functionals is discussed. The existence of optimal controls is studied for both the convex case and the nonconvex case, and the sparsity structure of the optimal controls p... Read More about Infinite Horizon Sparse Optimal Control.

Invisible control of self-organizing agents leaving unknown environments (2016)
Journal Article
Albi, G., Bongini, M., Cristiani, E., & Kalise, D. (2016). Invisible control of self-organizing agents leaving unknown environments. SIAM Journal on Applied Mathematics, 76(4), 1683-1710. https://doi.org/10.1137/15M1017016

© 2016 Society for Industrial and Applied Mathematics. In this paper we are concerned with multiscale modeling, control, and simulation of self-organizing agents leaving an unknown area under limited visibility, with special emphasis on crowds. We fi... Read More about Invisible control of self-organizing agents leaving unknown environments.

An Efficient Policy Iteration Algorithm for Dynamic Programming Equations (2015)
Journal Article
Alla, A., Falcone, M., & Kalise, D. (2015). An Efficient Policy Iteration Algorithm for Dynamic Programming Equations. SIAM Journal on Scientific Computing, 37(1), A181-A200. https://doi.org/10.1137/130932284

© 2015 Society for Industrial and Applied Mathematics. We present an accelerated algorithm for the solution of static Hamilton–Jacobi–Bellman equations related to optimal control problems. Our scheme is based on a classic policy iteration procedure,... Read More about An Efficient Policy Iteration Algorithm for Dynamic Programming Equations.