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A reflection of our ultimate understanding of a complex system is our ability to control its behavior. Typically, control has multiple prerequisites: It requires an accurate map of the network that governs the interactions between the…
In this paper we consider autonomous driving of miniature race cars. The viability kernel is used to efficiently generate finite look-ahead trajectories that maximize progress while remaining recursively feasible with respect to static…
Mean-field control problems have received continuous interest over the last decade. Despite being more intricate than in classical optimal control, the linear-quadratic setting can still be tackled through Riccati equations. Remarkably, we…
We present a general representation for solving problems in many-body perturbation theory. By projecting the single-particle Green's function to an auxiliary space we show how one can convert an arbitrary Feynman graph to a universal kernel…
In this study, we provide an interpretation of the dual differential Riccati equation of Linear-Quadratic (LQ) optimal control problems. Adopting a novel viewpoint, we show that LQ optimal control can be seen as a regression problem over…
Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…
A major application of the mathematical concept of graph in quantum mechanics is to model networks of electrical wires or electromagnetic wave-guides. In this paper, we address the dynamics of a particle trapped on such a network in…
In stochastic control applications, typically only an ideal model (controlled transition kernel) is assumed and the control design is based on the given model, raising the problem of performance loss due to the mismatch between the assumed…
In optimal control problems, disturbances are typically dealt with using robust solutions, such as H-infinity or tube model predictive control, that plan control actions feasible for the worst-case disturbance. Yet, planning for every…
Efforts toward a comprehensive description of behavior have indeed facilitated the development of representation-based approaches that utilize deep learning to capture behavioral information. As behavior complexity increases, the expressive…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
Kullback Leibler (KL) control problems allow for efficient computation of optimal control by solving a principal eigenvector problem. However, direct applicability of such framework to continuous state-action systems is limited. In this…
In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial…
Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this…
An optimal control problem described by the Hamilton-Jacobi-Bellman equation can be developed into a problem that can be solved by general computational fluid dynamics packages. We describe how this formulation would allow a classical…
The emergence of mutant lineages within a viral species has become a public health problem, as the existing treatments and drugs are usually more effective on the original lineages than in the mutant ones. The following manuscript presents…
Hilbertian kernel methods and their positive semidefinite kernels have been extensively used in various fields of applied mathematics and machine learning, owing to their several equivalent characterizations. We here unveil an analogy with…
This work is concerned with a hierarchical framework of optimal control problems connecting interacting particle systems, the mean field limit equations, and associated hydrodynamic models. By assuming the existence of solutions, we…
The behavior composition problem involves automatically building a controller that is able to realize a desired, but unavailable, target system (e.g., a house surveillance) by suitably coordinating a set of available components (e.g., video…
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…