Abstracts

Title: Trajectory Design and Mission Analysis Trade-Offs for the Moon-Enabled Sun Occultation Mission 

Abstract: The Moon-Enabled Sun Occultation Mission (MESOM) is a UK-led mission concept that aims at collecting very high-quality images of the inner sun corona by flying a spacecraft near the apex of the Moon’s umbral shadow once a month and thereby recreating total solar eclipse conditions in Space. 

This talk presents the trajectory design studies and mission analysis trade-offs that underpin the MESOM concept. Fuel-optimal trajectories based on both chemical and electric propulsion will be introduced, and their performance assessed against mission timelines and propellant budgets.

Title:  Dynamics of coupled circadian clocks: comparison of free-running and coupled systems periods

Abstract: The core mechanism underlying circadian rhythms is a gene regulatory network consisting of about 5 genes whose expressions oscillate with a period around 24 hours. This genetic oscillator, or circadian clock, is present in every cell of our body. The interactions in a network of coupled circadian clocks are still very poorly understood, but disrupted or desynchronized circadian rhythms are typically associated with disease.
A challenging problem in oscillatory systems is that of period computation and, furthermore, understanding the relation between the free-running period of each oscillator and the coupled system period. Here, we analyse and estimate the periods of two uncoupled or coupled circadian clocks, based on an analogous piecewise linear system obtained through a succession of model reductions. These estimates are written in terms of the model’s parameters and lead to the following observation for two circadian clocks: the coupled system period is always lower than the mean of the periods of the free-running oscillators.

Title: Indirect stabilization of N -level quantum systems

Abstract: We study the stabilizability of a N -level quantum systems using an indirect control architecture mediated by a noisy ancilla. The aim is to find necessary and/or sufficient conditions on the interaction Hamiltonian that guarantee that the target reduced state is globally asymptotically stable. After outlining the general theoretical framework for arbitrary N, we focus on the two-level case (N = 2), for which we derive a complete set of necessary and sufficient conditions for asymptotic stability.
Finally, we illustrate the analytical results with a simple numerical example on a two-spin system, showing convergence to a Bell state for a set of random initial conditions. 

Title:  Nonlinear and Optimal Control for Low-Thrust Orbital Transfer 

Abstract: TBA

Title: Hyperexponential stability and stabilization 

Abstract: Accelerated rates of convergence, such as finite/fixed-time ones, gain their popularity due to their important advantages, which include not only the boundedness of transients, but also remarkable robustness with respect to external perturbations and delays. The practical implementation of finite/fixed-time control or estimation algorithms, however, requires an additional attention, and finding a consistent discretization is frequently difficult. One of the reasons for that is complexity of realization of these convergence rates in discrete-time systems. An attempt to overcome this difficulty was performed recently by passing to hyperexponentially converging systems, which is a class of dynamics with asymptotic transients but faster than in any linear systems. This kind of decay is easy to find in time-delay or discrete-time systems. Several definitions and results on development of hyperexponential stability and stabilization are introduced. In particular, the controls with time-varying or nonlinear gains, and time-delay sign approximation for chattering reduction are presented.  

Title: Multiscale Neuromorphic Control – Methods and Practice

Abstract: Our sensorimotor experience is inherently multiscale, both in time and in space. We can see both the forest and the trees. We make split-second decisions while planning our lives. We dexterously manipulate tiny objects while balancing on a bike. By contrast, artificial sensing, decision-making, and action are still typically analyzed and designed as fundamentally single-scale signal-processing steps within a fundamentally single-scale feedback control loop.
I will first review the multiscale nature of sensorimotor control in biological systems. I will then provide an overview of both well-established and ongoing research—methodological as well as applied—in neuromorphic control theory that aims to overcome the current multiscale sensing, decision-making, and action gap between biological systems and machines.

Title: Can neural networks solve high dimensional optimal feedback control problems?

Abstract: Deep Reinforcement Learning has established itself as a standard method for solving nonlinear optimal feedback control problems. In this method, the optimal value function (and in some variants also the optimal feedback law) is stored using a deep neural network. Hence, the applicability of this approach to high-dimensional problems crucially relies on the network's ability to store a high-dimensional function. It is known that for general high-dimensional functions, neural networks suffer from the same exponential growth of the number of coefficients as traditional grid based methods, the so-called curse of dimensionality. In this talk, we use methods from distributed optimal control to describe optimal control problems in which this problem does not occur. The talk is based on joint work with Mario Sperl, Dante Kalise, and Luca Saluzzi. 

Abstract: TBA

Title: Flatness and dynamic feedback linearization via successive one-fold prolongations 

Abstract: In this presentation, we revisit the relationships between differential flatness and feedback linearization, and propose a constructive algorithm for dynamic feedback linearization of two-input control systems. The method relies on successive prolongations of an input that is suitably chosen at each step of the algorithm.

Unlike static feedback linearization, where the linearizability distributions are required to be involutive, this condition is no longer necessary for dynamic feedback linearization via successive one-fold prolongations. Instead, the first non-involutive distribution must contain a maximal involutive subdistribution of corank one.
The main idea of the proposed algorithm is to iteratively replace the first non-involutive distribution by its involutive corank one subdistribution, thereby ensuring that the prolonged system gains at least one new involutive distribution at each step of the algorithm. This provides constructive and sufficient conditions for differential flatness. 

Title: Structure preservation and trim turnpike property in continuous and discretized optimal control problems 

Abstract: Geometric structure plays an important role for the analysis and solution of optimal control problems. For example, the system of necessary optimality conditions exhibits a symplectic structure which should be preserved using numerical methods for the approximation of solutions. The use of symplectic integration methods leads to stable and accurate long time behaviour of state, control and adjoint trajectories.

Another relevant structure in optimal control which has been studied intensively during the last years is the turnpike property in optimal control. It refers to optimal trajectories that remain exponential close for most of a time horizon, to a steady optimal regime which is determined by the optimal solution of the corresponding static problem. There are many extensions towards turnpikes being not only stationary trajectories but period orbits or - as recently discovered - relative equilibria for optimal control problems with symmetries. This kind of turnpike is called a trim turnpike, and the limiting trajectory is given by a trim primitive. In this case, symmetry reduction of the state-adjoint system makes it possible to identify the limiting trajectory and then describe the convergence behavior of optimal solutions. This phenomenon is especially relevant for mechanical systems, where symmetries naturally arise and are related to conservation laws.

Titre: Feedback control of open-quantum systems  

Abstract: The density operators of open quantum systems are governed by  so-called Stochastic Master Equations (SME). They can be stabilized either with classical controllers or quantum ones.  This talk presents these SME and feedback schemes on two key physical systems: the Haroche photon box in discrete time; the super-conducting cat-qubit in continuous time. 

Title: Controllability of Liouville transport equations for mechanical systems

Abstract: We study the $L^p$-approximate controllability of Liouville transport equations along mechanical Hamiltonian vector fields.
We first characterize the orbits of densities under the actions of Hamiltonian diffeomorphisms in the cases where the underlying manifold is an Euclidean space or a flat torus. We then provide conditions under which the Liouville transport equation is $L^p$-approximate controllable or even approximately controllable in the group of Hamiltonian diffeomorphisms.
The talk is based on a joint work with Bettina Kazandjian and Eugenio Pozzoli.