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In this paper we use an affine connection formulation to study an optimal control problem for a class of nonholonomic, under-actuated mechanical systems. In particular, we aim at minimizing the norm-squared of the control input to move the…

Optimal control problems are formulated and efficient computational procedures are proposed for attitude dynamics of a rigid body with symmetry. The rigid body is assumed to act under a gravitational potential and under a structured control…

We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the…

This paper presents, using dynamical system theory, a framework for investigating the turnpike property in nonlinear optimal control. First, it is shown that a turnpike-like property appears in general dynamical systems with hyperbolic…

The advent of quantum devices, which exploit the two essential elements of quantum physics, coherence and entanglement, has sparked renewed interest in the control of open quantum systems. Successful implementations face the challenge to…

Adiabatic quantum computation employs a slow change of a time-dependent control function (or functions) to interpolate between an initial and final Hamiltonian, which helps to keep the system in the instantaneous ground state. When the…

The spontaneous creation of disclinations is a defining characteristic of active nematics, which is rarely observed in equilibrium systems or other active matter systems. Thus, understanding the mechanics of disclinations is crucial for…

Starting from a three-dimensional description of an active nematic layer, we employ an asymptotic theory to derive a series of low-dimensional continuum models that capture the coupled dynamics of flat and curved films, including variations…

In this work we deal with the optimal design and optimal control of structures undergoing large rotations. In other words, we show how to find the corresponding initial configuration and the corresponding set of multiple load parameters in…

Attempts from different disciplines to provide a fundamental understanding of deep learning have advanced rapidly in recent years, yet a unified framework remains relatively limited. In this article, we provide one possible way to align…

Predicting how the brain can be driven to specific states by means of internal or external control requires a fundamental understanding of the relationship between neural connectivity and activity. Network control theory is a powerful tool…

Fishes, cetaceans, and many other aquatic vertebrates undulate their bodies to propel themselves through water. Swimming requires an intricate interplay between sensing the environment, making decisions, controlling internal dynamics, and…

The field of optimal control typically requires the assumption of perfect knowledge of the system one desires to control, which is an unrealistic assumption for biological systems, or networks, typically affected by high levels of…

The adaptive and surprising emergent properties of biological materials self-assembled in far-from-equilibrium environments serve as an inspiration for efforts to design nanomaterials and their properties. In particular, controlling the…

This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…

We present a framework to take new measurements in nematic systems that contain active elements such as molecular motors. Spatio-temporal fields of stress, traction, velocity, pressure, and forces are estimated jointly from microscopy…

This paper presents a mathematical framework for optimizing drug delivery in cancer treatment using a nonlocal model of solid tumor growth. We present a coupled system of partial differential equations that incorporate long-range cellular…

In recent papers it has been suggested that human locomotion may be modeled as an inverse optimal control problem. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem that has to be determined. We…

Learning is a complex dynamical process shaped by a range of interconnected decisions. Careful design of hyperparameter schedules for artificial neural networks or efficient allocation of cognitive resources by biological learners can…

Optimal sampled-data control of a nonlinear system is considered with the stable-manifold approach and extensive use of numerical techniques. The idea is to notice the Hamiltonian system associated with the considered optimal control…