Arash Komaee

Towards Control of Magnetic Fluids in Patients: Directing Therapeutic Nanoparticles to Disease Locations

This article describes a range of results, from passive magnet design to optimal feedback control of a distributed ferrofluid. Representing magnetic forces as the gradient of a magnetic energy allowed design and demonstration, in animal experiments, of a simple open-loop two-magnet system to inject nanoparticles into the inner ear. Then a petri-dish test bed was used to develop and test optimal closed-loop manipulation of a single ferrofluid droplet.The demonstrated algorithms exploited the quadratic dependence of the magnetic forces on control inputs while accounting for magnet time delays and spatial discontinuities in the optimal control. All dimensional parameters were reduced to three essential nondimensional numbers, and ferrofluid behavior was mapped across the entire feasible drug delivery parameter space.

Steering a Ferromagnetic Particle by Optimal Magnetic Feedback Control

A class of feedback control policies for steering a magnetic particle in a viscous fluid and actuated by a magnetic field is presented. The magnetic field which is generated by an array of electromagnets can be adequately shaped by controlling the voltages of the electromagnets. Control design relies on a dynamical model which exploits the low-pass character of the electromagnets, the opposing viscous drag on the magnetic particle, and the nonlinear (quadratic) nature of the dependence of the magnetic force on the electrical currents passing through the electromagnets. It is shown that under a set of practically achievable conditions, the nonlinearity of the model can be canceled by incorporating an inverse nonlinear map in the controller so that the closed-loop system operates like a linear system. A systematic framework for determining an optimal inverse map and investigating its properties is developed and two important cases of minimum control effort and maximum robustness are discussed. The ability to control the magnetic particle along arbitrary trajectories is verified both in simulations and in an experiment.

Steering a ferromagnetic particle by magnetic feedback control: Algorithm design and validation

We present results for planar manipulation of a single drop of magnetic nano-particles (a ferrofluid) in a liquid by feedback control of an array of electromagnets. Control design is based on a first-principles physical model of the magnetic fields, the resulting magnetic forces, and opposing viscous drag on the ferrofluidic drop, and it exploits the nonlinear (quadratic) nature of the dependence of the magnetic force on the electromagnet actuations. An ability to control the droplet along arbitrary trajectories is verified both in simulations and in an experiment.

Channel estimation for free-space optical communication

Optical fade caused by atmospheric turbulence impairs the performance of optical communication through atmosphere. Adaptive techniques of signal detection, power control, and channel coding can be employed to reduce the degrading effect of this phenomenon. For implementation of these techniques, the knowledge of channel state is required. This paper develops a channel estimator to extract the strength of optical fade from the observations of channel output. Further, it is shown how to incorporate this estimation in an adaptive threshold test for the purpose of optimal binary signal detection.

Magnetic steering of a distributed ferrofluid spot towards a deep target with minimal spreading

In magnetic drug targeting, where drugs are attached to magnetic nanoparticles and external magnets are then used to focus the therapy to, for example, solid tumors, there is a need to better control and focus the distribution of particles (the ferrofluid) to deep targets. This paper considers a key next question: how to move a single spot of ferrofluid to a deep target with minimal spreading. The problem is challenging since the applied magnetic forces have a natural tendency to stretch the ferrofluid spot. A control policy is designed and verified by simulations to optimally control multiple electromagnets in concert to move a single spot of ferrofluid from the edge of a domain to a deep central target with minimal spreading.

Nonlinear Filters for Bayesian Estimation of Pulse Arrival Time in Additive White Gaussian Noise

Bayesian estimation of the arrival time of a single pulse is considered in the presence of a white noise. The employed model is a stochastic process consisted of a randomly delayed causal pulse and an additive white Gaussian noise, where the prior density of the delay is known. The history of this stochastic process is given at every point in time and the problem is to obtain the conditional expectation of an arbitrary function of the arrival time. The paper adopts a stochastic differential equation approach to develop nonlinear filters to efficiently compute this estimation. The filtering problem is resolved for a number of pulse shapes which allow for a finite-dimensional solution. These pulse shapes include step, exponential, and rectangular functions, as well as a piecewise constant function which well approximates a broad class of waveforms. The application of this filtering problem in real-time pulse arrival detection is discussed. The task of this operation is to report the event of pulse arrival as soon after occurrence as possible. The performance of nonlinear filtering is numerically verified for this application.

State estimation from space-time point process observations with an application in optical beam tracking

A stochastic model is considered which involves a linear system driven by Wiener process and the observations of a space-time point process whose intensity depends on the state of this linear system. It is shown that the problem of estimating the state of this continuous-time system can be reduced to estimating the state of a discrete-time linear stochastic system with a Gaussian process noise and a generally non-Gaussian measurement noise. Two types of estimators are developed for this discrete-time system: a linear minimum mean squared estimator and a nonlinear estimator based on the successive projection of the posterior density of the state vector on a Gaussian family of density functions. These discrete-time estimators are employed to determine two classes of estimators for the original continuous-time system. An application to optical beam tracking is presented.

Potential Canals for Control of Nonlinear Stochastic Systems in the Absence of State Measurements

This paper considers design of an open-loop control to direct the state of a nonlinear stochastic system from a random initial state toward a targeted stable equilibrium generated by a predefined constant control. Under this constant control, the system is assumed to have multiple stable equilibria, so that starting from a random initial state, the system can settle eventually at any of these equilibria, not necessarily the targeted one. To direct the system toward the targeted equilibrium, an initial phase of dynamic (time-varying) control is needed before application of the constant control. The concept of potential canal is introduced in this paper to develop a methodology for design of such dynamic control. This methodology is primarily intended to be used in directed self-assembly-a technology for ordering charged nanoparticles into desired nanostructures by manipulating external electrical fields. The features of the developed control are demonstrated for directed self-assembly in one dimension.

Feedback Control for Transportation of Magnetic Fluids With Minimal Dispersion: A First Step Toward Targeted Magnetic Drug Delivery

In targeted magnetic drug delivery, drugs attached to magnetic nanoparticles are delivered to targeted regions of the body (e.g., tumors) at high concentrations by the application of external magnetic fields. Beyond many technical difficulties posed by the complexities of the human body, the performance of this scheme is limited in concept by the inherent tendency of the magnetic fields to disperse any constellation of magnetic particles moving under their applied forces. This tendency causes a gradual loss of concentration when a spot of ferrofluid (suspension of magnetic nanoparticles in water) moves inside a magnetic field. To minimize this undesirable effect to an acceptable level, a feedback control policy for the dynamic control of electromagnets is presented to drive a ferrofluid spot from the edge of a domain to a central target with minimal dispersion. Representing the spot of ferrofluid by its center of mass and the covariance matrix of its distribution, these control goals are formulated as an optimal control problem that constrains the motion of the former, while minimizing the trace of the latter (as a measure of dispersion). To simplify the solution of this problem, the ferrofluid dynamics, which is precisely governed by a partial differential equation, is approximated by a finite-dimensional set of state-space equations, and a suboptimal control is developed for this simpler model by further approximation of the Hamilton-Jacobi-Bellman equation. Simulation results are presented for the closed-loop system, which demonstrate that the proposed control is able to move the ferrofluid spot to a central target with reasonably small dispersion.

Detection and channel estimation for optical communication over atmospheric turbulent channels

Atmospheric turbulence impairs the performance of free-space optical links by perturbing optical power at the receiving terminal. The resulting reduction in the link performance can be partially compensated if the strength of the optical fade (channel state) is known to the receiver. For an atmospheric optical channel with on-off keying modulation, the optimal estimator of the channel state is determined and a nonlinear filtering scheme is developed to efficiently compute the estimation. In addition, the optimal method of incorporating this estimation in reconstruction of the receiving message is presented.