The first control-oriented model of the interaction of an electrosurgical probe with organic tissue, based on a 1-D PDE with a moving boundary, is introduced. To attain the desired electrosurgically-induced tissue changes using this model, a non-collocated output feedback moving boundary control law is proposed. The latter is realized through a novel non-collocated pointwise temperature-based state observer for the two-phase Stefan problem. Simulation demonstrates that the controller proposed meets the performance objective. The controller implementation is also discussed.
We study the problem of tracking multiple diffusing particles using a laser scanning fluorescence microscope. The goal is to design trajectories for the laser to maximize the information contained in the measured intensity signal about the particles' trajectories. Our approach consists of a two level scheme: in the lower level we use an extremum seeking controller to track a single particle by first seeking it then orbiting around it. In the higher level controller, we decide which particle should be observed at each instant, with the goal of efficiently estimating each particle position while not losing track of any of them. Using simulations, we show that this technique is able to collect photons efficiently and to track multiple particles with low position estimation error.
Single particle tracking plays an important role in studying physical and kinetic properties of biomolecules. In this work, we introduce the application of Expectation Maximization (EM) based algorithms for solving localization and parameter estimation problems in SPT using data captured from scientific complementary metal-oxide semiconductor (sCMOS) camera sensors. Two representative methods are considered for generating the filtered and smoothed distributions needed by EM: Sequential Monte Carlo - EM, and Unscented - EM. The SMC method uses particle filtering and particle smoothing to handle general distributions, while the U scheme reduces the computational burden through the use of an unscented Kalman Filter and an unscented Rauch-Tung Striebel Smoother. We also investigate the influence of the number of images in the dataset on the final estimates through intensive simulations as well as the computational efficiency of the two methods.
Developing mathematical models of the feedback control process underlying animal behavior is of critical importance to understand their interactions with the environment and emotional responses. For instance, fish geotaxis (the tendency to swim at the bottom of the tank) is known to be a highly sensitive measure of anxiety, but how and why animals tend to display such a complex response is yet to be fully clarified. Leveraging the theory of stochastic differential equations, we develop a data-driven model of geotaxis in the form of a feedback control loop where fish use information about the hydrostatic pressure to dive towards the bottom of the tank. The proposed framework extends open-loop models by incorporating a simple, yet effective, control mechanism to explain geotaxis. We focus on the zebrafish animal model, which is a species of choice in the study of anxiety disorders. We calibrate the model using available experimental data on acute ethanol treatment of adult zebrafish, and demonstrate its effectiveness across a wide range of comparisons between theoretical predictions and empirical observations.
In environments with uncertain dynamics, synthesis of optimal control policies mandates exploration. The applicability of classical learning algorithms to real-world problems is often limited by the number of time steps required for learning the environment model. Given some local side information about the differences in transition probabilities of the states, potentially obtained from the agent's onboard sensors, we generalize the idea of indirect sampling for accelerated learning to propose an algorithm that balances between exploration and exploitation. We formalize this idea by introducing the notion of the value of information in the context of a Markov decision process with unknown transition probabilities, as a measure of the expected improvement in the agent's current estimate of transition probabilities by taking a particular action. By exploiting available local side information and maximizing the estimated value of learned information at each time step, we accelerate the learning process and subsequent synthesis of the optimal control policy. Further, we define the notion of agent safety, a vital consideration for physical systems, in the context of our problem. Under certain assumptions, we provide guarantees on the safety of an agent exploring with our algorithm that exploits local side information. We illustrate agent safety and the improvement in learning speed using numerical experiments in the setting of a Mars rover, with data from onboard sensors acting as the local side information.
Single Particle Tracking (SPT) is a powerful class of tools for analyzing the dynamics of individual biological macromolecules moving inside living cells. The acquired data is typically in the form of a sequence of camera images that are then post-processed to reveal details about the motion. In this work, we develop a local time-varying estimation algorithm for estimating motion model parameters from the data considering nonlinear observations. Our approach uses several well-known existing tools, namely the Expectation Maximization (EM) algorithm combined with an Unscented Kalman filter (UKF) and an Unscented Rauch-Tung-Striebel smoother (URTSS), and applies them to the time-varying case through a sliding window methodology. Due to the shot noise characteristics of the photon generation process, this model uses a Poisson distribution to capture the measurement noise inherent in imaging. In order to apply our time-varying approach to the UKF, we first need to transform the measurements into a model with additive Gaussian noise. This is carried out using a variance stabilizing transform. Results from simulations show that our approach is successful in tracing time-varying diffusion constants at a range of physically relevant signal levels. We also discuss the initialization for the EM algorithm based on the available data.