Distributed Extremum-Seeking Control with Applications to High-Altitude Balloons

The real-time optimization of large-scale systems is a difficult problem due to the need for complex models involving uncertain parameters and the high computational cost of solving such problems by a decentralized approach. Extremum-seeking control (ESC) is a model-free real-time optimization technique which can estimate unknown parameters and can optimize nonlinear time-varying systems using only a measurement of the cost function to be minimized. In this thesis, we develop a distributed version of extremum-seeking control which allows large-scale systems to be optimized without models and with minimal computing power. First, we develop a continuous-time distributed extremum-seeking controller. It has three main components: consensus, parameter estimation, and optimization. The consensus provides each local controller with an estimate of the cost to be minimized, allowing them to coordinate their actions. Using this cost estimate, parameters for a local input-output model are estimated, and the cost is minimized by following a gradient descent based on the estimate of the gradient. Next, a similar distributed extremum-seeking controller is developed in discrete-time. Finally, we consider an interesting application of distributed ESC: formation control of high-altitude balloons for high-speed wireless internet. These balloons must be steered into a favourable formation where they are spread out over the Earth and provide coverage to the entire planet. Distributed ESC is applied to this problem, and is shown to be effective for a system of 1200 ballons subjected to realistic wind currents. The approach does not require a wind model and uses a cost function based on a Voronoi partition of the sphere. Distributed ESC is able to steer balloons from a few initial launch sites into a formation which provides coverage to the entire Earth and can maintain a similar formation as the balloons move with the wind around the Earth.

LEARNING IMPULSE CONTROL IN A NOVEL ANIMAL MODEL: SYNAPTIC, CELLULAR, AND PHARMACOLOGICAL SUBSTRATES

Impulse control, an executive process that restrains inappropriate actions, is impaired in numerous psychiatric conditions. This thesis reports three experiments that utilized a novel animal model of impulse control, the response inhibition (RI) task, to examine the substrates that underlie learning this task. In the first experiment, rats were trained to withhold responding on the RI task, and then euthanized for electrophysiological testing. Training in the RI task increased the AMPA/NMDA ratio at the synapses of pyramidal neurons in the prelimbic, but not infralimbic, region of the medial prefrontal cortex. This enhancement paralleled performance as subjects underwent acquisition and extinction of the inhibitory response. AMPA/NMDA was elevated only in neurons that project to the ventral striatum. Thus, this experiment identified a synaptic correlate of impulse control. In the second experiment, a separate group of rats were trained in the RI task prior to electrophysiological testing. Training in the RI task produced a decrease in membrane excitability in prelimbic, but not infralimbic, neurons as measured by maximal spiking evoked in response to increasing current injection. Importantly, this decrease was strongly correlated with successful inhibition in the task. Fortuitously, subjects trained in an operant control condition showed elevated infralimbic, but not prelimbic, excitability, which was produced by learning an anticipatory signal that predicted imminent reward availability. These experiments revealed two cellular correlates of performance, corresponding to learning two different associations under distinct task conditions. In the final experiment, rats were trained on the RI task under three conditions: Short (4-s), long (60-s), or unpredictable (1-s to 60-s) premature phases. These conditions produced distinct errors on the RI task. Interestingly, amphetamine increased premature responding in the short and long conditions, but decreased premature responding in the unpredictable condition. This dissociation may arise from interactions between amphetamine and underlying cognitive processes, such as attention, timing, and conditioned avoidance. In summary, this thesis showed that learning to inhibit a response produces distinct synaptic, cellular, and pharmacological changes. It is hoped that these advances will provide a starting point for future therapeutic interventions of disorders of impulse control.