In this paper, we present an incremental probability model for dynamic systems. This model combines historical data and new, real-time sequential data as it becomes available. Traditionally, models and algorithms assume the data follows a Gaussian distribution or other specified form. Instead, we propagate the transition probabilities directly which allows us to build the probability distribution from data. This provides a more realistic algorithm for probabilistic forecasting. To address large scale problems, our method is made computationally efficient by using an incremental model to construct probabilities relative to the nominal (or mean) of the state which is allowed to change over time. A mean-field approach further reduces computation while preserving statistical dependencies.

The classic approach for estimating parameters of a model using historical data is to solve a nonlinear least squares optimization problem using numerical methods. We develop an I-frame methodology to solve the nonlinear least squares problem quickly which can be applied to both offline and online (where data is streamed in real time) parameter estimation. Using the concept of I-frames from imaging and animation, we approximate a solution to the nonlinear least squares problem via a two-step process, an I-frame optimization, and an incremental optimization. The I-frame optimization solves for the parameters using a subset of data points and the incremental optimization adjusts the parameters in between the I-frames. We show that the criterion of generating I-frames can affect the average squared error of the final solution. Our methodology benefits from being scalable as the number of parameters and amount of data increases with an appropriate I-frame generation criterion.

We develop a population-based algorithm for the optimization of multiple, nonconvex, nondifferentiable, and possibly discontinuous objective functions. The algorithm employs Markov kernels, Hit-and-Run, and Pattern Hit-and-Run for exploration of the solution space and Pareto ordering rules for the selection of the population and to update the approximate Pareto optimal list. Our multiobjective interacting particle algorithm asymptotically converges to the stationary distribution associated with the Pareto ordering rules. We present numerical benchmark results on test problems.

Efficient solar-energy harvesting is fundamental to solar cell technology. Much research effort has been devoted to the construction of new light-harvesting structures, including the use of semiconductor quantum dots (QDs), to improve the widespread availability of solar cells. In this paper, a new light-harvesting architecture is considered, which utilizes quantum dots. The proposed architecture is composed of quantum phase-locked loops (QPLLs) to enhance the harvesting efficiency of QD solar cells by utilizing feedback control principles. The purpose of QPLL is to synchronize the phases of monochromatic light harvested by the antenna systems. This paper addresses a deterministic modeling and control formulation of the QPLL. The QPLL consists of a tracking controller and a proportional-integral (PI) controller. Simulation results for the controllers are presented and discussed.