Bharath Bhikkaji

Shravan Mohan, Bharath Bhikkaji

This paper considers the problem of designing a multilevel pulse width modulated waveform (PWM) with a prescribed harmonic content. Multilevel PWM design plays a major role in many diverse engineering disciplines. In power electronics, multilevel PWM design corresponds to determining the inverter switching times and levels for selective harmonic elimination and harmonic compensation. In mechatronics, the same design corresponds to shaping input signals to damp residual vibrations in flexible structures. More generally, in most applications, the aim of PWM design is to minimize the total harmonic distortion while adhering to a prescribed harmonic content. The solution approach presented in this paper is based on linear programming with the objective of minimizing the total harmonic distortion. This objective is achieved within an arbitrarily small bound of the optimal solution. In addition, the linear programming formulation makes the design of such switching waveforms computationally tractable and efficient. Simulations are provided for corroboration.

Srihari P, Bharath Bhikkaji

This paper examines Federated learning (FL) in a Stochastic Approximation (SA) framework. FL is a collaborative way to train neural network models across various participants or clients without centralizing their data. Each client will train a model on their respective data and send the weights across to a the server periodically for aggregation. The server aggregates these weights which are then used by the clients to re-initialize their neural network and continue the training. SA is an iterative algorithm that uses approximate sample gradients and tapering step size to locate a minimizer of a cost function. In this paper the clients use a stochastic approximation iterate to update the weights of its neural network. It is shown that the aggregated weights track an autonomous ODE. Numerical simulations are performed and the results are compared with standard algorithms like FedAvg and FedProx. It is observed that the proposed algorithm is robust and gives more reliable estimates of the weights, in particular when the clients data are not identically distributed.

Shravan Mohan, Mithun Im, Bharath Bhikkaji

The aim of this paper is to design a band-limited optimal input with power constraints for identifying a linear multi-input multi-output system. It is assumed that the nominal system parameters are specified. The key idea is to use the spectral decomposition theorem and write the power spectrum as $ϕ_{u}(jω)=\frac{1}{2}H(jω)H^*(jω)$. The matrix $H(jω)$ is expressed in terms of a truncated basis for $\mathcal{L}^2\left(\left[-ω_{\mbox{cut-off}},ω_{\mbox{cut-off}}\right]\right)$. With this parameterization, the elements of the Fisher Information Matrix and the power constraints turn out to be homogeneous quadratics in the basis coefficients. The optimality criterion used are the well-known $\mathcal{D}-$optimality, $\mathcal{A}-$optimality, $\mathcal{T}-$optimality and $\mathcal{E}-$optimality. The resulting optimization problem is non-convex in general. A lower bound on the optimum is obtained through a bi-linear formulation of the problem, while an upper bound is obtained through a convex relaxation. These bounds can be computed efficiently as the associated problems are convex. The lower bound is used as a sub-optimal solution, the sub-optimality of which is determined by the difference in the bounds. Interestingly, the bounds match in many instances and thus, the global optimum is achieved. A discussion on the non-convexity of the optimization problem is also presented. Simulations are provided for corroboration.