A Primal-Dual Method for Optimal Control and Trajectory Generation in High-Dimensional Systems

Presented is a method for efficient computation of the Hamilton-Jacobi (HJ) equation for time-optimal control problems using the generalized Hopf formula. Typically, numerical methods to solve the HJ equation rely on a discrete grid of the solution space and exhibit exponential scaling with dimension. The generalized Hopf formula avoids the use of grids and numerical gradients by formulating an unconstrained convex optimization problem. The solution at each point is completely independent, and allows a massively parallel implementation if solutions at multiple points are desired. This work presents a primal-dual method for efficient numeric solution and presents how the resulting optimal trajectory can be generated directly from the solution of the Hopf formula, without further optimization. Examples presented have execution times on the order of milliseconds and experiments show computation scales approximately polynomial in dimension with very small high-order coefficients.Comment: Updated references and funding sources. To appear in the proceedings of the 2018 IEEE Conference on Control Technology and Application

Regularization and Kernelization of the Maximin Correlation Approach

Robust classification becomes challenging when each class consists of multiple subclasses. Examples include multi-font optical character recognition and automated protein function prediction. In correlation-based nearest-neighbor classification, the maximin correlation approach (MCA) provides the worst-case optimal solution by minimizing the maximum misclassification risk through an iterative procedure. Despite the optimality, the original MCA has drawbacks that have limited its wide applicability in practice. That is, the MCA tends to be sensitive to outliers, cannot effectively handle nonlinearities in datasets, and suffers from having high computational complexity. To address these limitations, we propose an improved solution, named regularized maximin correlation approach (R-MCA). We first reformulate MCA as a quadratically constrained linear programming (QCLP) problem, incorporate regularization by introducing slack variables in the primal problem of the QCLP, and derive the corresponding Lagrangian dual. The dual formulation enables us to apply the kernel trick to R-MCA so that it can better handle nonlinearities. Our experimental results demonstrate that the regularization and kernelization make the proposed R-MCA more robust and accurate for various classification tasks than the original MCA. Furthermore, when the data size or dimensionality grows, R-MCA runs substantially faster by solving either the primal or dual (whichever has a smaller variable dimension) of the QCLP.Comment: Submitted to IEEE Acces

VirtFogSim: A parallel toolbox for dynamic energy-delay performance testing and optimization of 5G Mobile-Fog-Cloud virtualized platforms

It is expected that the pervasive deployment of multi-tier 5G-supported Mobile-Fog-Cloudtechnological computing platforms will constitute an effective means to support the real-time execution of future Internet applications by resource- and energy-limited mobile devices. Increasing interest in this emerging networking-computing technology demands the optimization and performance evaluation of several parts of the underlying infrastructures. However, field trials are challenging due to their operational costs, and in every case, the obtained results could be difficult to repeat and customize. These emergingMobile-Fog-Cloud ecosystems still lack, indeed, customizable software tools for the performance simulation of their computing-networking building blocks. Motivated by these considerations, in this contribution, we present VirtFogSim. It is aMATLAB-supported software toolbox that allows the dynamic joint optimization and tracking of the energy and delay performance of Mobile-Fog-Cloud systems for the execution of applications described by general Directed Application Graphs (DAGs). In a nutshell, the main peculiar features of the proposed VirtFogSim toolbox are that: (i) it allows the joint dynamic energy-aware optimization of the placement of the application tasks and the allocation of the needed computing-networking resources under hard constraints on acceptable overall execution times, (ii) it allows the repeatable and customizable simulation of the resulting energy-delay performance of the overall system; (iii) it allows the dynamic tracking of the performed resource allocation under time-varying operational environments, as those typically featuring mobile applications; (iv) it is equipped with a user-friendly Graphic User Interface (GUI) that supports a number of graphic formats for data rendering, and (v) itsMATLAB code is optimized for running atop multi-core parallel execution platforms. To check both the actual optimization and scalability capabilities of the VirtFogSim toolbox, a number of experimental setups featuring different use cases and operational environments are simulated, and their performances are compared

Subspace System Identification via Weighted Nuclear Norm Optimization

We present a subspace system identification method based on weighted nuclear norm approximation. The weight matrices used in the nuclear norm minimization are the same weights as used in standard subspace identification methods. We show that the inclusion of the weights improves the performance in terms of fit on validation data. As a second benefit, the weights reduce the size of the optimization problems that need to be solved. Experimental results from randomly generated examples as well as from the Daisy benchmark collection are reported. The key to an efficient implementation is the use of the alternating direction method of multipliers to solve the optimization problem.Comment: Submitted to IEEE Conference on Decision and Contro