Algorithmic Verification of Continuous and Hybrid Systems

We provide a tutorial introduction to reachability computation, a class of computational techniques that exports verification technology toward continuous and hybrid systems. For open under-determined systems, this technique can sometimes replace an infinite number of simulations.Comment: In Proceedings INFINITY 2013, arXiv:1402.661

Piecewise Linear Control Systems

This thesis treats analysis and design of piecewise linear control systems. Piecewise linear systems capture many of the most common nonlinearities in engineering systems, and they can also be used for approximation of other nonlinear systems. Several aspects of linear systems with quadratic constraints are generalized to piecewise linear systems with piecewise quadratic constraints. It is shown how uncertainty models for linear systems can be extended to piecewise linear systems, and how these extensions give insight into the classical trade-offs between fidelity and complexity of a model. Stability of piecewise linear systems is investigated using piecewise quadratic Lyapunov functions. Piecewise quadratic Lyapunov functions are much more powerful than the commonly used quadratic Lyapunov functions. It is shown how piecewise quadratic Lyapunov functions can be computed via convex optimization in terms of linear matrix inequalities. The computations are based on a compact parameterization of continuous piecewise quadratic functions and conditional analysis using the S-procedure. A unifying framework for computation of a variety of Lyapunov functions via convex optimization is established based on this parameterization. Systems with attractive sliding modes and systems with bounded regions of attraction are also treated. Dissipativity analysis and optimal control problems with piecewise quadratic cost functions are solved via convex optimization. The basic results are extended to fuzzy systems, hybrid systems and smooth nonlinear systems. It is shown how Lyapunov functions with a discontinuous dependence on the discrete state can be computed via convex optimization. An automated procedure for increasing the flexibility of the Lyapunov function candidate is suggested based on linear programming duality. A Matlab toolbox that implements several of the results derived in the thesis is presented

Tensor Computation: A New Framework for High-Dimensional Problems in EDA

Many critical EDA problems suffer from the curse of dimensionality, i.e. the very fast-scaling computational burden produced by large number of parameters and/or unknown variables. This phenomenon may be caused by multiple spatial or temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit simulation), nonlinearity of devices and circuits, large number of design or optimization parameters (e.g. full-chip routing/placement and circuit sizing), or extensive process variations (e.g. variability/reliability analysis and design for manufacturability). The computational challenges generated by such high dimensional problems are generally hard to handle efficiently with traditional EDA core algorithms that are based on matrix and vector computation. This paper presents "tensor computation" as an alternative general framework for the development of efficient EDA algorithms and tools. A tensor is a high-dimensional generalization of a matrix and a vector, and is a natural choice for both storing and solving efficiently high-dimensional EDA problems. This paper gives a basic tutorial on tensors, demonstrates some recent examples of EDA applications (e.g., nonlinear circuit modeling and high-dimensional uncertainty quantification), and suggests further open EDA problems where the use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and System

Layout-level Circuit Sizing and Design-for-manufacturability Methods for Embedded RF Passive Circuits

The emergence of multi-band communications standards, and the fast pace of the consumer electronics markets for wireless/cellular applications emphasize the need for fast design closure. In addition, there is a need for electronic product designers to collaborate with manufacturers, gain essential knowledge regarding the manufacturing facilities and the processes, and apply this knowledge during the design process. In this dissertation, efficient layout-level circuit sizing techniques, and methodologies for design-for-manufacturability have been investigated. For cost-effective fabrication of RF modules on emerging technologies, there is a clear need for design cycle time reduction of passive and active RF modules. This is important since new technologies lack extensive design libraries and layout-level electromagnetic (EM) optimization of RF circuits become the major bottleneck for reduced design time. In addition, the design of multi-band RF circuits requires precise control of design specifications that are partially satisfied due to manufacturing variations, resulting in yield loss. In this work, a broadband modeling and a layout-level sizing technique for embedded inductors/capacitors in multilayer substrate has been presented. The methodology employs artificial neural networks to develop a neuro-model for the embedded passives. Secondly, a layout-level sizing technique for RF passive circuits with quasi-lumped embedded inductors and capacitors has been demonstrated. The sizing technique is based on the circuit augmentation technique and a linear optimization framework. In addition, this dissertation presents a layout-level, multi-domain DFM methodology and yield optimization technique for RF circuits for SOP-based wireless applications. The proposed statistical analysis framework is based on layout segmentation, lumped element modeling, sensitivity analysis, and extraction of probability density functions using convolution methods. The statistical analysis takes into account the effect of thermo-mechanical stress and process variations that are incurred in batch fabrication. Yield enhancement and optimization methods based on joint probability functions and constraint-based convex programming has also been presented. The results in this work have been demonstrated to show good correlation with measurement data.Ph.D.Committee Chair: Swaminathan, Madhavan; Committee Member: Fathianathan, Mervyn; Committee Member: Lim, Sung Kyu; Committee Member: Peterson, Andrew; Committee Member: Tentzeris, Mano

Theory and Applications of Robust Optimization

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of the methodology. In addition to surveying prominent theoretical results of RO, we also present some recent results linking RO to adaptable models for multi-stage decision-making problems. Finally, we highlight applications of RO across a wide spectrum of domains, including finance, statistics, learning, and various areas of engineering.Comment: 50 page

A Survey on Multisensor Fusion and Consensus Filtering for Sensor Networks

Multisensor fusion and consensus filtering are two fascinating subjects in the research of sensor networks. In this survey, we will cover both classic results and recent advances developed in these two topics. First, we recall some important results in the development ofmultisensor fusion technology. Particularly, we pay great attention to the fusion with unknown correlations, which ubiquitously exist in most of distributed filtering problems. Next, we give a systematic review on several widely used consensus filtering approaches. Furthermore, some latest progress on multisensor fusion and consensus filtering is also presented. Finally, conclusions are drawn and several potential future research directions are outlined.the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61374039, 61304010, 11301118, and 61573246, the Hujiang Foundation of China under Grants C14002 and D15009, the Alexander von Humboldt Foundation of Germany, and the Innovation Fund Project for Graduate Student of Shanghai under Grant JWCXSL140