Joëlle Skaf

Analysis and Synthesis of State-Feedback Controllers With Timing Jitter

We consider a continuous-time linear system with sampled constant linear state-feedback control and a convex quadratic performance measure. The sample times, however, are subject to variation within some known interval. We use linear matrix inequality (LMI) methods to derive a Lyapunov function that establishes an upper bound on performance degradation due to the timing jitter. The same Lyapunov function can be used in a heuristic for finding a bad timing jitter sequence, which gives a lower bound on the possible performance degradation. Numerical experiments show that these two bounds are often close, which means that our bound is tight. We show how LMI methods can be used to synthesize a constant state-feedback controller that minimizes the performance bound, for a given level of timing jitter.

Self-Tuning for Maximized Lifetime Energy-Efficiency in the Presence of Circuit Aging

This paper presents an integrated framework, together with control policies, for optimizing dynamic control of self-tuning parameters of a digital system over its lifetime in the presence of circuit aging. A variety of self-tuning parameters such as supply voltage, operating clock frequency, and dynamic cooling are considered, and jointly optimized using efficient algorithms described in this paper. Our optimized self-tuning approach satisfies performance constraints at all times, and maximizes a lifetime computational power efficiency (LCPE) metric, which is defined as the total number of clock cycles achieved over lifetime divided by the total energy consumed over lifetime. We present three control policies: 1) progressive-worst-case-aging (PWCA), which assumes worst-case aging at all times; 2) progressive-on-state-aging (POSA), which estimates aging by tracking active/sleep modes, and then assumes worst-case aging in active mode and long recovery effects in sleep mode; and 3) progressive-real-time-aging-assisted (PRTA), which acquires real-time information and initiates optimized control actions. Various flavors of these control policies for systems with dynamic voltage and frequency scaling (DVFS) are also analyzed. Simulation results on benchmark circuits, using aging models validated by 45 nm measurements, demonstrate the effectiveness and practicality of our approach in significantly improving LCPE and/or lifetime compared to traditional one-time worst-case guardbanding. We also derive system design guidelines to maximize self-tuning benefits.

Design of Affine Controllers via Convex Optimization

We consider a discrete-time time-varying linear dynamical system, perturbed by process noise, with linear noise corrupted measurements, over a finite horizon. We address the problem of designing a general affine causal controller, in which the control input is an affine function of all previous measurements, in order to minimize a convex objective, in either a stochastic or worst-case setting. This controller design problem is not convex in its natural form, but can be transformed to an equivalent convex optimization problem by a nonlinear change of variables, which allows us to efficiently solve the problem. Our method is related to the classical -design procedure for time-invariant, infinite-horizon linear controller design, and the more recent purified output control method. We illustrate the method with applications to supply chain optimization and dynamic portfolio optimization, and show the method can be combined with model predictive control techniques when perfect state information is available.

Hyperspectral Image Unmixing via Alternating Projected Subgradients

We consider the problem of factorizing a hyperspectral image into the product of two nonnegative matrices, which represent nonnegative bases for image spectra and mixing coefficients, respectively. This spectral unmixing problem is a nonconvex optimization problem, which is very difficult to solve exactly. We present a simple heuristic for approximately solving this problem based on the idea of alternating projected subgradient descent. Finally, we present the results of applying this method on the 1990 AVIRIS image of Cuprite, Nevada and show that our results are in agreement with similar studies on the same data.

Nonlinear Q-Design for Convex Stochastic Control

In this note we describe a version of the Q-design method that can be used to design nonlinear dynamic controllers for a discrete-time linear time-varying plant, with convex cost and constraint functions and arbitrary disturbance distribution. Choosing a basis for the nonlinear Q-parameter yields a convex stochastic optimization problem, which can be solved by standard methods such as sampling. In principle (for a large enough basis, and enough sampling) this method can solve the controller design problem to any degree of accuracy; in any case it can be used to find a suboptimal controller, using convex optimization methods. We illustrate the method with a numerical example, comparing a nonlinear controller found using our method with the optimal linear controller, the certainty-equivalent model predictive controller, and a lower bound on achievable performance obtained by ignoring the causality constraint.

Optimized self-tuning for circuit aging

We present a framework and control policies for optimizing dynamic control of various self-tuning parameters over lifetime in the presence of circuit aging. Our framework introduces dynamic cooling as one of the self-tuning parameters, in addition to supply voltage and clock frequency. Our optimized self-tuning satisfies performance constraints at all times and maximizes a lifetime computational power efficiency (LCPE) metric, which is defined as the total number of clock cycles achieved over lifetime divided by the total energy consumed over lifetime. Our framework features three control policies: 1. Progressive-worst-case-aging (PWCA), which assumes worst-case aging at all times; 2. Progressive-on-state-aging (POSA), which estimates aging by tracking active/sleep mode, and then assumes worst-case aging in active mode and long recovery effects in sleep mode; 3. Progressive-real-time-aging-assisted (PRTA), which estimates the actual amount of aging and initiates optimized control action. Simulation results on benchmark circuits, using aging models validated by 45nm CMOS stress measurements, demonstrate the practicality and effectiveness of our approach. We also analyze design constraints and derive system design guidelines to maximize self-tuning benefits.

Filter Design With Low Complexity Coefficients

We introduce a heuristic for designing filters that have low complexity coefficients, as measured by the total number of nonzeros digits in the binary or canonic signed digit (CSD) representations of the filter coefficients, while still meeting a set of design specifications, such as limits on frequency response magnitude, phase, and group delay. Numerical examples show that the method is able to attain very low complexity designs with only modest relaxation of the specifications.

Spectral unmixing with nonnegative matrix factorization

The present study is an illustration of the application of Nonnegative Matrix Factorization (NMF) to the problem of linear unmixing of mineral endmembers in hyperspectral images. NMF can be seen as for nonnegative linear coding of the data points. We will show how a novel implementation of the NMF is able to perform both endmember extraction and abundance calculation. A synthetic example, used to illustrate the issue shows that NMF correctly identifies endmembers in a random mixing of real library spectra.

Analysis and synthesis of distributed system throttlers

In this paper, we investigate the performance analysis and synthesis of distributed system throttlers (DST). A throttler is a mechanism that limits the flow rate of incoming metrics, e.g., byte per second, network bandwidth usage, capacity, traffic, etc. This can be used to protect a services backend/clients from getting overloaded, or to reduce the effects of uncertainties in demand for shared services. We study performance deterioration of DSTs subject to demand uncertainty. We then consider network synthesis problems that aim to improve the performance of noisy DSTs via communication link modifications as well as server update cycle modifications.