Preface 1. Introduction Overview A Brief History of LMIs in Control Theory Notes on the Style of the Book Origin of the Book 2. Some Standard Problems Involving LMIs. Linear Matrix Inequalities Some Standard Problems Ellipsoid Algorithm Interior-Point Methods Strict and Nonstrict LMIs Miscellaneous Results on Matrix Inequalities Some LMI Problems with Analytic Solutions 3. Some Matrix Problems. Minimizing Condition Number by Scaling Minimizing Condition Number of a Positive-Definite Matrix Minimizing Norm by Scaling Rescaling a Matrix Positive-Definite Matrix Completion Problems Quadratic Approximation of a Polytopic Norm Ellipsoidal Approximation 4. Linear Differential Inclusions. Differential Inclusions Some Specific LDIs Nonlinear System Analysis via LDIs 5. Analysis of LDIs: State Properties. Quadratic Stability Invariant Ellipsoids 6. Analysis of LDIs: Input/Output Properties. Input-to-State Properties State-to-Output Properties Input-to-Output Properties 7. State-Feedback Synthesis for LDIs. Static State-Feedback Controllers State Properties Input-to-State Properties State-to-Output Properties Input-to-Output Properties Observer-Based Controllers for Nonlinear Systems 8. Lure and Multiplier Methods. Analysis of Lure Systems Integral Quadratic Constraints Multipliers for Systems with Unknown Parameters 9. Systems with Multiplicative Noise. Analysis of Systems with Multiplicative Noise State-Feedback Synthesis 10. Miscellaneous Problems. Optimization over an Affine Family of Linear Systems Analysis of Systems with LTI Perturbations Positive Orthant Stabilizability Linear Systems with Delays Interpolation Problems The Inverse Problem of Optimal Control System Realization Problems Multi-Criterion LQG Nonconvex Multi-Criterion Quadratic Problems Notation List of Acronyms Bibliography Index.

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Linear Matrix Inequalities in System and Control Theory

Data Mining Practical Machine Learning Tools and Techniques

A newly described coronavirus named severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), which is the causative agent of coronavirus disease 2019 (COVID-19), has infected over 2.3 million people, led to the death of more than 160,000 individuals and caused worldwide social and economic disruption1,2. There are no antiviral drugs with proven clinical efficacy for the treatment of COVID-19, nor are there any vaccines that prevent infection with SARS-CoV-2, and efforts to develop drugs and vaccines are hampered by the limited knowledge of the molecular details of how SARS-CoV-2 infects cells. Here we cloned, tagged and expressed 26 of the 29 SARS-CoV-2 proteins in human cells and identified the human proteins that physically associated with each of the SARS-CoV-2 proteins using affinity-purification mass spectrometry, identifying 332 high-confidence protein–protein interactions between SARS-CoV-2 and human proteins. Among these, we identify 66 druggable human proteins or host factors targeted by 69 compounds (of which, 29 drugs are approved by the US Food and Drug Administration, 12 are in clinical trials and 28 are preclinical compounds). We screened a subset of these in multiple viral assays and found two sets of pharmacological agents that displayed antiviral activity: inhibitors of mRNA translation and predicted regulators of the sigma-1 and sigma-2 receptors. Further studies of these host-factor-targeting agents, including their combination with drugs that directly target viral enzymes, could lead to a therapeutic regimen to treat COVID-19. A human–SARS-CoV-2 protein interaction map highlights cellular processes that are hijacked by the virus and that can be targeted by existing drugs, including inhibitors of mRNA translation and predicted regulators of the sigma receptors.

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A SARS-CoV-2 protein interaction map reveals targets for drug repurposing.

The Theory of Matrices. By F R. Gantmacher. Two volumes, pp. 374 and 276. 1959. (Translated from the Russian by K. A. Hirsch; Chelsea Publishing Company, New York)

Survey paper: Set invariance in control

Microgrids are subsystems of the distribution grid, which comprises generation capacities, storage devices, and controllable loads, operating as a single controllable system either connected or isolated from the utility grid. In this paper, we present a study on applying a model predictive control approach to the problem of efficiently optimizing microgrid operations while satisfying a time-varying request and operation constraints. The overall problem is formulated using mixed-integer linear programming (MILP), which can be solved in an efficient way by using commercial solvers without resorting to complex heuristics or decompositions techniques. Then, the MILP formulation leads to significant improvements in solution quality and computational burden. A case study of a microgrid is employed to assess the performance of the online optimization-based control strategy and the simulation results are discussed. The method is applied to an experimental microgrid located in Athens, Greece. The experimental results show the feasibility and the effectiveness of the proposed approach.

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A Model Predictive Control Approach to Microgrid Operation Optimization

Nonlinear phenomena in closed-loop pulsewidth modulated (PWM) DC/DC converters are analyzed. We introduce a new discrete time nonlinear map-the A-switching map-which is related to the asynchronous switchings, i.e., the changes of converter configuration occurring within the modulating period. This map is compared with the stroboscopic map, which is typically used in the study of DC/DC converters. Analytical conditions for the occurrence of periodic orbits and flip bifurcations are obtained. Moreover, necessary conditions for infinite local stretching on the phase space are derived. Finally, a possible explanation of the sudden jump to chaos exhibited by DC/DC converters is proposed. Analytical and numerical results can be applied to all fundamental DC/DC converter topologies. The case of the voltage-controlled buck converter is treated in detail.

Switchings, bifurcations, and chaos in DC/DC converters

A gearshift control strategy for modern automated manual transmissions (AMTs) with dry clutches is proposed. The controller is designed through a hierarchical approach by discriminating among five different AMT operating phases: engaged, slipping-opening, synchronization, go-to-slipping, and slipping-closing. The control schemes consist of decoupled and cascaded feedback loops based on measurements of engine speed, clutch speed, and throwout bearing position, and on estimation of the transmitted torque. Models of driveline, dry clutch, and controlled actuator are estimated on experimental data of a medium size gasoline car and used to check through simulations the effectiveness of the proposed controller.

Gearshift control for automated manual transmissions

Use of Model Predictive Control for Experimental Microgrid Optimization

Deep brain stimulation (DBS) is an effective therapy to treat movement disorders including essential tremor, dystonia, and Parkinson's disease. Despite over a decade of clinical experience the mechanisms of DBS are still unclear, and this lack of understanding makes the selection of stimulation parameters quite challenging. The objective of this work was to develop a closed-loop control system that automatically adjusted the stimulation amplitude to reduce oscillatory neuronal activity, based on feedback of electrical signals recorded from the brain using the same electrode as implanted for stimulation. We simulated a population of 100 intrinsically active model neurons in the Vim thalamus, and the local field potentials (LFPs) generated by the population were used as the feedback (control) variable for closed loop control of DBS amplitude. Based on the correlation between the spectral content of the thalamic activity and tremor (Hua , 1998), (Lenz , 1988), we implemented an adaptive minimum variance controller to regulate the power spectrum of the simulated LFPs and restore the LFP power spectrum present under tremor conditions to a reference profile derived under tremor free conditions. The controller was based on a recursively identified autoregressive model (ARX) of the relationship between stimulation input and LFP output, and showed excellent performances in tracking the reference spectral features through selective changes in the theta (2-7 Hz), alpha (7-13 Hz), and beta (13-35 Hz) frequency ranges. Such changes reflected modifications in the firing patterns of the model neuronal population, and, differently from open-loop DBS, replaced the tremor-related pathological patterns with patterns similar to those simulated in tremor-free conditions. The closed-loop controller generated a LFP spectrum that approximated more closely the spectrum present in the tremor-free condition than did open loop fixed intensity stimulation and adapted to match the spectrum after a change in the neuronal oscillation frequency. This computational study suggests the feasibility of closed-loop control of DBS amplitude to regulate the spectrum of the local field potentials and thereby normalize the aberrant pattern of neuronal activity present in tremor.

Luigi Glielmo

Papers

A Model Predictive Control Approach to Microgrid Operation Optimization

Switchings, bifurcations, and chaos in DC/DC converters

Gearshift control for automated manual transmissions

Use of Model Predictive Control for Experimental Microgrid Optimization

Closed-Loop Control of Deep Brain Stimulation: A Simulation Study