Robust and Resilient State Dependent Control of Discrete-Time Nonlinear Systems with General Performance Criteria

A novel state dependent control approach for discrete-time nonlinear systems with general performance criteria is presented. This controller is robust for unstructured model uncertainties, resilient against bounded feedback control gain perturbations in achieving optimality for general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. For the system model, unstructured uncertainty description is assumed, which incorporates commonly used types of uncertainties, such as norm-bounded and positive real uncertainties as special cases. By solving a state dependent linear matrix inequality at each time step, sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this paper unify existing results on nonlinear quadratic regulator, H∞ and positive real control to provide a novel robust control design. The effectiveness of the proposed technique is demonstrated by simulation of the control of inverted pendulum

Stochastically Resilient Observer Design for a Class of Continuous-Time Nonlinear Systems

This work addresses the design of stochastically resilient or non-fragile continuous-time Luenberger observers for systems with incrementally conic nonlinearities. Such designs maintain the convergence and/or performance when the observer gain is erroneously implemented due possibly to computational errors i.e. round off errors in computing the observer gain or changes in the observer parameters during operation. The error in the observer gain is modeled as a random process and a common linear matrix inequality formulation is presented to address the stochastically resilient observer design problem for a variety of performance criteria. Numerical examples are given to illustrate the theoretical results

An LMI Approach to Discrete-Time Observer Design with Stochastic Resilience

Much of the recent work on robust control or observer design has focused on preservation of stability of the controlled system or the convergence of the observer in the presence of parameter perturbations in the plant or the measurement model. The present work addresses the important problem of stochastic resilience or non-fragility of a discrete-time Luenberger observer which is the maintenance of convergence and/or performance when the observer is erroneously implemented possibly due to computational errors i.e. round off errors in digital implementation or sensor errors, etc. A common linear matrix inequality framework is presented to address the stochastic resilient design problem for various performance criteria in the implementation based on the knowledge of an upper bound on the variance of the random error in the observer gain. Present results are compared to earlier designs for stochastic robustness. Illustrative examples are given to complement the theoretical results

Resilient Observer Design for Discrete-Time Nonlinear Systems with General Criteria

A class of discrete-time nonlinear system and measurement equations having incrementally conic nonlinearities and finite energy disturbances is considered. A linear matrix inequality based resilient observer design approach is presented to guarantee the satisfaction of a variety of performance criteria ranging from simple estimation error boundedness to dissipativity in the presence of bounded perturbations on the gain. Some simulation examples are included to illustrate the proposed design methodology

Global burden of 288 causes of death and life expectancy decomposition in 204 countries and territories and 811 subnational locations, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BACKGROUND Regular, detailed reporting on population health by underlying cause of death is fundamental for public health decision making. Cause-specific estimates of mortality and the subsequent effects on life expectancy worldwide are valuable metrics to gauge progress in reducing mortality rates. These estimates are particularly important following large-scale mortality spikes, such as the COVID-19 pandemic. When systematically analysed, mortality rates and life expectancy allow comparisons of the consequences of causes of death globally and over time, providing a nuanced understanding of the effect of these causes on global populations. METHODS The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2021 cause-of-death analysis estimated mortality and years of life lost (YLLs) from 288 causes of death by age-sex-location-year in 204 countries and territories and 811 subnational locations for each year from 1990 until 2021. The analysis used 56 604 data sources, including data from vital registration and verbal autopsy as well as surveys, censuses, surveillance systems, and cancer registries, among others. As with previous GBD rounds, cause-specific death rates for most causes were estimated using the Cause of Death Ensemble model-a modelling tool developed for GBD to assess the out-of-sample predictive validity of different statistical models and covariate permutations and combine those results to produce cause-specific mortality estimates-with alternative strategies adapted to model causes with insufficient data, substantial changes in reporting over the study period, or unusual epidemiology. YLLs were computed as the product of the number of deaths for each cause-age-sex-location-year and the standard life expectancy at each age. As part of the modelling process, uncertainty intervals (UIs) were generated using the 2·5th and 97·5th percentiles from a 1000-draw distribution for each metric. We decomposed life expectancy by cause of death, location, and year to show cause-specific effects on life expectancy from 1990 to 2021. We also used the coefficient of variation and the fraction of population affected by 90% of deaths to highlight concentrations of mortality. Findings are reported in counts and age-standardised rates. Methodological improvements for cause-of-death estimates in GBD 2021 include the expansion of under-5-years age group to include four new age groups, enhanced methods to account for stochastic variation of sparse data, and the inclusion of COVID-19 and other pandemic-related mortality-which includes excess mortality associated with the pandemic, excluding COVID-19, lower respiratory infections, measles, malaria, and pertussis. For this analysis, 199 new country-years of vital registration cause-of-death data, 5 country-years of surveillance data, 21 country-years of verbal autopsy data, and 94 country-years of other data types were added to those used in previous GBD rounds. FINDINGS The leading causes of age-standardised deaths globally were the same in 2019 as they were in 1990; in descending order, these were, ischaemic heart disease, stroke, chronic obstructive pulmonary disease, and lower respiratory infections. In 2021, however, COVID-19 replaced stroke as the second-leading age-standardised cause of death, with 94·0 deaths (95% UI 89·2-100·0) per 100 000 population. The COVID-19 pandemic shifted the rankings of the leading five causes, lowering stroke to the third-leading and chronic obstructive pulmonary disease to the fourth-leading position. In 2021, the highest age-standardised death rates from COVID-19 occurred in sub-Saharan Africa (271·0 deaths [250·1-290·7] per 100 000 population) and Latin America and the Caribbean (195·4 deaths [182·1-211·4] per 100 000 population). The lowest age-standardised death rates from COVID-19 were in the high-income super-region (48·1 deaths [47·4-48·8] per 100 000 population) and southeast Asia, east Asia, and Oceania (23·2 deaths [16·3-37·2] per 100 000 population). Globally, life expectancy steadily improved between 1990 and 2019 for 18 of the 22 investigated causes. Decomposition of global and regional life expectancy showed the positive effect that reductions in deaths from enteric infections, lower respiratory infections, stroke, and neonatal deaths, among others have contributed to improved survival over the study period. However, a net reduction of 1·6 years occurred in global life expectancy between 2019 and 2021, primarily due to increased death rates from COVID-19 and other pandemic-related mortality. Life expectancy was highly variable between super-regions over the study period, with southeast Asia, east Asia, and Oceania gaining 8·3 years (6·7-9·9) overall, while having the smallest reduction in life expectancy due to COVID-19 (0·4 years). The largest reduction in life expectancy due to COVID-19 occurred in Latin America and the Caribbean (3·6 years). Additionally, 53 of the 288 causes of death were highly concentrated in locations with less than 50% of the global population as of 2021, and these causes of death became progressively more concentrated since 1990, when only 44 causes showed this pattern. The concentration phenomenon is discussed heuristically with respect to enteric and lower respiratory infections, malaria, HIV/AIDS, neonatal disorders, tuberculosis, and measles. INTERPRETATION Long-standing gains in life expectancy and reductions in many of the leading causes of death have been disrupted by the COVID-19 pandemic, the adverse effects of which were spread unevenly among populations. Despite the pandemic, there has been continued progress in combatting several notable causes of death, leading to improved global life expectancy over the study period. Each of the seven GBD super-regions showed an overall improvement from 1990 and 2021, obscuring the negative effect in the years of the pandemic. Additionally, our findings regarding regional variation in causes of death driving increases in life expectancy hold clear policy utility. Analyses of shifting mortality trends reveal that several causes, once widespread globally, are now increasingly concentrated geographically. These changes in mortality concentration, alongside further investigation of changing risks, interventions, and relevant policy, present an important opportunity to deepen our understanding of mortality-reduction strategies. Examining patterns in mortality concentration might reveal areas where successful public health interventions have been implemented. Translating these successes to locations where certain causes of death remain entrenched can inform policies that work to improve life expectancy for people everywhere. FUNDING Bill & Melinda Gates Foundation

Reduced-Order Filtering of Jump Markov Systems with Noise-Free Measurements

In continuous-time Kalman filtering for jump Markov systems, it is required that the measurement noise covariance be nonsingular. In this work, the case of noise-free measurements is considered and it is proposed that a reduced-order filter be used to overcome this singularity problem. This filter is optimal in the minimum variance sense and is of dimension (n−p) where n and p are the state and measurement vector dimensions, respectively. After the optimal filter equations are derived for the finite-time case, we focus on the infinite-time case and characterize the set of all assignable estimation error covariances and parametrize the set of all estimator gains. The conditions for the existence of the optimal steady-state filter are obtained in terms of the system theoretic properties of the original signal model

Fixed-order Dissipative Estimator Design for Uncertain Stochastic Systems

A general class of discrete-time uncertain nonlinear stochastic systems with quadratic sum constraints is considered. A linear fixed order state estimator for state estimation is presented for various estimation error performance criteria in a unified framework. The observer is of order equal to the difference between the state and output vector dimensions. The performance criteria considered in this paper include guaranteed-cost suboptimal versions of estimation objectives like H2, H∞, stochastic passivity, etc. The design of fixed-order linear state estimators that satisfy these criteria are given using a common matrix inequality formulation

A Reduced-Order Stochastic Observer Approach to Optimal State Estimation with Noise-Free Measurements

In a continuous-time Kalman filter, it is required that the measurement noise covariance be non-singular. If the measurements are noise-free, then this condition does not hold and, in practice, the measurement data are differentiated to define a derived measurement function to build what is known as Deyst filter. It is proposed here that a reduced-order observer be used in deriving the linear minimum-variance filter to construct state estimates based on the original measurement data with no need for differentiation. This filter is of dimension (n−p) where n and p are the state and measurement vector dimensions, respectively. In this work, we consider both the finite-time and infinite-time results. The set of all assignable estimation error covariances are characterized and the set of all estimator gains are parametrized in addition to the linear minimum variance optimal results. The conditions for the existence of the optimal steady-state filter are obtained in terms of the system theoretic properties of the original signal model. A simple example is included to illustrate the effectiveness of the proposed technique. Copyright © 2001 John Wiley & Sons, Ltd

Stochastic Stabilizability of a Class of Discrete-Time Non-Linear Systems

This paper presents a characterization of all state covariances assignable by a linear static output feedback controller to a class of discrete-time non-linear stochastic systems and a parametrization of all such controllers that will achieve a desired covariance. These results indirectly provide similar results for fixed-order dynamic feedback compensators. This characterization enables one to test the stochastic stabilizability of such systems by output feedback. An alternative formulation of stochastic stabilizability by output feedback is also included. Then, these results are specialized to the state feedback case and presented together with the previous results of the authors\u27 to form a more complete and unified picture of stochastic stabilizability conditions

On LMI Formulations of Some Problems Arising in Nonlinear Stochastic System Analysis

This work involves formulation of some problems arising in the analysis of a class of discrete-time nonlinear stochastic systems in terms of linear matrix inequalities. This allows one to utilize a wide variety of numerical techniques available for tackling both the feasibility problem and the actual numerical solution in an efficient manner