Optimal Control of Nonlinear Switched Systems: Computational Methods and Applications

A switched system is a dynamic system that operates by switching between different subsystems or modes. Such systems exhibit both continuous and discrete characteristics—a dual nature that makes designing effective control policies a challenging task. The purpose of this paper is to review some of the latest computational techniques for generating optimal control laws for switched systems with nonlinear dynamics and continuous inequality constraints. We discuss computational strategiesfor optimizing both the times at which a switched system switches from one mode to another (the so-called switching times) and the sequence in which a switched system operates its various possible modes (the so-called switching sequence). These strategies involve novel combinations of the control parameterization method, the timescaling transformation, and bilevel programming and binary relaxation techniques. We conclude the paper by discussing a number of switched system optimal control models arising in practical applications

New insights into the genetic etiology of Alzheimer's disease and related dementias

Characterization of the genetic landscape of Alzheimer's disease (AD) and related dementias (ADD) provides a unique opportunity for a better understanding of the associated pathophysiological processes. We performed a two-stage genome-wide association study totaling 111,326 clinically diagnosed/'proxy' AD cases and 677,663 controls. We found 75 risk loci, of which 42 were new at the time of analysis. Pathway enrichment analyses confirmed the involvement of amyloid/tau pathways and highlighted microglia implication. Gene prioritization in the new loci identified 31 genes that were suggestive of new genetically associated processes, including the tumor necrosis factor alpha pathway through the linear ubiquitin chain assembly complex. We also built a new genetic risk score associated with the risk of future AD/dementia or progression from mild cognitive impairment to AD/dementia. The improvement in prediction led to a 1.6- to 1.9-fold increase in AD risk from the lowest to the highest decile, in addition to effects of age and the APOE ε4 allele

Solvation enthalpy and the thermodynamics of hydration of trans-cyclohexyl-1,4-diamine and cis-cyclohexyl-1,2-diamine

The enthalpy of solution of trans-cyclohexyl-1,4-diamine and cis-cyclohexyl-1,2-diamine in water was determined by calorimetry. The enthalpy of hydration was determined from this quantity and from the enthalpy of sublimation/vaporization presented in another paper by the authors. Considering the solvation process resulting from cavity creation in the solvent and variation of solute conformation transfer steps, the enthalpy corresponding to solute-solvent interaction was estimated. The entropies of solvation and interaction were calculated from the values given for the enthalpies in the present paper and those available for the Gibbs free energies.http://www.sciencedirect.com/science/article/B6WHM-4P7788D-1/1/08d12dc60548e86cd10853255d09209

Optimal discrete-valued control computation

In this paper, we consider an optimal control problem in which the control takes values from a discrete set and the state and control are subject to continuous inequality constraints. By introducing auxiliary controls and applying a time-scaling transformation, we transform this optimal control problem into an equivalent problem subject to additional linear and quadratic constraints. The feasible region defined by these additional constraints is disconnected, and thus standard optimization methods struggle to handle these constraints. We introduce a novel exact penalty function to penalize constraint violations, and then append this penalty function to the objective. This leads to an approximate optimal control problem that can be solved using standard software packages such as MISER. Convergence results show that when the penalty parameter is sufficiently large, any local solution of the approximate problem is also a local solution of the original problem. We conclude the paper with some numerical results for two difficult train control problems

Initial viral load and the outcomes of SARS

BACKGROUND: Severe acute respiratory syndrome (SARS) is caused by a novel coronavirus. It may progress to respiratory failure, and a significant proportion of patients die. Preliminary data suggest that a high viral load of the SARS coronavirus is associated with adverse outcomes in the intensive care unit, but the relation of viral load to survival is unclear. METHODS: We prospectively studied an inception cohort of 133 patients with virologically confirmed SARS who were admitted to 2 general acute care hospitals in Hong Kong from Mar. 24 to May 4, 2003. The patients were followed until death or for a minimum of 90 days. We used Cox proportional hazard modelling to analyze potential predictors of survival recorded at the time of presentation, including viral load from nasopharyngeal specimens (measured by quantitative reverse transcriptase polymerase chain reaction [PCR] of the SARS-associated coronavirus). RESULTS: Thirty-two patients (24.1%) met the criteria for acute respiratory distress syndrome, and 24 patients (18.0%) died. The following baseline factors were independently associated with worse survival: older age (61–80 years) (adjusted hazard ratio [HR] 5.24, 95% confidence interval [CI] 2.03–13.53), presence of an active comorbid condition (adjusted HR 3.36, 95% CI 1.44–7.82) and higher initial viral load of SARS coronavirus, according to quantitative PCR of nasopharyngeal specimens (adjusted HR 1.21 per log(10) increase in number of RNA copies per millilitre, 95% CI 1.06–1.39). INTERPRETATION: We found preliminary evidence that higher initial viral load is independently associated with worse prognosis in SARS. Mortality data for patients with SARS should be interpreted in light of age, comorbidity and viral load. These considerations will be important in future studies of SARS