The numerical control of the motion of a passive particle in a point vortex flow

This work reports numerical explorations in the advection of one passive tracer by point vortices living in the unbounded plane. The main objective is to find the energy-optimal displacement of one passive particle (point vortex with zero circulation) surrounded by N point vortices. The direct formulation of the corresponding control problems is presented for the case of N = 1, N = 2, N = 3 and N = 4 vortices. The restrictions are due to (i) the ordinary differential equations that govern the displacement of the passive particle around the point vortices, (ii) the available time T to go from the initial position z0 to the final destination zf; and (iii) the maximum absolute value umax that is imposed on the control variables. The resulting optimization problems are solved numerically. The numerical results show the existence of nearly/quasi-optimal control.info:eu-repo/semantics/publishedVersio

Deciding Together?:Best Interests and Shared Decision-Making in Paediatric Intensive Care

In the western healthcare, shared decision making has become the orthodox approach to making healthcare choices as a way of promoting patient autonomy. Despite the fact that the autonomy paradigm is poorly suited to paediatric decision making, such an approach is enshrined in English common law. When reaching moral decisions, for instance when it is unclear whether treatment or non-treatment will serve a child’s best interests, shared decision making is particularly questionable because agreement does not ensure moral validity. With reference to current common law and focusing on intensive care practice, this paper investigates what claims shared decision making may have to legitimacy in a paediatric intensive care setting. Drawing on key texts, I suggest these identify advantages to parents and clinicians but not to the child who is the subject of the decision. Without evidence that shared decision making increases the quality of the decision that is being made, it appears that a focus on the shared nature of a decision does not cohere with the principle that the best interests of the child should remain paramount. In the face of significant pressures toward the displacement of the child’s interests in a shared decision, advantages of a shared decision to decisional quality require elucidation. Although a number of arguments of this nature may have potential, should no such advantages be demonstrable we have cause to revise our commitment to either shared decision making or the paramountcy of the child in these circumstances

Estimating confidence intervals in predicted responses for oscillatory biological models

BACKGROUND: The dynamics of gene regulation play a crucial role in a cellular control: allowing the cell to express the right proteins to meet changing needs. Some needs, such as correctly anticipating the day-night cycle, require complicated oscillatory features. In the analysis of gene regulatory networks, mathematical models are frequently used to understand how a network’s structure enables it to respond appropriately to external inputs. These models typically consist of a set of ordinary differential equations, describing a network of biochemical reactions, and unknown kinetic parameters, chosen such that the model best captures experimental data. However, since a model’s parameter values are uncertain, and since dynamic responses to inputs are highly parameter-dependent, it is difficult to assess the confidence associated with these in silico predictions. In particular, models with complex dynamics - such as oscillations - must be fit with computationally expensive global optimization routines, and cannot take advantage of existing measures of identifiability. Despite their difficulty to model mathematically, limit cycle oscillations play a key role in many biological processes, including cell cycling, metabolism, neuron firing, and circadian rhythms. RESULTS: In this study, we employ an efficient parameter estimation technique to enable a bootstrap uncertainty analysis for limit cycle models. Since the primary role of systems biology models is the insight they provide on responses to rate perturbations, we extend our uncertainty analysis to include first order sensitivity coefficients. Using a literature model of circadian rhythms, we show how predictive precision is degraded with decreasing sample points and increasing relative error. Additionally, we show how this method can be used for model discrimination by comparing the output identifiability of two candidate model structures to published literature data. CONCLUSIONS: Our method permits modellers of oscillatory systems to confidently show that a model’s dynamic characteristics follow directly from experimental data and model structure, relaxing assumptions on the particular parameters chosen. Ultimately, this work highlights the importance of continued collection of high-resolution data on gene and protein activity levels, as they allow the development of predictive mathematical models

Robust stability of nonlinear model predictive control with extended Kalman filter and target setting

This work deals with the closed-loop robust stability of nonlinear model predictive control (NMPC) coupled with an extended Kalman filter (EKF). First, we point out the gaps between the practical formulations and theoretical research. Then, we show that the estimation error dynamics of an EKF are input-to-state stable (ISS) in the presence of nonvanishing perturbations. Moreover, a target setting optimization problem is proposed to solve the target state corresponding to the desired set points, which are used in the objective function in NMPC formulation. Thus, the objective function is a Lyapunov function candidate, and the input-to-state practical stability (ISpS) of the closed-loop system can be established. Moreover, we see that the stability property deteriorates because of the estimation error. Simulation results of the proposed scheme are presented.Copyright (c) 2012 John Wiley & Sons, Ltd

Robust stability of nonlinear model predictive control based on extended Kalman filter

This work deals with state estimation and process control for nonlinear systems, especially when nonlinear model predictive control (NMPC) is integrated with extended Kalman filter (EKF) as the state estimator. In particular, we focus on the robust stability of NMPC and EKF in the presence of plant-model mismatch. The convergence property of the estimation error from the EKE in the presence of non-vanishing perturbations is established based on our previous work [1]. In addition, a so-called one way interaction is shown that the EKE error is not influenced by control action from the NMPC. Hence, the EKF analysis is still valid in the output-feedback NMPC framework, even though there is no separation principle for general nonlinear systems. With this result, we study the robust stability of the output-feedback NMPC under the impact of the estimation error. It turns out the output-feedback NMPC with EKF is Input-to-State practical Stable (ISpS). Finally, two offset-free strategies of output-feedback NMPC are presented and illustrated through a simulation example. (C) 2011 Elsevier Ltd. All rights reserved

Development of robust extended Kalman filter and moving window estimator for simultaneous state and parameter/disturbance estimation

Simultaneous occurrence of gross errors (outliers/biases/drifts) in the measured signals, and drifting disturbances/parameter variations affecting the system dynamics can lead to biased state estimates, and, in turn, can lead to deterioration in the performance of model-based monitoring and control schemes. In this work, robust recursive and moving window based Bayesian state and parameter estimators are developed that are robust w.r.t. gross errors in the measurements and can simultaneously estimate non-additive unmeasured disturbance/parameter variations. Using Bayes' rule, the update step of Kalman filter (KF) is recast as an optimization problem. The optimization is then modified by replacing the likelihood term in the objective function with cost function defined by an M-estimator. The M-estimators considered in this work are Huber's Fair function and Hampel's redescending estimator. The reformulated KF is then used as a basis for reformulating extended Kalman filter (EKF). This re-formulated EKF is then used for developing robust simultaneous state and parameter estimation schemes. In particular, a robust version of recently proposed moving window based state and parameter estimator [1] has been developed. The resulting formulation can be viewed as a hybrid approach, in which the gross errors in the measurements are dealt with in a passive manner, with an active elimination of model plant mismatch by estimating unmeasured disturbance/parameter variations simultaneously. The efficacy of the proposed robust state and parameter estimators is demonstrated by conducting simulation studies and experimental studies. Analysis of the simulation and experimental results reveal that the proposed robust recursive and moving window based state and parameter estimators significantly reduce or completely nullify the effect of gross errors on the state estimates while simultaneously estimating drifting unmeasured disturbances/parameters. The simulation study also underscores the importance of simultaneous estimation of unmeasured disturbances/parameters while achieving robustness using the M-estimators. Moreover, Hampel's redescending estimator is found to be a better choice of M-estimator than the popular Huber's Fair function, as the redescending estimator can completely nullify the effect of gross errors on the state and parameter estimates. (C) 2018 Elsevier Ltd. All rights reserved

Stability of a class of discrete-time nonlinear recursive observers

This work provides a framework for nominal and robust stability analysis for a class of discrete-time nonlinear recursive observers (DNRO). Given that the system has linear output mapping, local observability and Jacobian matrices satisfying certain conditions, the nominal and robust stability of the DNRO is defined by the property of estimation error dynamics and is analyzed using Lyapunov theory. Moreover, a simultaneous state and parameter estimation scheme is shown to be Input-to-State Stable (ISS), and adaptively reduce plant-model mismatch on-line. Three design strategies of the DNRO that satisfy the stability results are given as examples, including the widely used extended Kalman filter, extended Luenberger observer, and the fixed gain observer

Integrating superstructure‐based design of molecules, processes, and flowsheets

The key to many chemical and energy conversion processes is the choice of the right molecule, for example, used as working fluid. However, the choice of the molecule is inherently coupled to the choice of the right process flowsheet. In this work, we integrate superstructure‐based flowsheet design into the design of processes and molecules. The thermodynamic properties of the molecule are modeled by the PC‐SAFT equation of state. Computer‐aided molecular design enables considering the molecular structure as degree of freedom in the process optimization. To consider the process flowsheet as additional degree of freedom, a superstructure of the process is used. The method results in the optimal molecule, process, and flowsheet. We demonstrate the method for the design of an organic Rankine cycle considering flowsheet options for regeneration, reheating, and turbine bleeding. The presented method provides a user‐friendly tool to solve the integrated design problem of processes, molecules, and process flowsheets