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Normal pressure hydrocephalus (NPH) is a chronic and progressive disease that affects predominantly elderly subjects. The most prevalent symptoms are gait disorders, generally determined by visual observation or measurements taken in complex laboratory environments. However, controlled testing environments can have a significant influence on the way subjects walk and hinder the identification of natural walking characteristics. The study aimed to investigate the differences in walking patterns between a controlled environment (10 m walking test) and real-world environment (72 h recording) based on measurements taken via a wearable gait assessment device. We tested whether real-world environment measurements can be beneficial for the identification of gait disorders by performing a comparison of patients’ gait parameters with an aged-matched control group in both environments. Subsequently, we implemented four machine learning classifiers to inspect the individual strides’ profiles. Our results on twenty young subjects, twenty elderly subjects and twelve NPH patients indicate that patients exhibited a considerable difference between the two environments, in particular gait speed (p-value p=0.0073), stride length (p-value p=0.0073), foot clearance (p-value p=0.0117) and swing/stance ratio (p-value p=0.0098). Importantly, measurements taken in real-world environments yield a better discrimination of NPH patients compared to the controlled setting. Finally, the use of stride classifiers provides promise in the identification of strides affected by motion disorders.

Background Shunt systems for hydrocephalus therapy are commonly based on passive mechanical pressure valves that are driven by the intracranial, intra-abdominal, and hydrostatic pressure. The differential pressure acting on the valve determines the drainage rate of cerebrospinal fluid (CSF) but is not a gauge of the physiological condition of the patient. Internal and external influences can cause over- or underdrainage and lead to pathological levels of intracranial pressure (ICP). Methods The first prototype of a ventricular intelligent and electromechanical shunt (VIEshunt) is developed, tested, and compared with previous efforts towards the development of a smart shunt. Its key components are a micro pump, a flow meter, a pressure sensor, an inertial measurement unit, a wireless communication interface, and a microcontroller. The VIEshunt prototype was tested in vitro using a hardware-in-the-loop (HiL) test bench that runs real-time patient simulations involving changes in intracranial and intra-abdominal pressure, as well as changes in posture ranging between supine and upright position. The prototype was subsequently tested in an in vivo pilot study based on an acute ovine animal model (n=1) with infusions of artificial CSF. Results During 24 h in vitro testing, the prototype detected the simulated posture changes of the patient and automatically adapted the controller reference. The posture-specific ICP references of 12 mmHg for supine and —3 mmHg for upright position were tracked without offset, thus preventing adverse over- and underdrainage during the investigated HiL test scenario. During acute in vivo testing, the prototype first regulated the mean ICP of a sheep from 22 mmHg down to 20 mmHg. Each of the three subsequent intraventricular bolus infusions of 1 mL saline solution increased mean ICP by approximately 11 mmHg. While natural absorption alone decreased ICP by only 5 mmHg within 9 min, the prototype was able to regulate ICP back to the pre-bolus pressure value within 5 min. Conclusion The developed VIEshunt prototype is capable of posture-dependent ICP regulation and CSF drainage control. Smart shunt systems based on VIEshunt could improve patient monitoring and enable optimal physiologic therapy by adapting to the individual patient. To derive statistically relevant conclusions for the performance of VIEshunt, future work will focus on the development of a next generation prototype for use in pre-clinical studies.

In plants, as in animals, the core mechanism to retain rhythmic gene expression relies on the interaction of multiple feedback loops. In recent years, molecular genetic techniques have revealed a complex network of clock components in Arabidopsis . To gain insight into the dynamics of these interactions, new components need to be integrated into the mathematical model of the plant clock. Our approach accelerates the iterative process of model identification, to incorporate new components, and to systematically test different proposed structural hypotheses. Recent studies indicate that the pseudo‐response regulators PRR7 and PRR9 play a key role in the core clock of Arabidopsis . We incorporate PRR7 and PRR9 into an existing model involving the transcription factors TIMING OF CAB (TOC1), LATE ELONGATED HYPOCOTYL (LHY) and CIRCADIAN CLOCK ASSOCIATED (CCA1). We propose candidate models based on experimental hypotheses and identify the computational models with the application of an optimization routine. Validation is accomplished through systematic analysis of various mutant phenotypes. We introduce and apply sensitivity analysis as a novel tool for analyzing and distinguishing the characteristics of proposed architectures, which also allows for further validation of the hypothesized structures. Synopsis In recent years, molecular genetic techniques have revealed a complex network of components in the Arabidopsis circadian clock. Mathematical models allow for a detailed study of the dynamics and architecture of such complex gene networks leading to a better understanding of the genetic interactions. It is important to maintain a constant iteration with experimentation, to include novel components as they are discovered and use the updated model to design new experiments. This study develops a framework to introduce new components into the mathematical model of the Arabidopsis circadian clock accelerating the iterative model development process and gaining insight into the system's properties. We used the interlocked feedback loop model published in Locke et al (2005) as the base model. In Arabidopsis , the first suggested regulatory loop involves the morning expressed transcription factors CIRCADIAN CLOCK‐ASSOCIATED 1 ( CCA1 ) and LATE ELONGATED HYPOCOTYL ( LHY ), and the evening expressed pseudo‐response regulator TIMING OF CAB EXPRESSION ( TOC1) . The hypothetical component X had been introduced to realize a longer delay between gene expression of CCA1/LHY and TOC1. The introduction of Y was motivated by the need for a mechanism to reproduce the dampening short period rhythms of the cca1/lhy double mutant and to include an additional light input at the end of the day. In this study, the new components pseudo‐response regulators PRR7 and PRR9 were added in negative feedback loops based on the biological hypothesis that they are activated by LHY and in turn repress LHY transcription (Farré et al , 2005 ; Figure 1 ). We present three iterations steps of model development ( Figure 1A–C ). A wide range of tools was used to establish and analyze new model structures. One of the challenges facing mathematical modeling of biological processes is parameter identification; they are notoriously difficult to determine experimentally. We established an optimization procedure based on an evolutionary strategy with a cost function mainly derived from wild‐type characteristics. This ensured that the model was not restricted by a specific set of parameters and enabled us to use a large set of biological mutant information to assess the predictive capability of the model structure. Models were evaluated by means of an extended phenotype catalogue, allowing for an easy and fair comparison of the structures. We also carried out detailed simulation analysis of component interactions to identify weak points in the structure and suggest further modifications. Finally, we applied sensitivity analysis in a novel manner, using it to direct the model development. Sensitivity analysis provides quantitative measures of robustness; the two measures in this study were the traces of component concentrations over time (classical state sensitivities) and phase behavior (measured by the phase response curve). Three major results emerged from the model development process. First, the iteration process helped us to learn about general characteristics of the system. We observed that the timing of Y expression is critical for evening light entrainment, which enables the system to respond to changes in day length. This is important for our understanding of the mechanism of light input to the clock and will add in the identification of biological candidates for this function. In addition, our results suggest that a detailed description of the mechanisms of genetic interactions is important for the systems behavior. We observed that the introduction of an experimentally based precise light regulation mechanism on PRR9 expression had a significant effect on the systems behavior. Second, the final model structure (Figure 1C ) was capable of predicting a wide range of mutant phenotypes, such as a reduction of TOC1 expression by RNAi ( toc1RNAi ), mutations in PRR7 and PRR9 and the novel mutant combinations prr9toc1RNAi and prr7prr9toc1RNAi . However, it was unable to predict the mutations in CCA1 and LHY . Finally, sensitivity analysis identified the weak points of the system. The developed model structure was heavily based on the TOC1/Y feedback loop. This could explain the model's failure to predict the cca1lhy double mutant phenotype. More detailed information on the regulation of CCA1 and LHY expression will be important to achieve the right balance between the different regulatory loops in the mathematical model. This is in accordance with genetic studies that have identified several genes involved in the regulation of LHY and CCA1 expression. The identification of their mechanism of action will be necessary for the next model development. We developed a mathematical model of the Arabidopsis circadian clock, including PRR7 and PRR9, which is able to predict several single, double and triple mutant phenotypes. Sensitivity Analysis was used to identify the properties and time sensing mechanisms of model structures. PRR7 and CCA1/LHY were identified as weak points of the mathematical model indicating where more experimental data is needed for further model development. Detailed dynamical studies showed that the timing of an evening light sensing element is essential for day length responsiveness

Tube-based model predictive control (MPC) methods leverage tubes to bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. This paper presents a novel tube‑based MPC formulation based on system level disturbance reachable sets (SL‑DRS), which leverage the affine system level parameterization (SLP). We show that imposing a finite impulse response (FIR) constraint on the affine SLP guarantees containment of all future deviations in a finite sequence of SL‑DRS. This allows us to formulate a system level tube‑MPC (SLTMPC) method using the SL‑DRS as tubes, which enables concurrent optimization of the nominal trajectory and the tubes, while using a positively invariant terminal set. Finally, we show that the SL‑DRS tubes can also be computed offline.

We consider the design of functional estimators, i.e., approaches to compute an estimate of a nonlinear function of the state of a general nonlinear dynamical system subject to process noise based on noisy output measurements. To this end, we introduce a novel functional detectability notion in the form of incremental input/output-to-output stability (\\(\\delta\\)-IOOS). We show that \\(\\delta\\)-IOOS is a necessary condition for the existence of a functional estimator satisfying an input-to-output type stability property. Additionally, we prove that a system is functional detectable if and only if it admits a corresponding \\(\\delta\\)-IOOS Lyapunov function. Furthermore, \\(\\delta\\)-IOOS is shown to be a sufficient condition for the design of a stable functional estimator by introducing the design of a full information estimation (FIE) approach for functional estimation. Together, we present a unified framework to study functional estimation with a detectability condition, which is necessary and sufficient for the existence of a stable functional estimator, and a corresponding functional estimator design. The practical need for and applicability of the proposed functional estimator design is illustrated with a numerical example of a power system.

We present a stochastic model predictive control (SMPC) framework for linear systems subject to possibly unbounded disturbances. State of the art SMPC approaches with closed-loop chance constraint satisfaction recursively initialize the nominal state based on the previously predicted nominal state or possibly the measured state under some case distinction. We improve these initialization strategies by allowing for a continuous optimization over the nominal initial state in an interpolation of these two extremes. The resulting SMPC scheme can be implemented as one standard quadratic program and is more flexible compared to state-of-the-art initialization strategies. As the main technical contribution, we show that the proposed SMPC framework also ensures closed-loop satisfaction of chance constraints and suitable performance bounds.

We present a robust adaptive model predictive control (MPC) framework for nonlinear continuous-time systems with bounded parametric uncertainty and additive disturbance. We utilize general control contraction metrics (CCMs) to parameterize a homothetic tube around a nominal prediction that contains all uncertain trajectories. Furthermore, we incorporate model adaptation using set-membership estimation. As a result, the proposed MPC formulation is applicable to a large class of nonlinear systems, reduces conservatism during online operation, and guarantees robust constraint satisfaction and convergence to a neighborhood of the desired setpoint. One of the main technical contributions is the derivation of corresponding tube dynamics based on CCMs that account for the state and input dependent nature of the model mismatch. Furthermore, we online optimize over the nominal parameter, which enables general set-membership updates for the parametric uncertainty in the MPC. Benefits of the proposed homothetic tube MPC and online adaptation are demonstrated using a numerical example involving a planar quadrotor.

We provide a stability and performance analysis for nonlinear model predictive control (NMPC) schemes subject to input constraints. Given an exponential stabilizability and detectability condition w.r.t. the employed state cost, we provide a sufficiently long prediction horizon to ensure asymptotic stability and a desired performance bound w.r.t. the infinite-horizon optimal controller. Compared to existing results, the provided analysis is applicable to positive semi-definite (detectable) cost functions, provides tight bounds using a linear programming analysis, and allows for a seamless integration of general positive-definite terminal cost functions in the analysis. The practical applicability of the derived theoretical results are demonstrated with numerical examples.

We propose integrating an explicit approximation of a predictive control barrier function (PCBF) in a safety filter framework. The approximated PCBF is implicitly defined through an optimal control problem and allows guaranteeing invariance of an implicitly defined safe set as well as stability of this safe set within a larger domain of attraction. By extending existing theoretical analysis of the PCBF, we establish inherent robustness of the original algorithm and translate the guarantees to input-to-state stability of the proposed algorithm with respect to possible approximation errors, recovering the same guarantees in the absence of approximation errors. The proposed algorithm allows certifying inputs with respect to state constraint satisfaction through a single function evaluation and filtering unsafe inputs through a control barrier function based safety filter, which is independent of the time horizon of the original predictive optimisation problem, resulting in significant online computational benefits. We demonstrate the stability properties of the proposed algorithm on a linear system example as well as its use a fast safety filter for miniature race cars in simulation.

One of the most challenging tasks in control theory is arguably the design of a regulator for nonlinear systems when the dynamics are unknown. To tackle it, a popular strategy relies on finding a direct map between system responses and the controller, and the key ingredient is a predictor for system outputs trained on past trajectories. Focusing on continuous-time, input-affine systems, we show that the so-called signature transform provides rigorous and practically effective features to represent and predict system trajectories. Building upon such a tool, we propose a novel signature-based control strategy that is promising in view of data-driven predictive control.