Predictive feedback in human simulated pendulum balancing

In studies of human balance, it is common to fit stimulus-response data by tuning the time-delay and gain parameters of a simple delayed feedback model. Many interpret this fitted model, a simple delayed feedback model, as evidence that predictive processes are not required to explain existing data on standing balance. However, two questions lead us to doubt this approach. First, does fitting a delayed feedback model lead to reliable estimates of the time-delay? Second, can a non-predictive controller provide an explanation compatible with the independently estimated time delay? For methodological and experimental clarity, we study human balancing of a simulated inverted pendulum via joystick and screen. A two-step approach to data analysis is used: firstly a non-parametric model—the closed-loop impulse response—is estimated from the experimental data; second, a parametric model is fitted to the non-parametric impulse-response by adjusting time-delay and controller parameters. To support the second step, a new explicit formula relating controller parameters to closed-loop impulse response is derived. Two classes of controller are investigated within a common state-space context: non-predictive and predictive. It is found that the time-delay estimate arising from the second step is strongly dependent on which controller class is assumed; in particular, the non-predictive control assumption leads to time-delay estimates that are smaller than those arising from the predictive assumption. Moreover, the time-delays estimated using the non-predictive control assumption are not consistent with a lower-bound on the time-delay of the non-parametric model whereas the corresponding predictive result is consistent. Thus while the goodness of fit only marginally favoured predictive over non-predictive control, if we add the additional constraint that the model must reproduce the non-parametric time delay, then the non-predictive control model fails. We conclude (1) the time-delay should be estimated independently of fitting a low order parametric model, (2) that balance of the simulated inverted pendulum could not be explained by the non-predictive control model and (3) that predictive control provided a better explanation than non-predictive control.     

Intermittent control: a computational theory of human control

The paradigm of continuous control using internal models has advanced understanding of human motor control. However, this paradigm ignores some aspects of human control, including intermittent feedback, serial ballistic control, triggered responses and refractory periods. It is shown that event-driven intermittent control provides a framework to explain the behaviour of the human operator under a wider range of conditions than continuous control. Continuous control is included as a special case, but sampling, system matched hold, an intermittent predictor and an event trigger allow serial open-loop trajectories using intermittent feedback. The implementation here may be described as ??continuous observation, intermittent action??. Beyond explaining unimodal regulation distributions in common with continuous control, these features naturally explain refractoriness and bimodal stabilisation distributions observed in double stimulus tracking experiments and quiet standing, respectively. Moreover, given that human control systems contain significant time delays, a biological-cybernetic rationale favours intermittent over continuous control: intermittent predictive control is computationally less demanding than continuous predictive control. A standard continuous-time predictive control model of the human operator is used as the underlying design method for an event-driven intermittent controller. It is shown that when event thresholds are small and sampling is regular, the intermittent controller can masquerade as the underlying continuous-time controller and thus, under these conditions, the continuous-time and intermittent controller cannot be distinguished. This explains why the intermittent control hypothesis is consistent with the continuous control hypothesis for certain experimental conditions.     

Predictive feedback control and Fitts–law

Fitts’ law is a well established empirical formula, known for encapsulating the “speed-accuracy trade-off”. For discrete, manual movements from a starting location to a target, Fitts’ law relates movement duration to the distance moved and target size. The widespread empirical success of the formula is suggestive of underlying principles of human movement control. There have been previous attempts to relate Fitts’ law to engineering-type control hypotheses and it has been shown that the law is exactly consistent with the closed-loop step-response of a time-delayed, first-order system. Assuming only the operation of closed-loop feedback, either continuous or intermittent, this paper asks whether such feedback should be predictive or not predictive to be consistent with Fitts law. Since Fitts’ law is equivalent to a time delay separated from a first-order system, known control theory implies that the controller must be predictive. A predictive controller moves the time-delay outside the feedback loop such that the closed-loop response can be separated into a time delay and rational function whereas a non- predictive controller retains a state delay within feedback loop which is not consistent with Fitts’ law. Using sufficient parameters, a high-order non-predictive controller could approximately reproduce Fitts’ law. However, such high-order, “non-parametric” controllers are essentially empirical in nature, without physical meaning, and therefore are conceptually inferior to the predictive controller. It is a new insight that using closed-loop feedback, prediction is required to physically explain Fitts’ law. The implication is that prediction is an inherent part of the “speed-accuracy trade-off”.     

A system identification approach for developing model predictive controllers of antibody quality attributes in cell culture processes

As the biopharmaceutical industry evolves to include more diverse protein formats and processes, more robust control of Critical Quality Attributes (CQAs) is needed to maintain processing flexibility without compromising quality. Active control of CQAs has been demonstrated using model predictive control techniques, which allow development of processes which are robust against disturbances associated with raw material variability and other potentially flexible operating conditions. Wide adoption of model predictive control in biopharmaceutical cell culture processes has been hampered, however, in part due to the large amount of data and expertise required to make a predictive model of controlled CQAs, a requirement for model predictive control. Here we developed a highly automated, perfusion apparatus to systematically and efficiently generate predictive models using application of system identification approaches. We successfully created a predictive model of %galactosylation using data obtained by manipulating galactose concentration in the perfusion apparatus in serialized step change experiments. We then demonstrated the use of the model in a model predictive controller in a simulated control scenario to successfully achieve a %galactosylation set point in a simulated fed‐batch culture. The automated model identification approach demonstrated here can potentially be generalized to many CQAs, and could be a more efficient, faster, and highly automated alternative to batch experiments for developing predictive models in cell culture processes, and allow the wider adoption of model predictive control in biopharmaceutical processes. © 2017 The Authors Biotechnology Progress published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers Biotechnol. Prog., 33:1647–1661, 2017     

A model of neuro-musculo-skeletal system for human locomotion under position constraint condition

The human locomotion was studied on the basis of the interaction of the musculo-skeletal system, the neural system and the environment. A mathematical model of human locomotion under position constraint condition was established. Besides the neural rhythm generator, the posture controller and the sensory system, the environment feedback controller and the stability controller were taken into account in the model. The environment feedback controller was proposed for two purposes, obstacle avoidance and target position control of the swing foot. The stability controller was proposed to imitate the self-balancing ability of a human body and improve the stability of the model. In the stability controller, the ankle torque was used to control the velocity of the body gravity center. A prediction control algorithm was applied to calculate the torque magnitude of the stability controller. As an example, human stairs climbing movement was simulated and the results were given. The simulation result proved that the mathematical modeling of the task was successful.     

Human stick balancing: an intermittent control explanation

There are two issues in balancing a stick pivoting on a finger tip (or mechanically on a moving cart): maintaining the stick angle near to vertical and maintaining the horizontal position within the bounds of reach or cart track. The (linearised) dynamics of the angle are second order (although driven by pivot acceleration), and so, as in human standing, control of the angle is not, by itself very difficult. However, once the angle is under control, the position dynamics are, in general, fourth order. This makes control quite difficult for humans (and even an engineering control system requires careful design). Recently, three of the authors have experimentally demonstrated that humans control the stick angle in a special way: the closed-loop inverted pendulum behaves as a non-inverted pendulum with a virtual pivot somewhere between the stick centre and tip and with increased gravity. Moreover, they suggest that the virtual pivot lies at the radius of gyration (about the mass centre) above the mass centre. This paper gives a continuous-time control-theoretical interpretation of the virtual-pendulum approach. In particular, by using a novel cascade control structure, it is shown that the horizontal control of the virtual pivot becomes a second-order problem which is much easier to solve than the generic fourth-order problem. Hence, the use of the virtual pivot approach allows the control problem to be perceived by the subject as two separate second-order problems rather than a single fourth-order problem, and the control problem is therefore simplified. The theoretical predictions are verified using the data previously presented by three of the authors and analysed using a standard parameter estimation method. The experimental data indicate that although all subjects adopt the virtual pivot approach, the less expert subjects exhibit larger amplitude angular motion and poorly controlled translational motion. It is known that human control systems are delayed and intermittent, and therefore, the continuous-time strategy cannot be correct. However, the model of intermittent control used in this paper is based on the virtual pivot continuous-time control scheme, handles time delays and moreover masquerades as the underlying continuous-time controller. In addition, the event-driven properties of intermittent control can explain experimentally observed variability.     

Limb Dominance Results from Asymmetries in Predictive and Impedance Control Mechanisms

Handedness is a pronounced feature of human motor behavior, yet the underlying neural mechanisms remain unclear. We hypothesize that motor lateralization results from asymmetries in predictive control of task dynamics and in control of limb impedance. To test this hypothesis, we present an experiment with two different force field environments, a field with a predictable magnitude that varies with the square of velocity, and a field with a less predictable magnitude that varies linearly with velocity. These fields were designed to be compatible with controllers that are specialized in predicting limb and task dynamics, and modulating position and velocity dependent impedance, respectively. Because the velocity square field does not change the form of the equations of motion for the reaching arm, we reasoned that a forward dynamic-type controller should perform well in this field, while control of linear damping and stiffness terms should be less effective. In contrast, the unpredictable linear field should be most compatible with impedance control, but incompatible with predictive dynamics control. We measured steady state final position accuracy and 3 trajectory features during exposure to these fields: Mean squared jerk, Straightness, and Movement time. Our results confirmed that each arm made straighter, smoother, and quicker movements in its compatible field. Both arms showed similar final position accuracies, which were achieved using more extensive corrective sub-movements when either arm performed in its incompatible field. Finally, each arm showed limited adaptation to its incompatible field. Analysis of the dependence of trajectory errors on field magnitude suggested that dominant arm adaptation occurred by prediction of the mean field, thus exploiting predictive mechanisms for adaptation to the unpredictable field. Overall, our results support the hypothesis that motor lateralization reflects asymmetries in specific motor control mechanisms associated with predictive control of limb and task dynamics, and modulation of limb impedance.     

Evaluation of multi-locus models for genome-wide association studies: a case study in sugar beet

Association mapping has become a widely applied genomic approach to dissect the genetic architecture of complex traits. A major issue for association mapping is the need to control for the confounding effects of population structure, which is commonly done by mixed models incorporating kinship information. In this case study, we employed experimental data from a large sugar beet population to evaluate multi-locus models for association mapping. As in linkage mapping, markers are selected as cofactors to control for population structure and genetic background variation. We compared different biometric models with regard to important quantitative trait locus (QTL) mapping parameters like the false-positive rate, the QTL detection power and the predictive power for the proportion of explained genotypic variance. Employing different approaches we show that the multi-locus model, that is, incorporating cofactors, outperforms the other models, including the mixed model used as a reference model. Thus, multi-locus models are an attractive alternative for association mapping to efficiently detect QTL for knowledge-based breeding.     

An intelligent control method based on fuzzy logic for a robotic testing system for the human spine

In previous biomechanical studies of the human spine, we implemented a hybrid controller to investigate load-displacement characteristics. We found that measurement errors in both position and force caused the controller to be less accurate than predicted. As an alternative to hybrid control, a fuzzy logic controller (FLC) has been developed and implemented in a robotic testing system for the human spine. An FLC is a real-time expert system that can emulate part of a human operator's knowledge by using a set of action rules. The FLC provides simple but robust solutions that cover a wide range of system parameters and can cope with significant disturbances. It can be viewed as a heuristic and modular way of defining a nonlinear, table-based control system. In this study, an FLC is developed which uses the force difference and the change in force difference as the input parameters, and the displacement as the output parameter. A rule-table based on these parameters is designed for the controller Experiments on a physical model composed of springs demonstrate the improved performance of the proposed method.     

Transition from persistent to anti-persistent correlations in postural sway indicates velocity-based control

The displacement of the center-of-pressure (COP) during quiet stance has often been accounted for by the control of COP position dynamics. In this paper, we discuss the conclusions drawn from previous analyses of COP dynamics using fractal-related methods. On the basis of some methodological clarification and the analysis of experimental data using stabilogram diffusion analysis, detrended fluctuation analysis, and an improved version of spectral analysis, we show that COP velocity is typically bounded between upper and lower limits. We argue that the hypothesis of an intermittent velocity-based control of posture is more relevant than position-based control. A simple model for COP velocity dynamics, based on a bounded correlated random walk, reproduces the main statistical signatures evidenced in the experimental series. The implications of these results are discussed.     

Modelling molecular interaction pathways using a two-stage identification algorithm

In systems biology, molecular interactions are typically modelled using white-box methods, usually based on mass action kinetics. Unfortunately, problems with dimensionality can arise when the number of molecular species in the system is very large, which makes the system modelling and behavior simulation extremely difficult or computationally too expensive. As an alternative, this paper investigates the identification of two molecular interaction pathways using a black-box approach. This type of method creates a simple linear-in-the-parameters model using regression of data, where the output of the model at any time is a function of previous system states of interest. One of the main objectives in building black-box models is to produce an optimal sparse nonlinear one to effectively represent the system behavior. In this paper, it is achieved by applying an efficient iterative approach, where the terms in the regression model are selected and refined using a forward and backward subset selection algorithm. The method is applied to model identification for the MAPK signal transduction pathway and the Brusselator using noisy data of different sizes. Simulation results confirm the efficacy of the black-box modelling method which offers an alternative to the computationally expensive conventional approach.     

Forecasting and control of lactate bifurcation in Chinese hamster ovary cell culture processes

Biomanufacturing exhibits inherent variability that can lead to variation in performance attributes and batch failure. To help ensure process consistency and product quality the development of predictive models and integrated control strategies is a promising approach. In this study, a feedback controller was developed to limit excessive lactate production, a widespread metabolic phenomenon that is negatively associated with culture performance and product quality. The controller was developed by applying machine learning strategies to historical process development data, resulting in a forecast model that could identify whether a run would result in lactate consumption or accumulation. In addition, this exercise identified a correlation between increased amino acid consumption and low observed lactate production leading to the mechanistic hypothesis that there is a deficiency in the link between glycolysis and the tricarboxylic acid cycle. Using the correlative process parameters to build mechanistic insight and applying this to predictive models of lactate concentration, a dynamic model predictive controller (MPC) for lactate was designed. This MPC was implemented experimentally on a process known to exhibit high lactate accumulation and successfully drove the cell cultures towards a lactate consuming state. In addition, an increase in specific titer productivity was observed when compared with non-MPC controlled reactors.     

Design of a side-view particle imaging velocimetry flow system for cell-substrate adhesion studies

Experimental models that mimic the flow conditions in microcapillaries have suggested that the local shear stresses and shear rates can mediate tumor cell and leukocyte arrest on the endothelium and subsequent sustained adhesion. However, further investigation has been limited by the lack of experimental models that allow quantitative measurement of the hydrodynamic environment over adherent cells. The purpose of this study was to develop a system capable of acquiring quantitative flow profiles over adherent cells. By combining the techniques of side-view imaging and particle image velocimetry (PIV), an in vitro model was constructed that is capable of obtaining quantitative flow data over cells adhering to the endothelium. The velocity over an adherent leukocyte was measured and the shear rate was calculated under low and high upstream wall shear. The microcapillary channel was modeled using computational fluid dynamics (CFD) and the calculated velocity profiles over cells under the low and high shear rates were compared to experimental results. The drag force applied to each cell by the fluid was then computed. This system provides a means for future study of the forces underlying adhesion by permitting characterization of the local hydrodynamic conditions over adherent cells.     

Modeling dynamical interactions between fast and slow movements: fast saccadic eye movement behavior in the presence of the slower VOR

An ongoing controversy has to do with the interactions between “fast” (saccadic, quick phase) and “slow” (all other) eye movements. By attacking such issues with both experimental and especially simulation studies using our nonlinear sixth order reciprocally innervated model of the eye mechanical system, insights can be gained into the nature of these nontrivial phenomena. In our present study we relied both (1) on simulation of saccades under a wide range of experimental conditions [vestibular ocular reflex (VOR) velocities from -100 to 100 deg/sec, VOR induced position ranges from -30 to 30 degrees, time-optimal saccades ranging from 2 to 40 degrees], and (2) on using a wide variety of computer simulation of eye movement models, ranging from nonlinear ones with first and especially second order multipulse step controller signal structures, to different controller signal interaction schemes, to simulation using linearized models. We have isolated two important nonlinear phenomena: a level I nonlinear mechanical interaction, dependent not only on the initial velocity but also on the “position effect,” a new finding; and a level II nonlinear neurological interaction, close to “squelching” of the VOR controller signals by the dominating saccadic signal. Furthermore, we have used our simulation findings to reinterpret others' experimental data on eye movement interactions, including saccadic-smooth pursuit, saccadic-vergence, and vestibular nystagmus.     

Model-based development of neuroprosthesis for paraplegic patients.

In paraplegic patients with upper motor neuron lesions the signal path from the central nervous system to the muscles is interrupted. Functional electrical stimulation applied to the lower motor neurons can replace the lacking signals. A so-called neuroprosthesis may be used to restore motor function in paraplegic patients on the basis of functional electrical stimulation. However, the control of multiple joints is difficult due to the complexity, nonlinearity, and time-variance of the system involved. Furthermore, effects such as muscle fatigue, spasticity, and limited force in the stimulated muscle further complicate the control task. Mathematical models of the human musculoskeletal system can support the development of neuroprosthesis. In this article a detailed overview of the existing work in the literature is given and two examples developed by the author are presented that give an insight into model-based development of neuroprosthesis for paraplegic patients. It is shown that modelling the musculoskeletal system can provide better understanding of muscular force production and movement coordination principles. Models can also be used to design and test stimulation patterns and feedback control strategies. Additionally, model components can be implemented in a controller to improve control performance. Eventually, the use of musculoskeletal models for neuroprosthesis design may help to avoid internal disturbances such as fatigue and optimize muscular force output. Furthermore, better controller quality can be obtained than in previous empirical approaches. In addition, the number of experimental tests to be performed with human subjects can be reduced. It is concluded that mathematical models play an increasing role in the development of reliable closed-loop controlled, lower extremity neuroprostheses.     

A novel formulation for blood trauma prediction by a modified power-law mathematical model

With the increasing use of artificial organs, blood damage has been raising ever more clinical concern. Blood trauma is in fact a major complication resulting from the implantation of medical devices and the use of life support apparatuses. Red blood cells damage predictive models furnish critical information on both the design and the evaluation of artificial organs, because their correct usage and implementation are thought to provide clear and rational guidance for the improvement of safety and efficacy. The currently adopted power-law shear-induced haemolysis prediction model lacks sensitivity with respect to the cumulative effect of previously applied stress magnitudes. An alternative model is proposed where a mechanical quantity was defined, able to describe the blood damage sustained by red cells under unsteady stress conditions, taking into account the load history. The proposed formulation predicted the same trend as the available experimental data. The obtained results have to be considered a preliminary validation of the basic hypothesis of this modified red blood cell damage prediction model. To date, the necessity to design further experiments to validate the proposed damage function clashes with the limitations inherent to current systems to get the time-varying shear stress completely under control.