Solutions to the Inverse LQR Problem with Application to Biological Systems Analysis

Learning Human Behavior in Shared Control: Adaptive Inverse Differential Game Approach

To enhance the collaborative intelligence of a machine, it is important for the machine to understand what behavior a human may adopt to interact with the machine when performing a task in shared control. In this study, an online behavior learning method is proposed for continuous-time linear human-in-the-loop shared control systems by using the system state data only. A two-player nonzero-sum linear quadratic dynamic game paradigm is used for modeling the control interaction between a human operator and an automation that actively compensates for human control action. In this game model, the cost function representing the human behavior is assumed to have an unknown weighting matrix. Here, we want to learn the human behavior or retrieve the weighting matrix by using the system state data only. Accordingly, a new adaptive inverse differential game (IDG) method, which integrates concurrent learning (CL) and linear matrix inequality (LMI) optimization, is proposed. First, a CL-based adaptive law and an interactive controller of the automation are developed to estimate the feedback gain matrix of the human online, and second, an LMI optimization problem is solved to determine the weighting matrix of the human cost function. Finally, simulation results on a cooperative shared control driver assistance system are provided to elucidate the feasibility of the developed method.

Online Inverse Optimal Control for Time-Varying Cost Weights

Inverse optimal control is a method for recovering the cost function used in an optimal control problem in expert demonstrations. Most studies on inverse optimal control have focused on building the unknown cost function through the linear combination of given features with unknown cost weights, which are generally considered to be constant. However, in many real-world applications, the cost weights may vary over time. In this study, we propose an adaptive online inverse optimal control approach based on a neural-network approximation to address the challenge of recovering time-varying cost weights. We conduct a well-posedness analysis of the problem and suggest a condition for the adaptive goal, under which the weights of the neural network generated to achieve this adaptive goal are unique to the corresponding inverse optimal control problem. Furthermore, we propose an updating law for the weights of the neural network to ensure the stability of the convergence of the solutions. Finally, simulation results for an example linear system are presented to demonstrate the effectiveness of the proposed strategy. The proposed method is applicable to a wide range of problems requiring real-time inverse optimal control calculations.

Quantitative Prediction of SYNTAX Score for Cardiovascular Artery Disease Patients via the Inverse Problem Algorithm Technique as Artificial Intelligence Assessment in Diagnostics

The quantitative prediction of the SYNTAX score for cardiovascular artery disease patients using the inverse problem algorithm (IPA) technique in artificial intelligence was explored in this study. A 29-term semi-empirical formula was defined according to seven risk factors: (1) age, (2) mean arterial pressure, (3) body surface area, (4) pre-prandial blood glucose, (5) low-density-lipoprotein cholesterol, (6) Troponin I, and (7) C-reactive protein. Then, the formula was computed via the STATISTICA 7.0 program to obtain a compromised solution for a 405-patient dataset with a specific loss function [actual-predicted]² as low as 3.177, whereas 0.0 implies a 100% match between the prediction and observation via "the lower, the better" principle. The IPA technique first created a data matrix [405 × 29] from the included patients' data and then attempted to derive a compromised solution of the column matrix of 29-term coefficients [29 × 1]. The correlation coefficient, r², of the regression line for the actual versus predicted SYNTAX score was 0.8958, showing a high coincidence among the dataset. The follow-up verification based on another 105 patients' data from the same group also had a high correlation coefficient of r² = 0.8304. Nevertheless, the verified group's low derived average AT (agreement) (AT_avg = 0.308 ± 0.193) also revealed a slight deviation between the theoretical prediction from the STATISTICA 7.0 program and the grades assigned by clinical cardiologists or interventionists. The predicted SYNTAX scores were compared with earlier reported findings based on a single-factor statistical analysis or scanned images obtained by sonography or cardiac catheterization. Cardiologists can obtain the SYNTAX score from the semi-empirical formula for an instant referral before performing a cardiac examination.

Energy Efficiency of Pressure Shock Damper in the Hydraulic Lifting and Leveling Module

This study evaluates the energy efficiency of pressure shock damping in a hydraulic lifting and leveling (HLL) module of a mobile robotic bricklaying system (RBS). The HLL module includes a servohydraulic actuator (SHA) and a hydraulic shock damper (HSD). The proposed adjustable HSD consists of a hydraulic accumulator circuit (HAC) and proportional damping valve. The frequency characteristics of the impedance and damping efficiency indices were used to evaluate the effectiveness of HSD damping. The dynamic responses of the SHA with and without HSD were analyzed based on a nonlinear state-space model. To control the damping of the pressure shock in the SHA-HSD system, a linear quadratic Gaussian (LQG) controller that follows two measurement signals was implemented. The LQG controller was adapted to the specific dynamic requirements of the SHA-HSD control system and nature of the RBS shock loads. The effectiveness of the LQG controller was evaluated during RBS operation under laboratory conditions. The main purpose of this study was to dynamically stabilize a leveled robot base subjected to shock loading during automatic operation of the RBS.

A SIX-PARAMETER SEMI-QUANTITATIVE ANALYSIS OF 251 PATIENTS FOR THE ENHANCED TRIGGERED TIMING OF HEAD AND NECK CT ANGIOGRAPHY SCANNING VIA THE INVERSE PROBLEM ALGORITHM

In this study, the correlation between triggered timing for head and neck CT angiography (TT CTA) scanning and the average of CT values of both left and right arterial to upper sinuses (LRA/US) reaching a maximal ratio was surveyed and explored using the inverse problem algorithm according to a six-factor semi-quantitative analysis of 251 patients. Six risk factors, namely TT CTA, mean arterial pressure (MAP), heart rate (HR), contrast media solution (CMS), given pressure (Pre), and body surface area (BSA) were used to identify a nonlinear first-order regression correlation between projected and actual LRA/US values. The respective 22 terms were derived via the STATISTICA program. In doing so, a customized loss function ([Formula: see text]) was defined according to the total fluctuation between theoretically projected and actual LRA/US values for all 216 patients. Thus, [Formula: see text] individual data points were included in the algorithm to optimize the compromised solution array [[Formula: see text]] of LRA/US values. The results exhibited a close correlation with loss function [Formula: see text], correlation coefficient [Formula: see text], and a 93.13% variance. Another group of 35 patients with similar symptoms was selected to verify the prediction accuracy and exhibited a high coincidence, although the reverse calculation-based correlation between CC CTA and LRA/US was still controversial from a clinical viewpoint. The proposed algorithm is considered quite instrumental in predicting the LRA/US with ischemic stroke symptoms in the CTA examination.

INVERSE PROBLEM ALGORITHM APPLICATION TO SEMI-QUANTITATIVE ANALYSIS OF 272 PATIENTS WITH ISCHEMIC STROKE SYMPTOMS: CAROTID STENOSIS RISK ASSESSMENT FOR FIVE RISK FACTORS

This study proposes the inverse problem algorithm (IPA) with five risk factors applied to the semi-quantitative analysis of carotid stenosis 272 patients with suspected ischemic stroke. The IPA is known to provide a substantiated machine learning-based prediction of the expected outcomes by solving an inverse matrix of variable coefficients. In case of carotid stenosis prediction, such risk factors as patient’s age, mean arterial pressure (MAP), glucose AC, low-density lipoprotein-cholesterol (LDL-C), and C-Reactive protein (CRP) were assessed for the main group of 217 patients. Their results were processed by the STATISTICA program with a customized loss function ([Formula: see text]), yielding the first-order nonlinear semi-empirical formula with 16 terms. The loss function was calculated via the total mismatch between the theoretical predictions and true carotid stenosis cases (%) for all 217 patients. Thus, the carotid stenosis (%) compromised solution array [[Formula: see text]] was optimized using [Formula: see text] individual data points via the proposed algorithm. The results showed a complete regression with loss function [Formula: see text]=2.3543, variance [Formula: see text]=87.46%, and correlation coefficient [Formula: see text]. The reference group of 55 more patients with the same preliminary diagnosis and symptoms was selected to validate the method predictive feasibility, which was found quite satisfactory. The decreasing order of three dominant risk factors was as follows: CRP, glucose AC, and MAP, whereas age and LDL-C weakly influenced the program computation results. The IPA showed a strong convergence by its default characteristic. The reduction of the number of variables in computation deteriorated the prediction accuracy, exhibiting the algorithm’s high sensitivity to the number of variables.

Quantifying trunk neuromuscular control using seated balancing and stability threshold

Performance during seated balancing is often used to assess trunk neuromuscular control, including evaluating impairments in back pain populations. Balancing in less challenging environments allows for flexibility in control, which may not depend on health status but instead may reflect personal preferences. To make assessment less ambiguous, trunk neuromuscular control should be maximally challenged. Thirty-four healthy subjects balanced on a robotic seat capable of adjusting rotational stiffness. Subjects balanced while rotational stiffness was gradually reduced. The rotational stiffness at which subjects could no longer maintain balance, defined as critical stiffness (k_Crit), was used to quantify the subjects' trunk neuromuscular control. A higher k_Crit reflects poorer control, as subjects require a more stable base to balance. Subjects were tested on three days separated by 24 hours to assess test-retest reliability. Anthropometric (height and weight) and demographic (age and sex) influences on k_Crit and its reliability were assessed. Height and age did not affect k_Crit; whereas, being heavier (p < 0.001) and female (p = 0.042) significantly increased k_Crit. Reliability was also affected by anthropometric and demographic factors, highlighting the potential problem of inflated reliability estimates from non-control related attributes. k_Crit measurements appear reliable even after removing anthropometric and demographic influences, with adjusted correlations of 0.612 (95%CI: 0.433-0.766) versus unadjusted correlations of 0.880 (95%CI: 0.797-0.932). Besides assessment, trainers and therapists prescribing exercise could use the seated balance task and k_Crit to precisely set difficulty level to a percentage of the subject's stability threshold to optimize improvements in trunk neuromuscular control and spine health.

Designing combination therapies using multiple optimal controls

Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We present a versatile framework to systematically explore the trade-offs that arise in designing combination therapy protocols using optimal control. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.

ASSESSMENT OF EFFECTIVE BLOOD CONCENTRATION READINGS FROM CLINICAL DATA ON PATIENTS WITH HEART FAILURE DISEASES AFTER DIGOXIN INTAKE: A PROJECTION BASED ON THE INVERSE PROBLEM ALGORITHM

In this study, a projection of effective blood concentration (EBC) readings of digoxin is made using the inverse problem algorithm based on clinical data for patients with heart failure diseases. Seven factors, including body surface area (BSA), blood urine nitrogen (BUN), creatinine, sodium (Na), potassium (K), magnesium (Mg) ion readings, and mean arterial pressure (MAP) were compiled with nonlinear regression fit to develop a projection function having 29 terms obtained from an inverse problem algorithm via the default function run in STATISTICA. Accordingly, data collected from the clinical 168 heart failure patients were normalized to be included in same domain range ([Formula: see text]1 to +1), and then calculated by the specific algorithm to optimize the numerical solution to evaluate EBC readings of digoxin. The evaluated first-order regression fit owned an optimal loss function ([Formula: see text]) coupled with correlation coefficient [Formula: see text] = 0.892 and variance of 89.20%. Furthermore, 45 patients having similar clinical syndromes were also adopted to verify the projection and implied with high agreement. The BUN factor dominated the projection and defined as the most significant coefficient in the analysis, and K ion, MAP, BSA, and Mg ion factors exhibited minor contributions to the projection. The repeated trials to lower number of factors from seven to a smaller number (namely 6, 5, 4, 3, 2, and 1) for simplifying method but resulting with unaccepted outcomes, with high loss function values and low linearity. However, the algorithm held its accuracy to handle the verified data that were out of the original bounds. The proposed algorithm demonstrated a useful analysis to handle the drug administration in pharmaceutical field.

Inferring Control Intent during Seated Balance using Inverse Model Predictive Control

Patients with Low Back Pain (LBP) are suggested to follow a protective coping strategy. Therefore, rehabilitation of these patients requires estimating their motor control strategies (the control intent). In this letter, we present an approach that infers the control intent by solving an inverse Model Predictive Control (iMPC) problem. The standard Model Predictive Control (MPC) structure includes constraints, therefore, it allows us to model the physiological constraints of motor control. We devised an iMPC algorithm to solve iMPC problems with experimentally collected output trajectories. We used experimental data of one healthy subject during a seated balance test that used a physical Human-Robot Interaction (pHRI). Results show that the estimated MPC weights reflected the task instructions given to the subject and yielded an acceptable goodness of fit. The iMPC solution suggests that the subject's control intent was dominated by minimizing the squared sum of a combination of the upper-body and lower-body angles and velocities.

Optimal control of acute myeloid leukaemia

Acute myeloid leukaemia (AML) is a blood cancer affecting haematopoietic stem cells. AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. In this work, we incorporate an immune response into a stem cell model of AML, since we find that previous models lacking an immune response are inappropriate for deriving optimal control strategies. Using optimal control theory, we produce continuous controls and bang-bang controls, corresponding to a range of objectives and parameter choices. Through example calculations, we provide a practical approach to applying optimal control using Pontryagin's Maximum Principle. In particular, we describe and explore factors that have a profound influence on numerical convergence. We find that the convergence behaviour is sensitive to the method of control updating, the nature of the control, and to the relative weighting of terms in the objective function. All codes we use to implement optimal control are made available.

Energy scaling of targeted optimal control of complex networks

Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the network, to place additional control inputs. Here, in contrast, we show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, while holding the number of control signals constant, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. We validate our conclusions in model and real networks to arrive at an energy scaling law to better design control objectives regardless of system size, energy restrictions, state restrictions, input node choices and target node choices.

The energy required to control a dynamical complex network can be prohibitively large when there are only a few control inputs. Here the authors demonstrate that if only a subset of the network is targeted the energy requirements decrease exponentially.