Robust Control of Exo-Abs, a Wearable Platform for Ubiquitous Respiratory Assistance

Breathing is one of the most vital functions for human survival. In normal conditions, breathing is accomplished via a complex coordinated effort contributed by various respiratory muscles in the abdomen [1]. However, aging, diseases, and neurological disorders can weaken the respiratory muscles, thereby deteriorating the quality of breathing. Respiratory muscles are known to weaken with aging [2]. In addition, diseases such as Parkinson's disease [3], stroke [4], and amyotrophic lateral sclerosis [5] as well as neuromuscular disorders such as spinal cord injury and muscular dystrophy are also known to weaken or even paralyze respiratory muscles [6–8]. Deteriorated breathing capacity often leads to compromises in other aspects related to the overall quality of life by causing, e.g., fatigue, dizziness, and cognitive decline as well as psychological issues including mental stress, depression, and anxiety [9]. Hence, breathing assistance to enable vital everyday activities during diseases and neurological disorders mentioned above is an urgent medical challenge to be addressed.

Despite its urgency and potential societal impact, ubiquitous breathing assistance technology (e.g., based on wearable platforms) available to patients with respiratory deficiency is limited. In fact, mechanical ventilator (including noninvasive positive pressure ventilator [10–13] and bag valve mask ventilator [14,15]) has been the most commonly used therapeutic option for weakened breathing. But, it has a number of shortcomings including: (i) it requires tracheal intubation or ventilation masks, which interferes with a user's respiratory functions other than breathing (e.g., coughing and speaking) and also causes facial inflammation and deformation [12]; and (ii) it is bulky and inconvenient to carry around, which seriously restricts a user's mobility and the potential to provide ubiquitous breathing assistance. Given that there are wearable-based respiratory monitoring technologies widely available to public [16–18], opportunities exist to likewise enable wearable-based ubiquitous respiratory assistance during everyday activities.

To bridge this gap, we developed the Exo-Abs, a wearable-enabled robotic platform for ubiquitous assistance of respiratory functions in patients with respiratory deficiency (Figs. 1(a) and 1(b)) [19]. Armed with an innovative belt-driven bio-inspired abdomen compression mechanism to amplify the inhaled/exhaled air, the Exo-Abs can provide assistance to a wide range of users with noncritical respiratory deficiency. In contrast to conventional mechanical ventilators, the Exo-Abs does not require chronic wearing of face masks, let alone tracheal intubation, thus minimizing interference with other key everyday respiratory functions to sustain the quality of life. In addition, the Exo-Abs does not require bulky pumps and air conditioning systems, thus achieving a much smaller form factor. In this way, the Exo-Abs is especially advantageous for ubiquitous respiratory assistance. In our prior work, we demonstrated its proof-of-concept in augmenting a user with basic respiratory functions including breathing, coughing, and speaking [19].

This paper concerns the development of a model-based closed-loop control algorithm for the Exo-Abs to automate its breathing assistance. To facilitate model-based development of closed-loop control algorithms, we developed a control-oriented mathematical model of the Exo-Abs. Then, we developed a robust absolutely stabilizing gain-scheduled proportional-integral (PI) control algorithm for automating the breathing assistance with the Exo-Abs, by (i) solving a linear matrix inequality (LMI) formulation of the Lyapunov stability condition against sector-bounded uncertainty and interindividual variability in the mechanics of the abdomen and the lungs and (ii) augmenting it with a heuristic yet effective gain scheduling algorithm guided by reference tracking error. Then, we conducted in silico evaluation based on realistic and plausible virtual patients (VPs) to assess the efficacy and robustness of the automated breathing assistance of the Exo-Abs under a wide range of variability in spontaneous breathing and Exo-Abs efficiency.

This paper is organized as follows. Section 2 describes the control-oriented model of the Exo-Abs. Section 3 describes the development of robust absolutely stabilizing gain-scheduled PI control for automating breathing assistance with the Exo-Abs. Section 4 presents main results, which are discussed in Sec. 5. Section 6 concludes the paper with possible future directions.

We used breathing recordings acquired from 10 male Exo-Abs users in our prior work [19]. These users included individuals with health (1), Parkinson's disease (1), cervical spinal cord injury (6), stroke (1), and amyotrophic lateral sclerosis (1). The recordings included high-resolution motor angular displacement and lung volume (i.e., inhaled and exhaled air, calculated by integrating the air flowrate measurement provided by the spirometer) measured at a high temporal resolution of 200 Hz among others. All the user recordings include unassisted breaths (6–15 per user, totaling 113) and Exo-Abs-assisted breaths (1–13 per user, totaling 66). Figure 2 shows a representative example of unassisted and Exo-Abs-assisted breaths (including both inhalation and exhalation).

where the time derivative terms pertaining to the elements in $ϕ(t)$ can be calculated using, e.g., the Euler approximation. From $σ$ in conjunction with the knowledge of the range of typical values associated with $R$ and $E$⁠, it can be shown that $kexoR$⁠, $ER$⁠, $z1$⁠, $z2$⁠, $p1$⁠, $p2$⁠, and $p3$ are structurally identifiable.

We inferred the structurally identifiable parameters in $Gexo(s)$ (i.e., $kexoR$, $ER$⁠, $z1$⁠, $z2$⁠, $p1$⁠, $p2$⁠, and $p3$⁠) using the experimental dataset in Sec. 2.1 by means of a collective variational inference (C-VI) method developed in our prior work [27]. Then, we evaluated the goodness of $Gexo(s)$⁠, i.e., its ability to user-specifically replicate the relationship between $θm(t)$ and $VL,exo(t)$ on an individual basis.

To estimate the identifiable parameters in $Gexo(s)$⁠, we calculated $VL,exo(t)$ (which is needed along with $θm(t)$ to fit the input–output relationship $L−1[VL,exo(s)]=L−1[Gexo(s)θm(s)]$ to the experimental dataset in the time domain) from the experimental dataset as follows. For the experimental dataset pertaining to each Exo-Abs user, we calculated the time series sequence of unassisted exhaled air (i.e., $VL,mus(t)$⁠) as the mean value of the time series sequences of the change in the lung volume during the exhalation phase associated with all the unassisted breaths of the user. Then, we calculated the time series sequences of exhaled air contributed by the Exo-Abs (i.e., $VL,exo(t)$⁠) pertaining to each Exo-Abs-assisted breath (i.e., $VL(t)$ resulting from exo-Abs assistance) by subtracting $VL,mus(t)$ calculated above from the time series sequences of total exhaled air (i.e., $VL(t)$⁠). In sum, the experimental dataset pertaining to each Exo-Abs user yielded $θm(t)$-$VL,exo(t)$ data for multiple (1-13) breaths, which add up to 66 breaths in total when all 10 Exo-Abs users in the experimental datasets are considered.

Then, we estimated the identifiable parameters in $Gexo(s)$ using the C-VI method. We estimated the posterior probability density functions (PDFs) associated with the identifiable parameters in $Gexo(s)$ at both individual (i.e., each breath) and cohort (i.e., all the breaths) levels as well as the sensor noise variance pertaining to $VL(t)$ in each breath. In brief, the C-VI method leverages variational inference approaches [28,29] to estimate analytical approximations to the posterior PDFs of the identifiable parameters by maximizing an evidence lower bound, which includes (i) a log-likelihood term to promote the similarity between the experimental $θm(t)$-$VL,exo(t)$ data versus $VL,exo(t)$ predicted by the mathematical model (i.e., $Gexo(s)$⁠) given $θm(t)$⁠; (ii) terms to enforce a priori knowledge on the identifiable parameters and the measurement noise in $VL(t)$⁠; (iii) a term to promote the hierarchical coupling between the breath-specific parameter values versus the cohort-level parameter values (i.e., the cohort-level parametric PDFs are inferred to likely encompass the breath-specific parametric PDFs); and (iv) an uncertainty quantification term to modulate the regularization effect [27]. In this way, we estimated the parametric PDFs pertaining to each of the 66 individual breaths as well as those pertaining to the entire breaths as a group. We repeated the parameter estimation process above for all the candidate empiric black-box mathematical models in Eq. (2) considered in this work.

We comparatively evaluated the goodness of the candidate mathematical models using the root-mean-squared error (RMSE) and r value between measured $VL,exo(t)$ and $VL,exo(t)$ simulated by the mathematical models, as well as the Akaike's Information Criterion (AIC) [30] as a measure of accuracy-complexity tradeoff. For each breath, we selected the optimal mathematical model as the one associated with the minimum AIC value across all the candidate mathematical models. Then, we selected the optimal mathematical model as the one which was most frequently selected across all the 66 breaths. Then, we used the cohort-level parametric PDFs pertaining to the optimal mathematical model as the virtual patient generator (VPG) to aid the development and evaluation of a closed-loop control algorithm for the Exo-Abs (in that a random sample taken from the cohort-level parametric PDFs can parameterize the mathematical model, i.e., $Gexo(s)$⁠, which can simulate plausible $VL,exo(t)$ in response to plausible $θm(t)$⁠).

The plant dynamics described in Sec. 2 is subject to multiple sources of uncertainty, including the uncertainty associated with the abdomen mechanics in Eq. (2), especially with respect to the efficiency of the Exo-Abs assistance which depends on the contact condition between the Exo-Abs and the abdomen (i.e., looseness and/or slack, which may be represented by small $kexo$ values in Eq. (2)), as well as the interindividual variability originating from the breathing mechanics and dynamics (which is represented by the parametric covariance in the VPG derived in Sec. 2). In addition, the control task presents a challenge in that the Exo-Abs must be controlled to assist a user track a (smooth yet) complex reference exhalation trajectory within a short period of time. In fact, the examination of the exhalation patterns in our experimental dataset suggests that typical exhalation pattern may be approximated by a cubic polynomial (see Fig. 2 for representative examples). Hence, a complex compensator armed with a system type of at least four may be required to enable zero steady-state tracking of the reference exhalation trajectory.

We propose to address these challenges by absolutely stabilizing gain-scheduled proportional-integral (PI) control. On the one hand, absolutely stabilizing control can provide robust stability against the uncertainty associated with the abdomen mechanics and the breathing dynamics. On the other hand, gain scheduling can improve the tracking capability of the Exo-Abs for nonlinear reference exhalation trajectories without the use of a sophisticated compensator. We developed an absolutely stabilizing control by (i) solving an LMI formulation of the Lyapunov stability condition against sector-bounded uncertainty and interindividual variability in the mechanics of the abdomen and the lungs and (ii) augmenting to it a heuristic yet effective gain scheduling algorithm. Then, we used the VPG derived in Sec. 2 to generate plausible VPs and used them to evaluate the efficacy and robustness of the automated breathing assistance of the Exo-Abs under a wide range of variability in spontaneous breathing and Exo-Abs efficiency. Details follow.

The closed-loop controlled Exo-Abs including the plant dynamics in Fig. 1(c) is shown in Fig. 3(a), where $C(s)$ is the transfer function of the compensator.

Note that Eq. (10) is a set of LMIs in $P$ once the P, I, D gains are given, meaning that a pair of P, I, and D gains is absolutely stabilizing if it yields a PD matrix $P$ satisfying the LMIs. Note also that Eqs. (5)–(10) reduces to PI control if $kD$ is set to zero.

In this paper, we found a region of absolutely stabilizing gains pertaining to PID and PI control as follows. First, we specified a wide search region encompassing candidate gain pairs. Second, we determined the sector bounds $ηˇ$ and $η̂$ based on the 95% confidence interval associated with the PDF of $kexoR$ in the VPG derived in Sec. 2. Third, we sampled 50 VPs from the VPG. Fourth, we iteratively solved the LMIs in Eq. (10) for (i) all the candidate gains in the search region as well as (ii) all the 50 VPs. Fifth, we determined the pair of gains satisfying Eq. (10) for all the 50 VPs as “probabilistically robust” absolutely stabilizing gains (in that the 50 VPs employed to guarantee robustness are probabilistically selected).

where $V˜L[i](t)$⁠, $θm[i](t)$⁠, and $θ˙m[i](t)$⁠, $i=1,…,50$ are $V˜L(t)$⁠, $θm(t)$⁠, and $θ˙m(t)$ pertaining to the $i$-th VP, while $ρ1$⁠, $ρ2$⁠, and $ρ3$ are prespecified weights which were selected based on trial and error to ensure smooth Exo-Abs operation with minimal fluctuation. We used these optimal PID and PI control algorithms as competitors in evaluating the efficacy of the proposed gain-scheduled PI control (Sec. 3.3).

We developed gain-scheduled PI control based on two main motivations: (i) reference exhalation trajectory is too complex (perhaps requiring system type ≥ 4) to perfectly track with PID or PI control (which merely results in a type 1 system), and (ii) the presence of sensor noise in $V˜L(t)$ suggests weakening, or even removal, of derivative action in PID control. In this regard, we hypothesized that gain-scheduled PI control may address both these challenges by (i) enabling context-relevant control action based on the tracking error while (ii) desensitizing the control algorithm to sensor noise.

where $k̂P$ and $kˇP$ are the maximum and minimum values of $kP$⁠, respectively, $k̂I$ and $kˇI$ are the maximum and minimum values of $kI$⁠, respectively, while $λP>0$ and $λI>0$ are constants which modulates the decrease in $kP$ and increase in $kI$⁠, respectively, in response to the magnitude of the reference tracking error (i.e., $V˜L(t)$⁠). We determined the configurable parameters $k̂P$ and $kˇP$ as well as $k̂I$ and $kˇI$ in Eq. (12) as follows. First, we derived the optimal user-specific PI gain pairs associated with the 50 VPs employed in Sec. 3.1, each of which minimizes the user-level cost function $Ji$ in Eq. (11) within the region of absolutely stabilizing PI gains. Second, we computed the mean and standard deviation (SD) of the optimal user-specific P and I gains across the 50 VPs. Third, we selected (i) $k̂P$ and $kˇP$ as mean+SD and mean-SD of user-specific P gains and (ii) $k̂I$ and $kˇI$ likewise as mean+SD and mean-SD of user-specific I gains, while ensuring that all the P and I gains in the region are absolutely stabilizing. To mitigate chattering in the PI gains in the course of gain scheduling, we applied 8-point moving average filtering to $kP(V˜L(t))$ and $kI(V˜L(t))$ in implementing Eq. (12).

To evaluate the robust absolutely stabilizing gain-scheduled PI control algorithm for the Exo-Abs, we sampled 50 additional random VPs from the VPG derived in Sec. 2. To conduct in silico simulations with the VPs, we specified the trajectory of inhaled and exhaled air during unassisted breathing, the reference exhaled air trajectory during Exo-Abs-assisted breathing, and the measurement noise as follows. First, the “representative” unassisted breathing (i.e., inhaled and exhaled air) trajectory was derived by averaging the amplitude- and time-normalized unassisted breathing trajectories of all the unassisted breaths in the experimental dataset, while the amplitude as well as the periods of inhalation and exhalation were approximated as a multidimensional Gaussian distribution. Then, for each VP, we generated a random sample from this distribution and applied the amplitude and periods in the sample to the representative unassisted breathing trajectory to derive the breathing trajectory pertaining to the VP. In conducting in silico simulations, we inputted this unassisted breathing trajectory as lung volume disturbance (i.e., $VL,mus(t)=L−1[1Rs+EPmus(s)]$⁠) instead of $Pmus(t)$ in Fig. 3(a). Second, we specified the reference exhaled air trajectory during Exo-Abs-assisted breathing as the unassisted breathing trajectory with its amplitude doubled (so that Exo-Abs can increase the inhaled/exhaled air by 100% relative to unassisted breathing). Third, we specified the measurement noise as white noise with variance equal to the maximum measurement noise variance across the 66 breaths of all the users derived in Sec. 2.3.

We compared gain-scheduled PI control versus PID and PI control with optimal gains determined by Eq. (11) using the 50 VPs described above in conjunction with the corresponding unassisted breathing trajectory and reference exhaled air trajectory during Exo-Abs-assisted breathing. Our metrics of interest included (i) reference tracking efficacy in terms of RMSE between $VLd(t)$ and $VL(t)$ (i.e., RMS of $V˜L(t)$⁠); (ii) control energy (in terms of RMS of motor angular displacement); and (iii) control variability (in terms of RMS of motor angular velocity). We determined the statistical significance in the difference in these performance metrics using Wilcoxon's rank sum test with Bonferroni correction for multiple comparisons (p < 0.0167).

In addition to the comparative evaluation, we evaluated gain-scheduled PI control in the presence of plausible variability in the operating condition of the Exo-Abs, including alterations in a user's breath and efficiency loss due to the loose contact between Exo-Abs and a user's abdomen.

Table 1 summarizes the goodness of the mathematical model (i.e., $Gexo(s)$⁠) pertaining to the five candidate black-box mathematical models of abdomen mechanics in Eq. (2), in terms of RMSE, r value, and AIC. Figure 4 shows representative examples of actual Exo-Abs-assisted exhaled air (i.e., the portion of the exhaled air contributed by the Exo-Abs) versus the same Exo-Abs-assisted exhaled air reproduced by the mathematical model. Figure 5 shows the PDFs of the mathematical model parameters at both subject and cohort levels inferred by the C-VI method. Figure 6 shows the contour plots of (a) exhalation tracking error (in RMSE), (b) control energy (in RMS of motor angular displacement), and (c) control variability (in RMS of motor angular velocity), averaged across 50 VPs generated for control design, in the absolutely stabilizing PI gain space. Table 2 summarizes the control efficacy of the optimal absolutely stabilizing PI and PID control as well as absolutely stabilizing gain-scheduled PI control associated with 50 VPs generated for control evaluation. Figure 7 shows a representative example of breaths with and without the Exo-Abs assistance pertaining to (a) optimal absolutely stabilizing PI control, (b) optimal absolutely stabilizing PID control, and (c) absolutely stabilizing gain-scheduled PI control, where (i) reference versus actual exhaled air, (ii) exhaled air tracking error, (iii) control actuation (i.e., motor angular displacement), and (iv) control actuation variability (i.e., motor angular velocity) are presented. Figure 8 shows the efficacy of the absolutely stabilizing gain-scheduled PI control in the presence of plausible variability in the operating condition of the Exo-Abs, including alterations in a user's breath and efficiency loss due to the loose contact between Exo-Abs and a user's abdomen.

Existing noninvasive breathing assist options usable in out-of-hospital settings, including noninvasive positive pressure ventilators and bag valve mask ventilators, interfere with essential everyday activities, thereby deteriorating the quality of life. We developed the Exo-Abs, a novel wearable robotic platform to assist various respiratory functions in patients with respiratory deficiency [19]. This paper intends to enable the automation of the Exo-Abs in assisting breathing functions. This paper has two novel contributions. First, we developed a control-oriented mathematical model of the Exo-Abs. Second, we developed a simple yet robust absolutely stabilizing control algorithm to automate breathing assistance in the Exo-Abs. Details follow.

The mathematical model of the Exo-Abs developed in this work showed validity and goodness in reproducing the dynamics associated with the respiratory assistance (Table 1, Fig. 4). The results indicate that hybrid combination of (i) physics-based mathematical model of lung mechanics and (ii) empiric mathematical model of abdomen mechanics may be a reasonable approach to derive a mathematical model for designing Exo-Abs control algorithms. First, the minimum-complexity physics-based representation of lung mechanics (including airway resistance and lung elastance), despite its simplicity, was adequate in capturing the effect of the Exo-Abs assistance on breathing patterns. Second, the linear black-box mathematical model of abdomen mechanics was likewise an effective representation to capture the complex interaction between the Exo-Abs and the user whose physics-based mathematical modeling is not trivial. The optimal mathematical model armed with the 3 pole-2 zero representation of the abdomen mechanics (“3 P/2Z” in Table 1) was associated with 13.2 ml median RMSE in reproducing the exhaled breath (which approximately amounts to 2.4% of the ground truth exhaled air volume on the average) and a very high median r value of 0.99 (Table 1), together with a (qualitatively) small uncertainty envelope in all subjects (Fig. 4).

The optimal structure (namely, the order and the relative degree) associated with the black-box mathematical model of abdomen mechanics was selected through a trial-and-error process guided by the AIC. Among the 5 candidate structures in Table 1, the 3 pole-2 zero structure was preferred in >50% of the 66 breaths, followed by the 2 pole-1 zero structure (preferred in 27%). Overall, structures with relative degree 1 appeared to be preferred. The 4 pole-3 zero structure resulted in deteriorated goodness of fit relative to its 3 pole-2 zero and 2 pole-1 zero counterparts, possibly due to the enforcement of unnecessary pole and zero which may only negatively impact the ability of the black-box mathematical model to fit the experimental dataset. Hence, we used the 3 pole-2 zero black-box mathematical model as the optimal representation for abdomen mechanics.

The PDFs associated with the mathematical model parameters exhibited a large interindividual variability (shown in 66 red lines in the diagonal entries in Fig. 5), which may support the robust absolutely stabilizing control approach pursued in this work. The cohort-level PDFs adequately captured the collective parameter distributions as well as their couplings (shown in black line in the diagonal and off-diagonal entries in Fig. 5, respectively).

In sum, the mathematical model has an appropriate structure to capture the essential dynamics associated with the Exo-Abs-enabled respiratory assistance. As well, the PDFs pertaining to the mathematical model parameters may be used as a VPG capable of generating a large number of VPs to enable trustworthy development and evaluation of closed-loop control algorithms for the Exo-Abs.

In our control design approach, robustness of the control algorithms against the uncertainty in the abdomen mechanics (i.e., $kexo$⁠) is achieved deterministically by way of the LMI-feasible control gains, while robustness against all the other uncertainty in the plant dynamics (due to interindividual variability in lung mechanics etc.) is achieved probabilistically by taking the control gains that satisfy the LMI pertaining to a large number of VPs randomly sampled from the VPG. The analysis of the LMI-feasible PI and PID gain regions showed that a large robust absolutely stabilizing PI and PID gain regions existed. Not surprisingly, there were LMI-infeasible gain regions. But, these regions were mostly associated with unsatisfactory control efficacy and thus were not relevant anyway (not shown).

The proposed absolutely stabilizing control approach is highly conservative in that it intends to achieve closed-loop stability against all possible uncertainty in the abdomen mechanics as long as $kexoR=η(t)$ resides within the sector bound. Regardless, it resulted in PI and PID control gains associated with practically useful control efficacy. In the case of PI control, tracking error improved as P and I gains were increased (Fig. 6(a)). However, it was accompanied by an increase in control energy (Fig. 6(b)) and control variability (i.e., fluctuation and chattering; Fig. 6(c)). For very large P and I gains, even tracking error was degraded due to control saturation and integrator wind-up, which led to a bang-bang behavior. In the case of PID control, the general trend was similar, although the dependence of tracking error, control energy, and control variability on the gains was more complex (not shown). In addition, PID control was more susceptible to measurement noise than PI control due to its derivative action.

Comparison of the optimal absolutely stabilizing PI and PID as well as absolutely stabilizing gain-scheduled PI control algorithms provided a few insights (Table 2, Fig. 7). First, PI control had limited tracking efficacy: it was not possible to achieve perfect reference tracking without unacceptable degree of control chattering. From the internal model control perspective, this limitation may also be attributed to the fact that the system type is not high enough: the single integrator provided by PI control can only guarantee the tracking of step reference trajectories, while the reference trajectory for the Exo-Abs (see Fig. 2) may require multiple (≥4) integrators in the compensator. Second, PID control could suppress the tracking error, but at the cost of a drastic increase in control variability (i.e., chattering). This weakness, together with its sensitivity to measurement noise, essentially rendered PID control an undesirable option. Third, gain-scheduled PI control could improve both tracking efficacy (relative to PI control) and control variability (relative to PID control) through a judicious tracking error-based scheduling of its P and I gains. Noting that tracking error in PI control increases initially and then decreases gradually in the exhalation cycle in most breaths (rows #1 and #2 in Fig. 7), gain-scheduled PI control suppresses initial tracking error using a large P gain (now that proportional action is faster than integral action). Then, it gradually increases I gain while decreasing P gain to improve reference tracking without inducing control chattering (rows #3 and #4 in Fig. 7). Notably, the gain scheduling algorithm assures that both P and I gains reside in the LMI-feasible region, thereby guaranteeing absolute stability.

The proposed gain-scheduled PI control showed effectiveness and robustness against plausible variability in the operating condition of the Exo-Abs, i.e., variability in a user's breath and the Exo-Abs-abdomen contact (Fig. 8). In the three scenarios considered in this work, gain-scheduled PI control maintained tracking error at practically the same level (Fig. 8(a)) by properly compensating for the variability, e.g., by increasing and decreasing the Exo-Abs assistance when a user's breath was shallower and de-eper than its nominal level, respectively, as well as increasing the Exo-Abs assistance when the Exo-Abs-abdomen contact became loose (Figs. 8(b)–8(c)). The results suggest that the Exo-Abs may resiliently operate well under a wide range of operating conditions while still ensuring the absolute stability of its automated operation.

In sum, the mathematical model and the control algorithm developed in this work may contribute to safe closed-loop controlled automation of the Exo-Abs.

However, this work has a limitation in terms of sample size: 10 males is small and can possibly be biased. We speculate that the black-box mathematical model of abdominal mechanics interacting with the Exo-Abs in Eq. (2) may still be effective by virtue of its flexibility. However, its optimal structure may change if a large number of diverse patients are considered. Hence, investigating the goodness of the mathematical model across a wide range of patient cohort will be a rewarding future work to strengthen the potential of the Exo-Abs to autonomously assist breathing function in many patients with guaranteed safety.

We developed and in silico evaluated a model-based closed-loop control algorithm for the Exo-Abs to automate its breathing assistance function. The control-oriented mathematical model of the Exo-Abs faithfully captured the complex abdomen-lung dynamics involved in the breathing assistance provided by the Exo-Abs. The robust absolutely stabilizing gain-scheduled PI control algorithm for the Exo-Abs showed promise in automating its breathing assistance. Future work is required to experimentally evaluate the efficacy, safety, and comfort of the closed-loop controlled breathing assistance provided by the Exo-Abs. In addition, future work is required to extend the scope of automation to many other everyday respiratory functions (including coughing and speaking).

• The U.S. Office of Naval Research under (Grant No. N00014-23-1-2828; Funder ID: 10.13039/100000006).

• The National Research Foundation of Korea under (Grant No. NRF-2016R1A5A1938472; Funder ID: 10.13039/501100003725).

• The Ministry of Health and Welfare, Republic of Korea (Korea Health Technology R&D Project, Korea health Industry Development Institute) (Grant No. HI19C1352; Funder ID: 10.13039/501100003625).

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.