Performance Of Closed-loop System Research Articles

Adaptive disturbance rejection neural output feedback control of hydraulic manipulator systems

This paper proposes an adaptive disturbance rejection neural output feedback control (ADRNC) scheme for multi-degree-of-freedom (n-DOF) hydraulic manipulator systems, subjected to unknown nonlinearities, external disturbances and unmeasured system states. The controller design is formulated by integrating Radial Basis Function Neural Networks (RBFNNs) with state and disturbance observers using the backstepping method. The RBFNNs are synthesized to handle unknown nonlinear functions and the residual estimate error, coupled with external disturbances, is estimated through the combination of state observer and disturbance observer. The unique features of the proposed controller lies in its capability to estimate both matched and unmatched lumped disturbances. The auxiliary disturbance estimation law is guided by the neural learning weights and estimated system states provided by state observers. By effectively utilizing neural networks to approximate and mitigate most nonlinear uncertainties, the workload of the disturbance observer is substantially reduced. High-gain feedback is therefore avoided and improved tracking performance can be expected. Moreover, to avoid the tedious analysis and the problem of “explosion of complexity” in the conventional backstepping method, we employ a first-order sliding-mode differentiator. Rigorous analysis via Lyapunov methods establishes the stability of the entire closed-loop system, ensuring guaranteed and satisfactory tracking performance under the integrated influence of unknown nonlinearities, unmeasured states, and external disturbances. Extensive simulations are conducted to verify the effectiveness of the nested control strategy.

A new model for compressor surge and stall control

This paper compares the bifurcations and closed-loop performances of two compressor models, Moore-Greitzer (MG) and a developed model based on MG (Shahriyari Khaleghi, SK). First, both models are linearized about two equilibrium points (pure surge and fully-developed rotating stall), and the perturbed state-space dynamics and input matrices are obtained. The compressor unstable regions are then identified using an eigenvalue and global bifurcation analysis. Furthermore, optimal LQR controllers are designed, and the performances of closed-loop systems are compared. The LQRs are designed to control the compression system near the peak pressure rise by suppressing surge or stall. Results reveal that if the initial operating point is in the positive slope region of the compressor characteristic and the initial amplitude of the disturbances is small, the LQR controller can stabilize the compressor in both models. However, when the disturbances are intensive, the two models respond differently: although the SK model damps a fair range of disturbances and predicts instability for excessively powerful disturbances, the MG model always damps them, even when extremely intense. Without a controller in the MG model, initial disturbances (even very large) can never grow and are always damped in the compressor’s negative slope region (obviously, the same applies to the controller). However, pending the amplitude of the disturbances (in the absence of a controller), the disturbances in the SK model may be damped or grow. The SK model can successfully control the instabilities if the disturbances are small. Nonetheless, the controller fails to dampen the instabilities for extreme disturbances, which is consistent with reality.

Early Real-World Performance of the MiniMed™ 780G Advanced Hybrid Closed-Loop System and Recommended Settings Use in the United States.

Background: The MiniMed™ 780G system (MM780G) with Guardian™ 4 sensor includes a 100 mg/dL glucose target (GT) and automated insulin corrections up to every 5 min and was recently approved for use in the United States. In the present study, early real-world MM780G performance and the use of recommended system settings (100 mg/dL GT with an active insulin time of 2 h), by individuals with type 1 diabetes, were evaluated. Methods: CareLink™ personal data uploaded between the launch of the MM780G to August 22, 2023 were aggregated and underwent retrospective analysis (based on user consent) and if users had ≥10 days of continuous glucose monitoring (CGM) data. The 24-h day CGM metrics, including mean glucose, percentage of time spent in (%TIR), above (%TAR), and below (%TBR) target range (70-180 mg/dL), in addition to delivered insulin and closed-loop (CL) exits, were compared between an overall group (n = 7499) and individuals who used recommended settings (each, for >95% of the time). An analysis of the same metrics for MiniMed™ 770G system (MM770G) users (n = 3851) who upgraded to the MM780G was also conducted (paired t-test or Wilcoxon signed-rank test, P < 0.05 considered statistically significant). Results: For MM780G users, CGM use, and time in CL were >90% and all MM780G CGM metrics exceeded consensus-recommended goals. With recommended settings (22% of all users), mean %TIR and %TITR (70-140 mg/dL) were 81.4% and 56.4%, respectively. For individuals who upgraded from the MM770G, %TIR and %TITR increased from 73.2% to 78.3% and 45.8% to 52.6%, respectively, while %TAR reduced from 25.1% to 20.2% (P < 0.001, for all three). CL exits/week averaged <1, for all MM780G users. Conclusions: Early real-world MM780G use in the United States demonstrated a high percentage of time in range with low time above and below range. These outcomes are similar to those observed for real-world MM780G use in other countries.

Fractional-Order Control Method Based on Twin-Delayed Deep Deterministic Policy Gradient Algorithm

In this paper, a fractional-order control method based on the twin-delayed deep deterministic policy gradient (TD3) algorithm in reinforcement learning is proposed. A fractional-order disturbance observer is designed to estimate the disturbances, and the radial basis function network is selected to approximate system uncertainties in the system. Then, a fractional-order sliding-mode controller is constructed to control the system, and the parameters of the controller are tuned using the TD3 algorithm, which can optimize the control effect. The results show that the fractional-order control method based on the TD3 algorithm can not only improve the closed-loop system performance under different operating conditions but also enhance the signal tracking capability.

Event-Triggered Multiasynchronous H∞ Control for Markov Jump Systems With Transmission Delay.

In this article, the issue of event-triggered multiasynchronous H∞ control for Markov jump systems with transmission delay is concerned. In order to reduce sampling frequency, multiple event-triggered schemes (ETSs) are introduced. Then hidden Markov model (HMM) is employed to describe multiasynchronous jumps among subsystems, ETSs, and controller. Based on the HMM, the time-delay closed-loop model is constructed. In particular, when triggered data are transmitted over networks, a large transmission delay may cause disorder of transmission data such that the time-delay closed-loop model cannot be developed directly. To overcome this difficulty, a packet loss schedule is presented and the unified time-delay closed-loop system is obtained. By the use of the Lyapunov-Krasovskii functional method, sufficient conditions with the controller design are formulated for guaranteeing the H∞ performance of the time-delay closed-loop system. Finally, the effectiveness of the proposed control strategy is demonstrated by two numerical examples.

Surrogate indirect adaptive controller tuning based on polynomial response surface method and bioinspired optimization: Application to the brushless direct current motor controller

The increment of autonomous systems has stimulated the research of new controller tuning techniques to face the unpredictable disturbances and parametric uncertainties inherent in any autonomous system that affect its performance. The indirect adaptive controller tuning approach based on the general dynamic model (IACTA-GDM) and bioinspired optimization is one of the most successful elections facing parametric uncertainties and disturbances, which are intricate to handle by other controller tuning techniques. However, this controller tuning approach is limited by the complexity of the dynamic model due to the computational burden, restricting its application to relatively small systems or systems with slow responses where the tuning is updated at large time intervals. The present work proposes a novel surrogate indirect adaptive controller tuning approach based on the response surface method (SIACTA-RSM) to address computational burden limitations. The proposal is tested on the speed regulation controller of a brushless direct current motor, with the aim of reducing the speed regulation error and the control system’s power consumption. The closed-loop system performance and the required computational time obtained by the proposed SIACTA-RSM are compared to the ones of a well-established IACTA-GDM. The descriptive and inferential statistics, as well as graphical comparisons, show that the system performance obtained by the SIACTA-RSM proposal is as competitive as the IACTA-GDM approach, keeping a mean difference among the results by up to 3.18% while reducing the computational burden of IACTA-GDM by up to 90%. These outcomes show that the SIACTA-RSM proposal is a reliable alternative to overcome the computational burden limitations that affect the IACTA-GDM approach while maintaining competitive performance.

Multi-Vehicle Navigation Using Cooperative Localization

This paper assesses the effectiveness of cooperative localization for improving the performance of closed-loop control systems for networks for autonomous multi-vehicle navigation. Nonlinear dynamic models of two- and three-dimensional vehicles are presented along with their linearized forms. A nonlinear control algorithm is then presented based on the dynamic model. Relative position measurement equations and their linearized forms are introduced. The state and measurement equations are then employed for the propagation and update steps of an EKF-based cooperative localization algorithm. Initially, a series of experiments with networks of quadcopters and mobile robots are presented to validate the performance of cooperative localization for state estimation with the continuous or intermittent presence of absolute measurements or their complete absence. Finally, the performance of the control algorithm is evaluated with and without cooperative localization to demonstrate its effectiveness for improving performance.

Event-Triggered Control for Networked Predictive Control Systems With Time Delay and External Disturbance

This paper develops a novel combination of the event-triggered disturbance estimation and rejection (DER) technique, and the networked predictive control (NPC) strategy for the networked control systems (NCSs) with external disturbance and time delay. Firstly, the Luenberger observers are constructed to estimate system state and disturbance, respectively. Next, with the aid of the observer-based NPC strategy, the effect of network-induced time delay is compensated effectively. Simultaneously, the DER technique is incorporated into the networked predictive controller design for the disturbance rejection. Furthermore, to cope with the networked bandwidth constraint, the event-triggered DER&NPC technique is embedded in the controller design of the considered NCSs to ensure the desired closed-loop system performance with a more efficient network resource utilization. Finally, two simulation examples are exploited to validate the proposed results.

Enhanced Output Tracking Control for Direct Current Electric Motor Systems Using Bio-Inspired Optimization

In this paper, an efficient output reference trajectory tracking control scheme for direct current electric motor systems based on bio-inspired optimization is proposed. The differential flatness structural property of the electric motor along with dynamic tracking error compensation is suitably exploited for the backstepping control design. Off-line optimal selection of control parameters, implementing bio-inspired ant colony and particle swarm optimization algorithms, is addressed by minimizing an objective function where the decision variables are the tracking error and control input effort. A novel adaptive version of the control approach based on B-spline artificial neural networks is provided as well. The introduced flat output feedback tracking control design approach can be further extended for other differentially flat dynamic systems. Considerably perturbed, diverse velocity and position reference trajectory tracking scenarios are developed for demonstrating the acceptable closed-loop system performance. The results prove the efficient and robust tracking of the position and velocity reference profiles planned for the operation of the controlled electric motor system under variable torque disturbances using bio-inspired optimization.

Non-Linear Prediction Scheme for an Omnidirectional Mobile Robot with Disturbed Time Delay

This work focuses on the trajectory tracking problem of an input-delayed omnidirectional mobile robot affected by a constant disturbance in the time delay. The trajectory-tracking solution is based on a prediction strategy that represents a generalization of the well-known sub-prediction strategy developed for the linear case. It is formally proven that the prediction scheme provides the future state of the system and that a feedback law based on the future predicted state solves the trajectory tracking problem under some assumptions related to the size of the disturbance and the number of sub-predictors considered. To evaluate the prediction-based strategy, numerical simulations are carried out showing an adequate performance of the overall closed-loop system.

Effect of drying air supply temperature and internal heat exchanger on performance of a novel closed-loop transcritical CO2 air source heat pump drying system

A novel closed-loop transcritical CO2 air-source heat pump drying (HPD) system with a relatively simple structure, higher drying temperature, and internal heat exchanger (IHX) for the drying of medical equipment was proposed and built. With or without the IHX in the system, the effects of different drying air supply temperatures on the performance of transcritical CO2 HPD system were studied experimentally. The results showed that the maximum drying air supply temperature (DAST) in the designed system could reach 72.9 °C. As the DAST raised, whether with or without the IHX in the system, the coefficient of heating performance (COPh), coefficient of system performance (COPsys), and specific moisture extraction rate (SMER) decreased gradually and moisture extraction rate (MER) increased continuously. When the DAST was 70 °C, COPh, COPsys, MER and SMER were respectively 3.68, 6.07, 3.27 kg/h and 1.68 kg/(kW·h) in the HPD system without the IHX, and were respectively 4.00, 6.89, 3.67 kg/h and 1.97 kg/(kW·h) in the HPD system with the IHX. In contrast, the compressor discharge pressure decreased 4.26 %–5.99 %, COPh increased 1.39 %–8.65 %, COPsys increased 1.89 %–13.57 %, MER increased 4.68 %–14.01 %, SMER increased 6.93 %–17.18 % in the HPD system with the IHX.

Encrypted decentralized model predictive control of nonlinear processes with delays

This work focuses on enhancing the operational safety, cybersecurity, computational efficiency, and closed-loop performance of large-scale nonlinear time-delay systems. This is achieved by employing a decentralized model predictive controller (MPC) with encrypted networked communication. Within this decentralized setup, the nonlinear process is partitioned into multiple subsystems, each controlled by a distinct Lyapunov-based MPC. These controllers take into account the interactions between subsystems by utilizing full state feedback, while computing the control inputs only corresponding to their respective subsystem. To address the performance degradation associated with input delays, we integrate a predictor with each LMPC to compute the states after the input delay period. The LMPC model is initialized with these predicted states. To cope with state delays, the LMPC model is formulated using differential difference equations (DDEs) that describe the state-delays in the system. Further, to enhance cybersecurity, all signals transmitted to and received from each subsystem are encrypted. A stability analysis is carried out for the encrypted decentralized MPC when it is utilized in a time-delay system. Bounds are set up for the errors arising from encryption, state-delays, and sample-and-hold implementation of the controller. Guidelines are established to implement this proposed control structure in any nonlinear time-delay system. The simulation results, conducted on a nonlinear chemical process network, illustrate the effective closed-loop performance of the decentralized MPCs alongside the predictor with encrypted communication when dealing with input and state delays in a large-scale process.

MiniMed 780G™ advanced hybrid closed-loop system performance in Egyptian patients with type 1 diabetes across different age groups: evidence from real-world users

BackgroundAdvanced hybrid closed loop (AHCL) system provides both automated basal rate and correction boluses to keep glycemic values in a target range.ObjectivesTo evaluate the real-world performance of the MiniMed™ 780G system among different age groups of Egyptian patients with type 1diabetes.MethodsOne-hundred seven AHCL system users aged from 3 to 71 years were enrolled. Data uploaded by patients were aggregated and analyzed. The mean glucose management indicator (GMI), percentage of time spent within glycemic ranges (TIR), time below range (TBR) and time above range (TAR) were determined.ResultsSix months after initiating Auto Mode, patients spent a mean of 85.31 ± 22.04% of the time in Auto Mode (SmartGuard) and achieved a mean GMI of 6.95 ± 0.58% compared with 7.9 ± 2.1% before AHCL initiation (p < 0.001). TIR 70–180 mg/dL was increased post-AHCL initiation from 63.48 ± 10.14% to 81.54 ± 8.43% (p < 0.001) while TAR 180–250 mg/dL, TAR > 250 mg/dL, TBR < 70 mg/dL and TBR < 54 mg/dL were significantly decreased (p < 0.001). After initiating AHCL, TIR was greater in children and adults compared with adolescents (82.29 ± 7.22% and 83.86 ± 9.24% versus 78.4 ± 7.34%, respectively; p < 0.05). The total daily dose of insulin was increased in all age groups primarily due to increased system-initiated insulin delivery including auto correction boluses and basal insulin.ConclusionsMiniMed™ 780G system users across different age groups achieved international consensus-recommended glycemic control with no serious adverse effects even in challenging age group as children and adolescents.

Safety and performance of a hybrid closed-loop insulin delivery system with carbohydrate suggestion in adults with type 1 diabetes prone to hypoglycemia

AimsTo evaluate the safety and performance of a hybrid closed-loop (HCL) system with automatic carbohydrate suggestion in adults with type 1 diabetes (T1D) prone to hypoglycemia. MethodsA 32-hour in-hospital pilot study, including a night period, 4 meals and 2 vigorous unannounced 45-minute aerobic sessions, was conducted in 11 adults with T1D prone to hypoglycemia. The primary outcome was the percentage of time in range 70–180 mg/dL (TIR). Main secondary outcomes were time below range < 70 mg/dL (TBR < 70) and < 54 (TBR < 54). Data are presented as median (10th-90th percentile ranges). ResultsThe participants, 6 (54.5%) men, were 24 (22–48) years old, and had 22 (9–32) years of T1D duration. All of them regularly used an insulin pump and a continuous glucose monitoring system. The median TIR was 78.7% (75.6–91.2): 92.7% (68.2–100.0) during exercise and recovery period, 79.3% (34.9–100.0) during postprandial period, and 95.4% (66.4–100.0) during overnight period. The TBR < 70 and TBR < 54 were 0.0% (0.0–6.6) and 0.0% (0.0–1.2), respectively. A total of 4 (3–9) 15-g carbohydrate suggestions were administered per person. No severe acute complications occurred during the study. ConclusionsThe HCL system with automatic carbohydrate suggestion performed well and was safe in this population during challenging conditions in a hospital setting.

Adaptive sliding mode control with pre-specified performance settings for AUV’s trajectory tracking

This article is concerned with the problem of adaptive prescribed performance trajectory tracking control for a six-degree-of-freedom Autonomous Underwater Vehicle. Firstly, a novel sliding mode surface with pre-specified performance settings is introduced, which possesses the capability to set the closed-loop system performance in advance. Secondly, the adaptive laws are constructed to estimate the upper bound of the concentrated disturbance terms composed of parameter uncertainties, external disturbances, and input deviations. On this basis, a sliding mode controller with predetermined performance specifications is constructed to ensure that the trajectory tracking errors converge to a predefined small neighborhood of the origin. Ultimately, simulation results are supplied to illustrate the effectiveness and superiority of the proposed method in ensuring the AUV’s trajectory tracking control.

Performance of closed-loop systems for intravenous drug administration: a systematic review and meta-analysis of randomised controlled trials.

Closed-loop drug delivery systems are autonomous computers able to administer medication in response to changes in physiological parameters (controlled variables). While limited evidence suggested that closed-loop systems can perform better than manual drug administration in certain settings, this technology remains a research tool with an uncertain risk/benefit profile. Our aim was comparing the performance of closed-loop systems with manual intravenous drug administration in adults. We searched MEDLINE, CENTRAL, and Embase from inception until November 2022, without restriction to language. We assessed for inclusion randomised controlled trials comparing closed-loop and manual administration of intravenous drugs in adults, intraoperatively or in the Intensive Care Unit. We identified 32 studies on closed-loop administration of propofol, noradrenaline, phenylephrine, insulin, neuromuscular blockers, and vasodilators. Most studies were at moderate or high risk of bias. The results showed that closed-loop systems reduced the duration of blood pressure outside prespecified targets during noradrenaline (MD 14.9%, 95% CI 9.6-20.2%, I2 = 66.6%) and vasodilators administration (MD 7.4%, 95% CI 5.2-9.7%, I2 = 62.3%). Closed-loop systems also decreased the duration of recovery after propofol (MD 1.3min, 95% CI 0.4-2.1min, I2 = 58.6%) and neuromuscular blockers (MD 9.0min, 95% CI 7.9-10.0min, I2 = 0%). The certainty of the evidence was low or very low for most outcomes. Automatic technology may be used to improve the hemodynamic profile during noradrenaline and vasodilators administration and reduce the duration of postanaesthetic recovery.Registration: This systematic review was registered with PROSPERO (CRD42022336950) on the 7th of June 2022.

Closed-Loop Stability of a Non-Minimum Phase Quadruple Tank System Using a Nonlinear Model Predictive Controller with EKF

The dynamics of a quadruple tank system (QTS) represent an extensive class of multivariate nonlinear uncertain systems found in the industry. It has been established that changes in split fractions affect the transmission zero location, thereby altering the operating conditions between the minimum and non-minimum phase regions. The latter is difficult to control as more fluid flows into the two upper tanks than into the two bottom tanks, resulting in competing effects between the initial and final system responses. This attribute, alongside nonlinearity, uncertainties, constraints, and a multivariate nature, can degrade closed-loop system performance, leading to instability. In this study, we addressed the aforementioned challenges by designing controllers for the regulation of the water flow in the two bottom tanks of the QTS. For comparative analysis, three controller algorithms—a nonlinear model predictive controller (NMPC), NMPC augmented with an extended Kalman filter (i.e., NMPC-EKF) and linear model predictive controller (LMPC)—were considered in the analysis and design of the control mechanism for the quadruple water level system in a non-minimum phase condition via the Matrix Laboratory (MATLAB) simulation package environment. The simulated and real-time results in the closed loop were analyzed, and the controller performances were considered based on faster setpoint responses, less oscillation, settling time, overshoot, and smaller integral absolute error (IAE) and integral square error (ISE) under various operational conditions. The study showed that the NMPC, when augmented with an EKF, is effective for the control of a QTS in the non-minimum phase and could be designed for more complex, nonlinear, and multivariable dynamics systems, even in the presence of constraints.

First Report on Real-World Outcomes with Evoked Compound Action Potential (ECAP)-Controlled Closed-Loop Spinal Cord Stimulation for Treatment of Chronic Pain.

A novel closed-loop spinal cord stimulation (SCS) system has recently been approved for use which records evoked compound action potentials (ECAPs) from the spinal cord and utilizes these recordings to automatically adjust the stimulation strength in real time. It automatically compensates for fluctuations in distance between the epidural leads and the spinal cord by maintaining the neural response (ECAP) at a determined target level. This data collection was principally designed to evaluate the performance of this first closed-loop SCS system in a 'real-world' setting under normal conditions of use in a single European center. In this prospective, single-center observational data collection, 22 patients were recruited at the outpatient pain clinic of the St. Antonius Hospital. All candidates were suffering from chronic pain in the trunk and/or limbs due to PSPS type 2 (persistent spinal pain syndrome). As standard of care, follow-up visits were completed at 3months, 6months, and 12months post-device activation. Patient-reported outcome data (pain intensity, patient satisfaction) and electrophysiological and device data (ECAP amplitude, conduction velocity, current output, pulse width, frequency, usage), and patient interaction with their controller were collected at baseline and during standard of care follow-up visits. Significant decreases in pain intensity for overall back or leg pain scores (verbal numerical rating score=VNRS) were observed between baseline [mean±SEM (standard error of the mean); n=22; 8.4±0.2)], 3months (n=12; 1.9±0.5), 6months (n=16; 2.6±0.5), and 12months (n=20; 2.0±0.5), with 85.0% of the patients being satisfied at 12months. Additionally, no significant differences in average pain relief at 3months and 12months between the real-world data (77.2%; 76.8%) and the AVALON (71.2%; 73.6%) and EVOKE (78.1%; 76.7%) studies were observed. These initial 'real-world' data on ECAP-controlled, closed-loop SCS in a real-world clinical setting appear to be promising, as they provide novel insights of the beneficial effect of ECAP-controlled, closed-loop SCS in a real-world setting. The presented results demonstrate a noteworthy maintenance of pain relief over 12months and corroborate the outcomes observed in the AVALON prospective, multicenter, single-arm study and the EVOKE double-blind, multicenter, randomized controlled trial. The data collection is registered on the International Clinical Trials Registry Platform (Trial NL7889).

Real-World Evidence Analysis of a Hybrid Closed-Loop System.

We analyzed real-world evidence to assess the performance of the mylife CamAPS FX hybrid closed-loop system. Users from 15 countries across different age groups who used the system between May 9, 2022, and December 3, 2022, and who had ≥30 days of continuous glucose monitor data, and ≥30% of closed-loop usage were included in the current analysis (N = 1805). Time in range (3.9-10 mmol/L) was 72.6 ± 11.5% (mean ± SD) for all users and increased by age from 66.9 ± 11.7% for users ≤6 years old to 81.8 ± 8.7% for users ≥65 years. Time spent in hypoglycemia (<3.9 mmol/L) was 2.3% [1.3, 3.6] (median [interquartile range]). Mean glucose and glucose management indicator were 8.4 ± 1.1 mmol/L and 6.9%, respectively. Time using closed-loop was high at 94.7% [90.0, 96.9]. Glycemic outcomes from the present real-world evidence are comparable to results obtained from previous randomized controlled studies and confirm the efficacy of this hybrid closed-loop system in real-world settings.

Predictor-Based Neural Dynamic Surface Control for Strict-Feedback Nonlinear Systems With Unknown Control Gains.

Neural dynamic surface control (NDSC) is an effective technique for the tracking control of nonlinear systems. The objective of this article is to improve closed-loop transient performance and reduce the number of learning parameters for a strict-feedback nonlinear system with unknown control gains. For this purpose, a predictor-based NDSC (PNDSC) approach is presented. It introduces Nussbaum functions and predictors into the traditional NDSC for nonlinear systems with unknown control gains. Unlike NDSC that uses surface errors to update the learning parameters of neural networks (NNs), the PNDSC employs prediction errors for the same purpose, leading to improved transient performance of closed-loop control systems. To reduce the number of learning parameters, the PNDSC is further embedded with the technique of the minimal number of learning parameters (MNLPs). This avoids the problem of the ``explosion of learning parameters'' as the order of the system increases. A Lyapunov-based stability analysis shows that all signals are bounded in the closed-loop systems under PNDSC embedded with MNLPs. Simulations are conducted to demonstrate the effectiveness of the PNDSC approach presented in this article.