Presence Of Parametric Uncertainties Research Articles

Updating reduced-order dynamic model for flexible-joint arm to design adaptive feedback linearization control

This study deals with the construction of an enhanced dynamic model for a lever-arm with flexible-joint to design a feedback linearization controller. The uncertainties of reduced-order model with nominal parameters are compensated via a complementary term to upgrade it to the actual system. The proposed method uses data fusion of encoder/gyroscope to remove the measurement errors. Mathematical analyses are provided to show the stochastic stability of the proposed scheme. Accordingly, a fuzzy adaptive solution is presented to effectively schedule the free parameters of the algorithm. The enhanced reduced-order model is used to design a feedback linearization law for control of lever-arm position. The controller adapts itself to the actual system, and is reliable and cost-effective because of using less sensors. The simulation studies indicate a higher accuracy of the proposed system compared with the controller designed by the full-order model in the presence of parametric uncertainties and disturbances. Also, experimental results conducted on a fabricated platform demonstrate the effectiveness of the suggested system to control the arm position in different scenarios. The comparative results with prevalent controllers indicate higher accuracy with smaller control input for the proposed controller to reject the disturbances and other uncertainties.

Reconstructing ventricular cardiomyocyte dynamics and parameter estimation using data-assimilation

Cardiac ventricular myocyte action potential dynamics are regulated by intricate and nonlinear interactions between the cell transmembrane potential and ionic currents and concentrations. Present technology limits the ability to measure transmembrane potential and multiple ionic currents simultaneously, which narrows the scope of experiments to provide a complete snapshot of the cardiac myocyte state. This limitation presents an obstacle for understanding how perturbations can trigger arrhythmias and more broadly how the myocyte responds to different conditions, such as changes in pacing rate or responses to drug treatment. In this study, we demonstrate that a data-assimilation approach can successfully reconstruct and predict the dynamics of a heterogeneous virtual cardiac ventricular myocyte population in the presence of parameter uncertainty. A population of heterogeneous cardiac ventricular myocytes is generated by varying ionic current conductance parameters, and additional observational uncertainty is mimicked by the addition of Gaussian noise to the transmembrane potential. We demonstrate that the data-assimilation approach accurately reconstructs transmembrane potential, with error less than the magnitude of the noise. Further, the data-assimilation approach successfully estimates the conductances of ionic currents generally with high accuracy and requiring low computational time. As a proof of concept, we apply the data-assimilation approach to reconstruct action potential dynamics from optical mapping experiments in an ex vivo isolated guinea pig heart. Critically, we demonstrate that the ionic conductance parameters estimated from a recording at one pacing frequency can accurately predict action potential dynamics at different rates.

Experimental Evaluation of the Robust Controllers Applied on a Single Inductor Multiple Output DC-DC Buck Converter to Minimize Cross Regulation Considering Parametric Uncertainties and CPL Power Variations

This paper presents two control design strategies for voltage regulation in a single inductor dual-output DC-DC buck converter system. Based on a nominal multiple input multiple output plant model and performance requirements, both a Linear Quadratic Regulator and a Decoupled PI control law are designed to control the power converter system under parametric uncertainties such as voltage source variation, constant power load variation, and load resistance variation. Therefore, the converter can cascade operation, which may cause the undesired effects of voltage oscillation and reduce the system’s stability margin. The control performance was assessed under both the uncertainties of resistive loading and the power variation in a constant power load. A single inductor dual-output DC-DC buck converter board was developed for experimental tests. The experimental results show that the Linear Quadratic Regulator strategy, compared to the PI strategy, presented a robust performance in the presence of parametric uncertainties in the resistive load-bearing; however, it was sensitive to uncertainties due to the presence of constant power loads.

How Many Monte Carlo Samples are Needed for Probabilistic Cost-Effectiveness Analyses?

ObjectivesProbabilistic sensitivity analysis (PSA) is conducted to account for the uncertainty in cost and effect of decision options under consideration. PSA involves obtaining a large sample of input parameter values (N) to estimate the expected cost and effect of each alternative in the presence of parameter uncertainty. When the analysis involves using stochastic models (eg, individual-level models), the model is further replicated P times for each sampled parameter set. We study how N and P should be determined. MethodsWe show that PSA could be structured such that P can be an arbitrary number (say, P=1). To determine N, we derive a formula based on Chebyshev’s inequality such that the error in estimating the incremental cost-effectiveness ratio (ICER) of alternatives (or equivalently, the willingness-to-pay value at which the optimal decision option changes) is within a desired level of accuracy. We described 2 methods to confirm, visually and quantitatively, that the N informed by this method results in ICER estimates within the specified level of accuracy. ResultsWhen N is arbitrarily selected, the estimated ICERs could be substantially different from the true ICER (even as P increases), which could lead to misleading conclusions. Using a simple resource allocation model, we demonstrate that the proposed approach can minimize the potential for this error. ConclusionsThe number of parameter samples in probabilistic cost-effectiveness analyses should not be arbitrarily selected. We describe 3 methods to ensure that enough parameter samples are used in probabilistic cost-effectiveness analyses.

Robustness of dynamic quantum control: Differential sensitivity bounds

Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the robustness of the resulting control schemes in the presence of model uncertainty; unlike in classical control, there are generally no analytical guarantees on the control performance with respect to inexact modeling of the system. In this paper, a new robustness measure based on the differential sensitivity of the gate fidelity error to parametric (structured) uncertainties is introduced, and bounds on the differential sensitivity to parametric uncertainties are used to establish performance guarantees for optimal controllers for a variety of quantum gate types, system sizes, and control implementations. Specifically, it is shown how a maximum allowable perturbation over a set of Hamiltonian uncertainties that guarantees a given fidelity error can be reliably computed. This measure of robustness is inversely proportional to the upper bound on the differential sensitivity of the fidelity error evaluated under nominal operating conditions. Finally, the results show that the nominal fidelity error and differential sensitivity upper bound are positively correlated across a wide range of problems and control implementations, suggesting that in the high-fidelity control regime, rather than there being a trade-off between fidelity and robustness, higher nominal gate fidelities are positively correlated with increased robustness of the controls in the presence of parametric uncertainties.

IMC based robust and innovative control strategies for higher-order DC-DC converter in DC microgrid applications

The extensive practice of DC-DC converter interfacing circuits to maintain DC link voltage in DC microgrid applications introduces unavoidable voltage regulation problems due to its nonlinearity. These unregulated voltages demean the performance and result in an unstable system. This brief proposes an internal model control (IMC) non-linear approach based robust proportional-integral-lead (PI-Lead) controller design for regulating a practical fifth-order DC-DC boost converter. The main innovation of this paper is the developed procedure for designing controller. The prominent feature of IMC filter coefficient is to fulfil the desired level of gain margin and phase margin to show the trade-off between performance and robustness. The proposed controller's performance is evaluated in the presence of uncertain disruptions and its effectiveness is verified by comparing it with the some conventional proportional-integral (PI) as well as with recently published IMC-proportional-integral-derivative (IMC-PID) and IMC-proportional integral derivative double derivative (IMC-PIDD2) controllers. The applicability of the proposed control methodology has been validated under varying supply and load current levels in presence of parametric uncertainty using a MATLAB/Simulink tool along with a low-cost microcontroller DSP F280379D based laboratory prototype.

Reinforcement learning based fractional fuzzy controller for photovoltaic systems

This article presents an innovative artificial nonlinear control technique for photovoltaic (PV) systems. A boost converter extracts maximum power from the PV system under different weather conditions. A fuzzy logic maximum power point (MPP) finding algorithm is used to determine the reference voltage of the PV system under various atmospheric conditions. It is assumed that the nonlinear dynamic model, parameters, and uncertainties of the converter are unknown. To estimate a precise model that contains nonlinearities, model uncertainties, and disturbances of the converter, proximal policy optimization (PPO) with a special reward function is applied. PPO is optimal in policy learning and sampling, fast to implement, and is a simple reinforcement learning (RL) algorithm. Then, estimations of dynamics and uncertainties are used to enhance the robustness of the suggested fractional order sliding mode controller. Furthermore, the controller coefficients are optimally adjusted by the PPO algorithm. The Lyapunov theorem is used for proving the control system's closed-loop stability. Also, the proposed methods can be generalized and used for other control systems. The simulation is conducted by MATLAB to evaluate the suggested controller's performance effectiveness. Robustness against the presence of parameter uncertainty is investigated. Moreover, the suggested technique is also compared with sliding mode controller.

Robust Control Based on Adaptative Fuzzy Control of Double-Star Permanent Synchronous Motor Supplied by PWM Inverters for Electric Propulsion of Ships

This study presents the development of an adaptive fuzzy control strategy for double-star PMSM-PWM inverters used in ship electrical propulsion. The approach addresses the current and speed tracking challenges of double-star permanent magnet synchronous motors (DSPMSMs) in the presence of parametric uncertainties. Initially, a modeling technique employing a matrix transformation method is introduced, generating decoupled and independent star windings to eliminate inductive couplings, while maintaining model consistency and torque control. The precise DSPMSM model serves as the foundation for an unknown nonlinear backstepping controller, approximated directly using an adaptive fuzzy controller. Through the Lyapunov direct method, system stability is demonstrated. All signals in the closed-loop system are ensured to be uniformly ultimately bounded (UUB). The proposed control system aims for low tracking errors, while also mitigating the impact of parametric uncertainties. The effectiveness of the adaptive fuzzy nonlinear control system is validated through tests conducted in hardware-in-the-loop (HIL) simulations, utilizing the OPAL-RT platform, OP4510.

A novel decoupled approach combining invertible cross-entropy method with Gaussian process modeling for reliability-based design and topology optimization

Design optimization considering the presence of uncertainties in parameters poses an extremely challenging problem. The source of difficulties comes with reliability-based formulations, where addressing the probabilistic problem exhausts the large computing efforts for failure estimations of the structure violating limit-state functions (LSFs). This paper proposes a novel decoupled approach for effectively solving reliability-based design optimization (RBDO) problems, namely an invertible cross-entropy (iCE) method advantageously combined with a Gaussian process regression (GPR) model, termed as iCE-GPR. The GPR model is applied to approximate the spectrum of LSFs under random parameters. Furthermore, to enhance the accurate prediction of the system failure probability, an active learning process is applied to systematically refine the GPR model by adding new learning points in the region with the largest uncertainty and high-reliability sensitivity through the maximization of an expected feasibility function (EFF). Based on the updated GPR model, the failure probability is estimated by a cost-effective cross-entropy (CE) method without any calls to the actual performance function. To perform the decoupling optimization process with the reliability analysis, the novel iCE, based on the CE method, is developed to update the most probable point (MPP) assigned for the next deterministic optimization process in determining the new optimal design. The method iteratively performs the deterministic optimization process based on the MPP underpinning LSFs sequentially updated by the active learning process. The proposed iCE-GPR method fast-converges the optimal design and significantly alleviates computational burdens associated with reliability analyses. The proposed method is also applied to solve a reliability-based topology optimization (RBTO) problem. Four numerical examples for both the RBDO and RBTO problems are provided to illustrate efficiency and robustness of the proposed iCE-GPR method.

Reinforcement learning for decision-making under deep uncertainty

Planning under complex uncertainty often asks for plans that can adapt to changing future conditions. To inform plan development during this process, exploration methods have been used to explore the performance of candidate policies given uncertainties. Nevertheless, these methods hardly enable adaptation by themselves, so extra efforts are required to develop the final adaptive plans, hence compromising the overall decision-making efficiency. This paper introduces Reinforcement Learning (RL) that employs closed-loop control as a new exploration method that enables automated adaptive policy-making for planning under uncertainty. To investigate its performance, we compare RL with a widely-used exploration method, Multi-Objective Evolutionary Algorithm (MOEA), in two hypothetical problems via computational experiments. Our results indicate the complementarity of the two methods. RL makes better use of its exploration history, hence always providing higher efficiency and providing better policy robustness in the presence of parameter uncertainty. MOEA quantifies objective uncertainty in a more intuitive way, hence providing better robustness to objective uncertainty. These findings will help researchers choose appropriate methods in different applications.

Tracking control of a flexible‐link manipulator based on an improved barrier function adaptive sliding mode

AbstractIn this paper, a novel controller designed for robust tracking control of a flexible‐link manipulator operating in the presence of parameter uncertainties and external disturbances within the joint space is introduced. The proposed controller employs an adaptive sliding mode control approach, incorporating an improved barrier function, to ensure that trajectory errors remain within predefined performance bounds. This design enhances the tracking performance without overestimating control‐switching gains. Additionally, a fixed‐time adaptive sliding mode control, featuring a rapid nonsingular terminal sliding mode variable, is introduced to expedite the convergence rate of the system state during the initial stages. The efficacy of the proposed control scheme is established through the Lyapunov method, demonstrating finite‐time convergence of the trajectory error to a specified neighborhood of zero. Experimental validation on a flexible‐link system supports the effectiveness and advantages of the proposed control strategy, as evidenced via comparisons with two existing adaptive control schemes.

Active underactuation fault‐tolerant backstepping attitude tracking control of a satellite with interval error constraints

AbstractUnderactuation poses a significant challenge to space mission control and performance. This article investigates the non‐linear attitude tracking control problem for a remote sensing satellite underactuated by a reaction wheel (RW) actuator fault. First, a timeline close to the in‐orbit reality of an underactuation fault is presented. Then, the fault detection and diagnosis strategy is performed in a finite‐time decision window. The failed actuator is excluded from the control loop by forming the proposed reconfiguration window to transition from a 3 RWs configuration to 2 RWs. The underactuation fault‐tolerant control is designed according to the active method, where the adaptive robust control law employed for fault‐free conditions is switched to the underactuated attitude tracking control (UATC). The structure of UATC is based on kinematic and adaptive backstepping dynamic controllers. The effect of unknown bounded external disturbances is considered with an adaptive estimation term. The asymptotic stability of the closed‐loop control system is proved via Lyapunov theory in the presence of parametric uncertainty. Due to the underactuation, a new approach proposed in the prescribed performance function is interval error constraints, which include the pointing accuracy and stability requirements in imaging time intervals. Finally, the results of the multidisciplinary simulation and experimental test confirm the applicability of the underactuation fault‐tolerant control.

Flight control design for a hypersonic waverider configuration: A non-linear model following control approach

AbstractDLR is currently investigating the potential of hypersonic flight systems in the context of different mission scenarios. One configuration type of higher interest for civil and military purposes is the hypersonic glide vehicle (HGV). Such HGVs operate over broad flight envelopes and pose complex flight dynamic characteristics. This article presents DLR’s generic hypersonic glide vehicle 2 (GHVG-2) and proposes an integrated non-linear flight control architecture that is based on the idea of the non-linear dynamic inversion and non-linear model following control methodologies. The proposed control scheme is designed to sufficiently and robustly handle the system dynamics of the over-actuated flight vehicle. The approach is first discussed, and the performance of the suggested control laws is later investigated via simulations of a high-fidelity non-linear flight dynamic model in the nominal case and under the presence of parametric uncertainties. The presented results demonstrate that the proposed NMFC approach provides benefits for the robust control of the regarded hypersonic system.

Adaptive formation control of nonholonomic multirobot systems with collision avoidance and connectivity maintenance

In this paper, an adaptive cooperative formation controller is developed to force a swarm of nonholonomic mobile robots with limited sensing ranges to move along the desired reference trajectory in a predetermined formation, while maintaining communication connectivity among the initial user-specified connected robots and guaranteeing no collision between the robots. Both kinematic models and dynamic systems with parametric uncertainties are discussed. The presence of parametric uncertainties is handled by adaptive control technique. A novel artificial potential function, which is based on a 4 times differential pseudo bump function, is constructed to achieve collision avoidance and connectivity maintenance. The control design is based on a fusion of potential function, adaptive backstepping technique, and Lyapunov synthesis. The cooperative formation controller is proven to be stable and can guarantee that there is no collision between any robots and the initial connectivity of the communication network can be always maintained. The proposed formation control approach is decentralized in the sense that the control action on each robot depends only on information from its neighbours and the desired trajectory of the group. Comparative simulation and experiment studies are performed to show the effectiveness of the proposed formation controller.

Robust fixed-time flight controller for a dual-system convertible UAV in the cruise mode

This paper investigates the attitude tracking control problem for the cruise mode of a dual-system convertible unmanned aerial vehicle (UAV) in the presence of parameter uncertainties, unmodeled uncertainties and wind disturbances. First, a fixed-time disturbance observer (FXDO) based on the bi-limit homogeneity theory is designed to estimate the lumped disturbance of the convertible UAV model. Then, a fixed-time integral sliding mode control (FXISMC) is combined with the FXDO to achieve strong robustness and chattering reduction. Bi-limit homogeneity theory and Lyapunov theory are applied to provide detailed proof of the fixed-time stability. Finally, numerical simulation experimental results verify the robustness of the proposed algorithm to model parameter uncertainties and wind disturbances. In addition, the proposed algorithm is deployed in a open-source UAV autopilot and its effectiveness is further demonstrated by hardware-in-the-loop experimental results.

Heave attenuation in offshore managed pressure drilling with an integral sliding mode controller

Managed pressure drilling (MPD) is a technique used to precisely control the pressure within the wellbore during the drilling process to overcome drilling challenges, such as heave disturbance caused by waves. The mismatched nature of the heave disturbance presents a control challenge, making it difficult to reduce the disturbance effectively. However, MPD utilizing an appropriate controller can provide a solution to this challenge. As a result, this paper proposes an integral sliding mode controller (Integral SMC) based on feedback linearization and a nonlinear disturbance observer to attenuate the heave disturbance effect and provide stability for MPD systems. A comparison study is conducted between the proposed controller and industrial controllers, such as Proportional Integral Derivative (PID) and manual controllers, using root mean square error (RMSE) as the evaluation metric. Additionally, the robustness of the proposed controller and the nonlinear disturbance observer in the presence of parameter uncertainty and measurement noise is investigated. The results demonstrate that the proposed controller is a viable solution to overcome the heave disturbance effect on offshore MPD systems.

Exponential super-twisting control for nonlinear systems with unknown polynomial perturbations

The study focuses on the control of nonlinear dynamic systems in the presence of parameter uncertainties, unmodeled dynamics, and external disturbances. The lumped perturbation is assumed to be bounded within a polynomial in the system state with the polynomial parameters and degrees unknown a priori such that it accommodates a quite wider range dynamic systems. Based on the studies in recent super-twisting algorithm designs and the idea from adaptive sliding mode control for nonlinear systems with uncertainties, we propose a novel adaptive super-twisting algorithm with exponential reaching law, or exponential super-twisting algorithm (ESTA), for the high-stability and acceptable accuracy control of the aimed nonlinear dynamics. The stability analysis and practical finite-time (PFT) convergence are proven using Lyapunov theory and an intuitive analysis of the control behaviour. Simulations are performed to compare the proposed ESTA with the existing super-twisting method and the traditional proportional integral differential control. The simulation results demonstrate the effectiveness of the proposed ESTA in terms of the fastest settling time and the smallest overshoot.

Robust Degradation State Identification in the Presence of Parameter Uncertainty and Outliers

Robust Degradation State Identification in the Presence of Parameter Uncertainty and Outliers

Modeling dynamics and stability analysis of pneumonia disease infection with parameters uncertainties control

In this work, a mathematical model of six compartments is formulated, showing the dynamic flow of pneumonia disease in the human population with treatment and vaccination interventions. Equilibria points and stability analyses were carried out using the Lyapunov function approach. Analytically, it is found that at the disease-free equilibrium state, local and global asymptotic stability behaviors are achieved when [Formula: see text] with instability if [Formula: see text]. However, at the endemic equilibrium point, asymptotic stability is attainable if [Formula: see text] and instability otherwise. The study indicates that pneumonia disease infection is successfully reduced when treatment and vaccination interventions are administered to the patients. The work also proposes an adaptive sliding mode control approach with a closed-loop control system to manage pneumonia epidemic model uncertainties. This approach intends to reduce disease transmission and infection through successful tracking of defined trajectories and managing uncertainties. For the control rates [Formula: see text], the technique managed to track the disease carriers and infectious agents accurately even in the presence of parameter uncertainties. In conclusion, an increase in the control rates [Formula: see text] in the existence of parameter uncertainty control systems significantly reduces the number of disease transmitters and infectious agents quicker than in their absence. Hence, this study signifies the pivotal role of treatment and vaccination in the control of pneumonia infection as well as the control of parameter uncertainties by the proposed method.

Adaptive Neural Consensus Observer Networks Design for a Class of Semilinear Parabolic PDE Systems.

This article concerns the investigation on the consensus problem for the joint state-uncertainty estimation of a class of parabolic partial differential equation (PDE) systems with parametric and nonparametric uncertainties. We propose a two-layer network consisting of informed and uninformed boundary observers where novel adaptation laws are developed for the identification of uncertainties. Particularly, all observer agents in the network transmit their information with each other across the entire network. The proposed adaptation laws include a penalty term of the mismatch between the parameter estimates generated by the other observer agents. Moreover, for the nonparametric uncertainties, radial basis function (RBF) neural networks are employed for the universal approximation of unknown nonlinear functions. Given the persistently exciting condition, it is shown that the proposed network of adaptive observers can achieve exponential joint state-uncertainty estimation in the presence of parametric uncertainties and ultimate bounded estimation in the presence of nonparametric uncertainties based on the Lyapunov stability theory. The effects of the proposed consensus method are demonstrated through a typical reaction-diffusion system example, which implies convincing numerical findings.