Fractional-Order Robust Control Design under parametric uncertain approach.

This paper presents a novel methodology that combines fractional-order control theory with robust control under a parametric uncertainty approach to enhance the performance of linear time-invariant uncertain systems with integer or fractional order, referred to as Fractional-Order Robust Control (FORC). In contrast to traditional approaches, the proposed methodology introduces a novel formulation of inequalities-based design, thus expanding the potential for discovering improved solutions through linear programming optimization. As a result, fractional order controllers are designed to guarantee desired transient and steady-state performance in a closed-loop system. To enable the digital implementation of the designed controller, an impulse response invariant discretization of fractional-order differentiators (IRID-FOD) is employed to approximate the fractional-order controllers to an integer-order transfer function. Additionally, Hankel's reduction order method is applied, thus making it suitable for hardware deployment. Experimental tests carried out in a thermal system and the assessment results, based on time-domain responses and robustness analysis supported by performance indices and set value analysis in a thermal system test-bed, demonstrate the improved and robust performance of the proposed FORC methodology compared to classical robust control under parametric uncertainty.

Global µ-synchronization for coupling delayed complex dynamical networks via event-triggered delayed impulsive control.

This paper mainly focuses on solving the global µ-synchronization issue of complex dynamical networks (CDNs) by a novel event-triggered impulsive control (ETIC) method with time delays. This method combines the advantages of impulsive control and event-triggered control and gets rid of the limitation that the Lyapunov function decreases strictly monotonically with the sequence of event triggers. An event-triggered mechanism is specifically designed to realize µ-synchronization for CDNs in this paper, which means that event-triggered control has been applied to µ-synchronization field for the first time. Compared with periodic impulsive control, ETIC only produces control effects when the event-triggered mechanism are met, which is more in line with the actual situation. By Lyapunov-Razumikhin, recursion, etc, some valid global µ-synchronization criteria of CDNs are obtained and also Zeno behavior is avoided. Additionally, coupled delays and uncertainties are considered in CDNs. Finally, two numerical examples are shown to demonstrate the correctness of the designed ETIC strategy.

A Passive Decomposition Based Robust Synchronous Motion Control of Multi-Motors and Experimental Verification.

Recently, with the trend of redundancy design, the importance of synchronous motion control of multiple motors has been emphasized in various fields such as automotive, construction, and industrial engineering. Therefore, this paper proposed a novel passive decomposition-based robust synchronous control strategy for a multi-motor system, guaranteeing that both the tracking error of each motor and the synchronous error between motors are ultimately and synchronously bounded, even under the presence of parametric uncertainty and unstructured external disturbance. Specifically, a passive decomposition is used to obtain the locked and shape systems from the original system, and then a sliding mode control system along with robust compensations is designed for each decomposed system to achieve the precise synchronous motion control of the n number of motors. Here, the controller for the locked system reduces the tracking errors of motors for a given desired trajectory, while the controller for the shaped system decreases the synchronous errors between motors. Furthermore, the control system is generally and conveniently formulated to adopt the arbitrary n number of motors that must track a given desired trajectory and be synchronized. Compared to other related studies, this work especially focused on increasing the robustness of the entire system using both high-order sliding mode control and two separate compensation terms for model uncertainty and unstructured external disturbance. Finally, to validate the effectiveness of the proposed synchronous control strategy, the extensive experimental studies on two/three/four-geared BLDC motors with a high dead-zone effect were conducted, and we also compared the synchronous control performance of the proposed control strategy with the other representative control approaches, a master-slave control scheme and an independent one to address the superiority of the proposed control system. Regardless of the number of motors, due to the robustness of the control system, it is found that the proposed control ensures the tracking and synchronous errors are less than 1 degree for the sine-wave trajectory while it guarantees that the errors are below 1.5 degree for the trapezoidal trajectory. This control approach can be widely and generally applied to the multiple motor control required in various engineering fields.

Adaptive fixed-time stabilization for a class of nonlinear uncertain systems.

Finite-time stability (FTS) has attained great interest in nonlinear control systems in recent two decades. Fixed-time stability (FxTS) is an improved version of FTS in consideration of its settling time independent of the initial values. In this article, the adaptive fixed-time stabilization issue is studied for a kind of nonlinear systems with nonlinear parametric uncertainties and uncertain control coefficients. Using the adaptive estimate and the adding one power integrator (AOPI) design tool, we propose a two-phase control strategy, which makes that the system states tend to the origin in fixed-time, and other signals are bounded on [0,+∞). We prove the main results by means of the recently developed fixed-time Lyapunov stability theory. Finally, we apply the proposed adaptive fixed-time stabilizing control strategy into the pendulum system, and the simulation results verify the efficacy of the presented method.

A fractional PI observer for incommensurate fractional order systems under parametric uncertainties.

The problem of state observation in incommensurate fractional order systems has been poorly studied. Currently some observers that have been proposed are based on a copy of the system, which causes them to be highly dependent on the system parameters, additionally they are redundant (estimate variables that are available). So this paper proposes a novel fractional observer against parametric uncertainties for a certain type of incommensurate fractional order systems. The fractional observer design is based on a property concerning observability in incommensurate fractional order systems which allows us to construct the observer only considering the available output and its fractional derivatives. On the other hand, the convergence analysis of the observation error is carried out using a particular approach of fractional order systems related to the Global Mittag-Leffler boundedness. We prove that there is a compact set GMLA (Globally Mittag-Leffler Attractive, according to Definition 4) where the system that represents the observation error dynamics is attractive and we also prove that the observation error is uniformly bounded. Additionally, the fractional observer is model-free i.e., a system copy is not required, this gives robustness in spite of parametric uncertainties and it is also reduced order therefore one observer must be designed for each variable that we want to estimate consequently the observer is non-redundant (no estimation of variables that are already available). Moreover, our proposed fractional observer can be designed for commensurate fractional order systems and we also show that if we consider integer derivative order, the proposed fractional observer presents certain properties. Finally, in order to show the effectiveness of the proposed fractional observer, an incommensurate fractional order Rössler hyperchaotic system is considered as a numerical example and an incommensurate fractional model of the COVID-19 pandemic as a real-world application.

Global net biome CO2 exchange predicted comparably well using parameter-environment relationships and plant functional types.

Accurate estimation and forecasts of net biome CO2 exchange (NBE) are vital for understanding the role of terrestrial ecosystems in a changing climate. Prior efforts to improve NBE predictions have predominantly focused on increasing models' structural realism (and thus complexity), but parametric error and uncertainty are also key determinants of model skill. Here, we investigate how different parameterization assumptions propagate into NBE prediction errors across the globe, pitting the traditional plant functional type (PFT)-based approach against a novel top-down, machine learning-based "environmental filtering" (EF) approach. To do so, we simulate these contrasting methods for parameter assignment within a flexible model-data fusion framework of the terrestrial carbon cycle (CARDAMOM) at a global scale. In the PFT-based approach, model parameters from a small number of select locations are applied uniformly within regions sharing similar land cover characteristics. In the EF-based approach, a pixel's parameters are predicted based on underlying relationships with climate, soil, and canopy properties. To isolate the role of parametric from structural uncertainty in our analysis, we benchmark the resulting PFT-based and EF-based NBE predictions with estimates from CARDAMOM's Bayesian optimization approach (whereby "true" parameters consistent with a suite of data constraints are retrieved on a pixel-by-pixel basis). When considering the mean absolute error of NBE predictions across time, we find that the EF-based approach matches or outperforms the PFT-based approach at 55% of pixels-a narrow majority. However, NBE estimates from the EF-based approach are susceptible to compensation between errors in component flux predictions and predicted parameters can align poorly with the assumed "true" values. Overall, though, the EF-based approach is comparable to conventional approaches and merits further investigation to better understand and resolve these limitations. This work provides insight into the relationship between terrestrial biosphere model performance and parametric uncertainty, informing efforts to improve model parameterization via PFT-free and trait-based approaches.

Constrained hybrid control for parametric uncertainty systems via step-function method.

In this paper, considering that sometimes signal transmission may be interrupted, or signal input errors may occur, we establish a novel class of parametric uncertainty hybrid control system models including the impulsive control signals under saturated inputs, which can reflect the signal transmission process more realistically. Based on the step-function method, improved polytopic representation approach and Schur complement, we find the stability conditions, which are less conservative than those with the traditional Lyapunov method, of the considered control system. In addition, we investigate the design of the control gains and the auxiliary control gains for easily finding the suitable control signals, the auxiliary signals and the estimation of the attraction domain. Moreover, our proposed methods are applied to the fixed time impulse problems of uncertain systems with or without Zeno behavior. Simulation results for the uncertain neural network systems are presented to show the feasibility and effectiveness of our stabilization methods using the step-function.

How Sensitive is Sensitivity Analysis?: Evaluation of Pharmacoeconomic Submissions in Korea.

Purpose: We aimed to describe the types of uncertainties examined in the economic evaluations submitted for reimbursement in Korea and their impact on the incremental cost-effectiveness ratio (ICER). Method: Fifty dossiers were submitted by pharmaceutical companies to the economic subcommittee of the Pharmaceutical Benefit Coverage Advisory Committee (PBCAC) from January 2014 to December 2018. The types of uncertainties were categorized as structural and parametric, and the frequencies of the sensitivity analysis per variables were analyzed. The impact of uncertainties was measured by the percent variance of the ICER relative to that of the base case analysis. Results: Of the 50 submissions, varying discount rate (44 submissions), followed by time horizon (38 submissions) and model assumptions (29 submissions), were most frequently used to examine structural uncertainty, while utility (42 submissions), resource use (41 submissions), and relative effectiveness (26 submissions) were used to examine parametric uncertainty. A total of 1,236 scenarios (a scenario corresponds to a case where a single variable is varied by a single range) were presented in the one-way sensitivity analyses, where parametric and structural sensitivity analyses comprised 679 and 557 scenarios, respectively. Varying drug prices had the highest impact on ICER (median variance 19.9%), followed by discount rate (12.2%), model assumptions (11.9%), extrapolation (11.8%), and time horizon (10.0%). Conclusions: Variables related to long-term assumptions, such as model assumptions, time horizon, extrapolation, and discounting rate, were related to a high level of uncertainty. Caution should be exercised when using immature data.

Model free adaptive control of the under-actuated robot manipulator with the chaotic dynamics.

Development of practical control approaches for the under-actuated chaotic systems such as the robot manipulators are challenging due to the unpredictable character of the chaotic dynamics, and the inevitable real-time application properties like delays, saturations, and uncertainties In this paper, we propose a model free digital adaptive control approach, which considers the time delay of the control signal, actuator saturation, and non-parametric uncertainties, for an under-actuated manipulator. We also develop a chaos control to learn the unbiased and smooth digital control policy inside the chaotic regions of the continuous time under-actuated manipulator. We perform real-time experiments in a dynamic environment with the proposed digital adaptive control. Then we compare the results of the learning and control with and without chaos control. We observe that the proposed model free adaptive control approach can accurately learn both the long-term predictor and unbiased control policy even in the chaotic regions of the under-actuated robot manipulator.

Sensitivity analysis of Wasserstein distributionally robust optimization problems.

We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for the first-order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints. We present applications to statistics, machine learning, mathematical finance and uncertainty quantification. In particular, we provide an explicit first-order approximation for square-root LASSO regression coefficients and deduce coefficient shrinkage compared to the ordinary least-squares regression. We consider robustness of call option pricing and deduce a new Black-Scholes sensitivity, a non-parametric version of the so-called Vega. We also compute sensitivities of optimized certainty equivalents in finance and propose measures to quantify robustness of neural networks to adversarial examples.

Vision-based neural predictive tracking control for multi-manipulator systems with parametric uncertainty.

To deal with the coordination problem for multi-manipulator trajectory tracking systems with parametric uncertainties, this paper proposes a two-layer control scheme incorporating a model predictive strategy and an extended state observer. In the kinematic layer, the visual information is implemented and a visual servoing error model is derived by the image-based visual servoing strategy. A recurrent neural network model predictive control approach is proposed to obtain velocities which are regarded as the reference signals for the dynamic layer. For dynamics, a linear time-varying dynamic model of the multi-manipulator system coupled with the object is established, where the parametric uncertainty is recognized as an added disturbance. An extended state observer is sequentially designed to estimate the disturbance by using pole placement method. The input-to-state practical stability of the system is further analyzed with a bounded disturbance. Finally, simulations and comparison are given to verify the effectiveness and robustness of the proposed algorithm.

Fuzzy Petri nets for modelling of uncertain biological systems.

The modelling of biological systems is accompanied with epistemic uncertainties that range from structural uncertainty to parametric uncertainty due to such limitations as insufficient understanding of the underlying mechanism and incomplete measurement data of a system. Fuzzy logic approaches such as fuzzy Petri nets (FPNs) are effective in addressing these issues. In this paper, we review FPNs that have been used for modelling uncertain biological systems, which we classify in three categories: basic fuzzy Petri nets, fuzzy quantitative Petri nets and Petri nets with fuzzy kinetic parameters. For each category of these FPNs, we summarize its modelling capabilities and current applications, discuss its merits and drawbacks and give suggestions for further research. This understanding on how to use FPNs for modelling uncertain biological systems will assist readers in selecting appropriate FPN classes for specific modelling circumstances. This review may also promote the extensive research and application of FPNs in the systems biology area.

Reinforcement Learning-Based Satellite Attitude Stabilization Method for Non-Cooperative Target Capturing.

When a satellite performs complex tasks such as discarding a payload or capturing a non-cooperative target, it will encounter sudden changes in the attitude and mass parameters, causing unstable flying and rolling of the satellite. In such circumstances, the change of the movement and mass characteristics are unpredictable. Thus, the traditional attitude control methods are unable to stabilize the satellite since they are dependent on the mass parameters of the controlled object. In this paper, we proposed a reinforcement learning method to re-stabilize the attitude of a satellite under such circumstances. Specifically, we discretize the continuous control torque, and build a neural network model that can output the discretized control torque to control the satellite. A dynamics simulation environment of the satellite is built, and the deep Q Network algorithm is then performed to train the neural network in this simulation environment. The reward of the training is the stabilization of the satellite. Simulation experiments illustrate that, with the iteration of training progresses, the neural network model gradually learned to re-stabilize the attitude of a satellite after unknown disturbance. As a contrast, the traditional PD (Proportion Differential) controller was unable to re-stabilize the satellite due to its dependence on the mass parameters. The proposed method adopts self-learning to control satellite attitudes, shows considerable intelligence and certain universality, and has a strong application potential for future intelligent control of satellites performing complex space tasks.

Robust synchronization of networked manipulators using distributed dynamic H∞ controllers.

In this note, the problem of synchronization of networked non-identical manipulators is investigated in the presence of model uncertainties. The notion of nonlinear H∞ control is employed to design distributed output-feedback dynamic controllers for robust synchronization of the robots. The parameters of the synchronizing controllers are computed by solving a set of computationally tractable matrix inequalities instead of finding the solution of complicated differential inequalities which are usually encountered in the nonlinear H∞ context. Comparative simulation results are presented to verify the efficiency and applicability of the proposed method.

Design of a completely model free adaptive control in the presence of parametric, non-parametric uncertainties and random control signal delay.

In this paper, an adaptive controller is developed for discrete time linear systems that takes into account parametric uncertainty, internal-external non-parametric random uncertainties, and time varying control signal delay. Additionally, the proposed adaptive control is designed in such a way that it is utterly model free. Even though these properties are studied separately in the literature, they are not taken into account all together in adaptive control literature. The Q-function is used to estimate long-term performance of the proposed adaptive controller. Control policy is generated based on the long-term predicted value, and this policy searches an optimal stabilizing control signal for uncertain and unstable systems. The derived control law does not require an initial stabilizing control assumption as in the ones in the recent literature. Learning error, control signal convergence, minimized Q-function, and instantaneous reward are analyzed to demonstrate the stability and effectiveness of the proposed adaptive controller in a simulation environment. Finally, key insights on parameters convergence of the learning and control signals are provided.

Passivity-based control framework for task-space bilateral teleoperation with parametric uncertainty over unreliable networks.

Bilateral teleoperation systems developed in joint-space or in task-space without taking into account parameter uncertainties and unreliable communication have limited practical applications. In order to ensure stability, improve tracking performance, and enhance applicability, a novel task-space control framework for bilateral teleoperation with kinematic/dynamic uncertainties and time delays/packet losses is studied. In this paper, we have demonstrated that with the proposed control algorithms, the teleoperation system is stable and position tracking is guaranteed when the system is subjected to parametric uncertainties and communication delays. With the transformation of scattering variables, a packet modulation, called Passivity-Based Packet Modulation (PBPM), is proposed to cope with data losses, incurred in transmission of data over unreliable network. Moreover, numerical simulations and experiments are also presented to validate the efficiency of the developed control framework for task-space bilateral teleoperation.

Observer-based robust control of one-sided Lipschitz nonlinear systems.

This paper presents an observer-based controller design for the class of nonlinear systems with time-varying parametric uncertainties and norm-bounded disturbances. The design methodology, for the less conservative one-sided Lipschitz nonlinear systems, involves astute utilization of Young's inequality and several matrix decompositions. A sufficient condition for simultaneous extraction of observer and controller gains is stipulated by a numerically tractable set of convex optimization conditions. The constraints are handled by a nonlinear iterative cone-complementary linearization method in obtaining gain matrices. Further, an observer-based control technique for one-sided Lipschitz nonlinear systems, robust against L2-norm-bounded perturbations, is contrived. The proposed methodology ensures robustness against parametric uncertainties and external perturbations. Simulation examples demonstrating the effectiveness of the proposed methodologies are presented.

Robust H(∞) positional control of 2-DOF robotic arm driven by electro-hydraulic servo system.

In this paper an H∞ positional feedback controller is developed to improve the robust performance under structural and parametric uncertainty disturbance in electro-hydraulic servo system (EHSS). The robust control model is described as the linear state-space equation by upper linear fractional transformation. According to the solution of H∞ sub-optimal control problem, the robust controller is designed and simplified to lower order linear model which is easily realized in EHSS. The simulation and experimental results can validate the robustness of this proposed method. The comparison result with PI control shows that the robust controller is suitable for this EHSS under the critical condition where the desired system bandwidth is higher and the external load of the hydraulic actuator is closed to its limited capability.

Robust finite-time chaos synchronization of uncertain permanent magnet synchronous motors.

In this paper, a robust finite-time chaos synchronization scheme is proposed for two uncertain third-order permanent magnet synchronous motors (PMSMs). The whole synchronization error system is divided into two cascaded subsystems: a first-order subsystem and a second-order subsystem. For the first subsystem, we design a finite-time controller based on the finite-time Lyapunov stability theory. Then, according to the backstepping idea and the adding a power integrator technique, a second finite-time controller is constructed recursively for the second subsystem. No exogenous forces are required in the controllers design but only the direct-axis (d-axis) and the quadrature-axis (q-axis) stator voltages are used as manipulated variables. Comparative simulations are provided to show the effectiveness and superior performance of the proposed method.

Optimal robust control of drug delivery in cancer chemotherapy: a comparison between three control approaches.

During the drug delivery process in chemotherapy, both of the cancer cells and normal healthy cells may be killed. In this paper, three mathematical cell-kill models including log-kill hypothesis, Norton-Simon hypothesis and Emax hypothesis are considered. Three control approaches including optimal linear regulation, nonlinear optimal control based on variation of extremals and H∞-robust control based on µ-synthesis are developed. An appropriate cost function is defined such that the amount of required drug is minimized while the tumor volume is reduced. For the first time, performance of the system is investigated and compared for three control strategies; applied on three nonlinear models of the process. In additions, their efficiency is compared in the presence of model parametric uncertainties. It is observed that in the presence of model uncertainties, controller designed based on variation of extremals is more efficient than the linear regulation controller. However, H∞-robust control is more efficient in improving robust performance of the uncertain models with faster tumor reduction and minimum drug usage.