Stability Of Closed-loop System Research Articles

Dynamic consensus and adaptive bias compensation for multi-agent linear systems over directed networks

Biased measurements in an inter-networked systems can have severe repercussions in closed-loop stability of the individual systems and decelerate dynamical consensus among the interacting agents. Bias in the measurement, even constant, cannot be dealt with ad hoc techniques of robust control, in the presence of additive perturbations, because the control gain amplifies the disturbance. One way to account for the effect of measurement bias is then to rely on adaptive control. This has been done in the literature in the context of individual systems, but to the best of our knowledge not for multi-agent systems, while ensuring consensus control. In this paper we provide a model-reference-adaptive-control scheme to ensure dynamic consensus of generic (stabilizable) linear systems interconnected over directed graphs and under the influence of constant bias measurements. Our controller ensures global asymptotic stability of the synchronization manifold and convergence of the bias estimates.

An Output Feedback Stabilizer for Uncertain MIMO Nonlinear Systems: Nonlinear Nominal Input Gain Function

This article presents a robust output feedback stabilizer for multi-input–multi-output nonlinear systems subject to external disturbances and system uncertainties. We assume that the system has a well-defined vector relative degree and the zero dynamics is input-to-state stable. Based on the assumption that there exists a state feedback controller that makes the origin of the nominal closed-loop system asymptotically stable, we present an output feedback stabilizer that recovers the stability of the nominal closed-loop system in the practical sense. We allow that the nominal system can have a nonlinear input gain matrix that is a function of system state, and this is done by modifying the structure of the disturbance observer-based robust outputfeedback controller. Simulation results on a practical system are included to validate the proposed controller.

Finite-time trajectory tracking control of quadrotor UAV via adaptive RBF neural network with lumped uncertainties

The trajectory tracking control of the quadrotor with model uncertainty and time-varying interference is studied. The RBF neural network is combined with the global fast terminal sliding mode (GFTSM) control method to converge tracking errors in finite time. To ensure the stability of the system, an adaptive law is designed to adjust the weight of the neural network by the Lyapunov method. The overall novelty of this paper is threefold, 1) Owing to the use of a global fast sliding mode surface, the proposed controller has no problem with slow convergence near the equilibrium point inherently existing in the terminal sliding mode control. 2) Benefiting from the novel equivalent control computation mechanism, the external disturbances and the upper bound of the disturbance are estimated by the proposed controller, and the unexpected chattering phenomenon is significantly attenuated. 3) The stability and finite-time convergence of the overall closed-loop system are strictly proven. The simulation results indicated that the proposed method achieves faster response speed and smoother control effect than traditional GFTSM.

Finite-Time Rapid Global Sliding-Mode Control for Quadrotor Trajectory Tracking

To enhance the position and attitude-control of quadrotor for trajectory tracking, we propose a fast decay function utilizing exponential property to improve the performance of global sliding-mode control, allowing the initial value to quickly reach equilibrium. The main research is focused on deriving the finite settling time using the proposed decay function and presenting a detailed calculation process, instead of making a simple modification to a monotonic exponential-decay function. Moreover, we adopt an adaptive control law to ensure the robustness of the quadrotor, even without knowing the upper bound for disturbances. In addition, we perform time-varying mass simulations because the quadrotor’s load mass may change during maneuvering. Furthermore, using the Lyapunov function, the stability of the entire closed-loop system is ensured by the step-by-step stabilization of each subsystem. The simulation results show that the rapid global sliding-mode control (RGSMC) we designed is more effective than the conventional global sliding-mode control and adaptive sliding mode control with respect to stabilization and tracking against external disturbances. Hence, the fast decay property of the proposed global function is verified.

Initial-Rectification Neuro-Adaptive Iterative Learning Control for Robot Manipulators With Input Deadzone and Nonzero Initial Errors

An initial-rectification adaptive iterative learning control scheme is proposed to solve the angle tracking problem of robot manipulators with input deadzone under nonzero initial errors. Lyapunov approach is utilized to design the controller. First, the initial-rectification auxiliary reference signal is constructed to overcome the obstacle caused by nonzero initial errors during ILC design. Second, adaptive ILC strategy and robust control strategy are adopted for dealing with deadzone nonlinearity. In addition, adaptive learning neural network is applied to approximate for uncertainties. The stability of closed-loop robotic system is rigorously proven by theoretical analysis. In the end, numerical simulation results are provided to verify the effectiveness of the proposed adaptive iterative learning control scheme.

Neural Network-Based Adaptive Asymptotic Prescribed Performance Tracking Control of Hydraulic Manipulators

Hydraulic manipulators are extremely complicated systems due to the highly nonlinear characteristics, strong coupling among multiple joints, and heavy modeling uncertainties, which greatly complicate the high-performance tracking controller development compared with conventional manipulators driven by electrical motors. To overcome the above obstacles, this article proposes a novel radial basis function neural network (RBFNN)-based adaptive asymptotic prescribed performance controller for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> -degrees of freedom (DOF) hydraulic manipulators. First, the entire manipulator system model containing actuator dynamics is derived. Then, the adaptive asymptotic prescribed performance controller is synthesized based on the backstepping framework, in which the RBFNN is employed to estimate the unknown joint coupling dynamics, while the RBFNN reconstruction error and uncertainties of the actuator dynamics are handled by the robust integral of the sign of the error (RISE) feedbacks. Meanwhile, a prescribed performance function (PPF), which characterizes both the certain transient and steady-state performance, is innovatively incorporated into the control design to restrict the joint tracking errors. The theoretical analysis proves that the proposed control strategy can achieve a prescribed tracking performance and the asymptotic stability of the whole closed-loop system can also be ensured. Finally, comparative simulations are conducted to verify the validity of the proposed controller.

Fault-Tolerant Tracking Control Optimization of Constrained LPV Systems Based on Embedded Preview Regulation and Reference Governance

This article presents some new improvements to the relevant constrained predictive fault-tolerant tracking control (FTTC) methods through embedding optimal preview regulation and reference governance. The main novelty of such a strategy is that some valuable information of finite future references can be adequately scheduled to optimize the robust tracking performance and significantly enlarge the fault-tolerant admissible region. In order to better describe the wide applicability of the proposed strategy, the robust FTTC problem for a class of LPV systems with state/input constraints is considered. Overall, the involved key designs consist of three parts. First, an unconstrained FTTC component is constructed by combining tracking error feedback, reference input regulation, and fault signal compensation. It is used to guarantee the robust tracking stability of closed-loop systems when the constraints are not activated. Second, a tube-based predictive FTTC policy with an embedded optimal preview regulator is designed to achieve the robust constraint satisfaction and transient response improvement. Third, an embedded reference governor is additionally integrated to significantly enlarge the size of the fault-tolerant admissible region. This design further reinforces the feasibility of constrained FTTC optimization. The effectiveness of these results is finally validated by a case study of a single transistor dc/dc Forward converter.

Master-Slave Synchronous Control of Dual-Drive Gantry Stage With Cogging Force Compensation

Dual-drive gantry stage has been widely applied to various industrial manufacturing fields with its unique structural advantages, and the synchronous control accuracy of the platform is crucial to the performance of the whole motion system. Therefore, an adaptive robust synchronous control scheme based on an improved master-slave structure is proposed, which is not only simple in structure but also easy to implement in engineering. The error dynamics model established in this article makes up for the lag of response of traditional master-slave control and improves the stability of closed-loop system. Online parameter adaptive algorithms deal with parameter uncertainties in the system, while robust control deals with unmodeled dynamics and external disturbances. In addition, nonlinear cogging force compensation is applied to the gantry biaxial system to further improve the control accuracy of tracking and synchronization. Finally, a dual-drive gantry stage system with good tracking and synchronization performance is obtained. The effectiveness and superiority of the proposed control strategy are verified by the comparison of several groups of experiments.

Predefined-Time Leader-Following Formation Control of Nonlinear Multiagent Systems under Switching Topologies

The paper proposes a predefined-time leader-following formation control scheme for nonlinear multi-agent systems with external perturbations under switching topologies. Unlike previous work on predefined-time containment control, we aim to create an isosceles triangle shaped formation instead of being covered by a generic convex hull by having followers follow the leader's trajectories. To ensure convergence along the sliding surface within a predefined-time, we present a nonlinear sliding surface. A terminal sliding mode controller is then used to obtain the desired formation within a predefined-time. The convergence time is independent of both initial values and control parameters. Using, common Lyapunov function, predefined-time stability of closed-loop system is investigated. Simulation examples demonstrate that the developed control protocol is feasible and robust.

Partial State Feedback Adaptive Disturbance Rejection Control

A unified disturbance rejection problem based on model reference adaptive control (MRAC) technique is addressed. When the full-state vector is not operational in feedback, we use partial-state signal y(t) to design a disturbance rejection controller. The parametrization and disturbance compensation techniques are necessary for designing adaptive control strategy to deal with systems uncertainties and unknown disturbances. This scheme guarantees the desired system performances, including closed-loop system stability as well as asymptotic output tracking. The proof progress of system stability is elaborated.

Resilient Load Frequency Control of Multi-Area Power Systems Under DoS Attacks

Cyber security of modern power systems has become increasingly significant due to their open communication architecture and expanding network connectivity exposed to malicious cyber attacks. Resilient control represents an effective means to preserve the survivability of the power system under cyber attacks. In this paper, we address the resilient load frequency control (LFC) design for multi-area power systems under a new class of time-constrained denial-of-service (DoS) attacks. First, different from the widely-explored duration- and frequency-constrained DoS attack models, we consider a general time-constrained DoS attack model where only the attack durations are confined into some bounds, which represents less a priori knowledge of an attacker’s actions. Second, instead of using a traditional yet conservative time-invariant Lyapunov function (TILF), we develop an attack-parameter-dependent time-varying Lyapunov function (TVLF) approach to enable a resilient LFC design without jeopardizing the desired closed-loop system stability and performance. Furthermore, we provide a formal stability and performance analysis condition as well as a design criterion for the desired DoS-resilient output feedback LFC controller. We also show that the minimum allowable sleeping period and the maximum allowable active period of the attacked LFC system can be explicitly disclosed. Finally, we present two simulation case studies on a two-area LFC system and a three-area LFC system to demonstrate the effectiveness of the obtained results.

A FPGA Based PI Adaptive Sliding Mode Controller for PEM Fuel Cell with Boost Converter

Proton exchange membrane (PEM) is one of the most popular fuel cells for renewable energy production, and this paper presents a DC/DC boost converter structure to improve energy efficiency. To achieve high output power as well as constant output voltage, a combined method consisting of proportional-integral controller and adaptive sliding mode technique is designed. Also, due to the use of adaptive technique, the proposed technique has the ability to cover the effects of uncertainty with an unknown high limit and in addition to improving the quality of output power and voltage of PEM, it eliminates permanent tracking error and guarantees closed loop system stability. To show the operational implementation capability and flexibility of the method, FPGA has been used, which in addition to showing real-time performance, provides the ability to execute the controller at high speeds. Operationality and the possibility of practical implementation of the planned scheme on the existing systems provide the possibility of increasing the efficiency of energy extraction without further investment. The stability of the closed-loop system is achieved using Lyapunov technique and the results of simulation and comparison indicate the optimal performance of the system under the planned scheme and high efficiency in comparison with existing approaches.

Development of a Sliding-Mode-Control-Based Path-Tracking Algorithm with Model-Free Adaptive Feedback Action for Autonomous Vehicles.

This paper presents a sliding mode control (SMC)-based path-tracking algorithm for autonomous vehicles by considering model-free adaptive feedback actions. In autonomous vehicles, safe path tracking requires adaptive and robust control algorithms because driving environment and vehicle conditions vary in real time. In this study, the SMC was adopted as a robust control method to adjust the switching gain, taking into account the sliding surface and unknown uncertainty to make the control error zero. The sliding surface can be designed mathematically, but it is difficult to express the unknown uncertainty mathematically. Information of priori bounded uncertainties is needed to obtain closed-loop stability of the control system, and the unknown uncertainty can vary with changes in internal and external factors. In the literature, ongoing efforts have been made to overcome the limitation of losing control stability due to unknown uncertainty. This study proposes an integrated method of adaptive feedback control (AFC) and SMC that can adjust a bounded uncertainty. Some illustrative and representative examples, such as autonomous driving scenarios, are also provided to show the main properties of the designed integrated controller. The examples show superior control performance, and it is expected that the integrated controller could be widely used for the path-tracking algorithms of autonomous vehicles.

Hybrid Adaptive Controller Design with Hysteresis Compensator for a Piezo-Actuated Stage

Piezo-actuated stage (P-AS) has become the topic of considerable interest in the realm of micro/nanopositioning technology in the recent years owing to its advantages, such as high positioning accuracy, high response speed, and large output force. However, rate-dependent (RD) hysteresis, which is an inherent nonlinear property of piezoelectric materials, considerably restricts the application of P-AS. In this research paper, we develop a Hammerstein model to depict the RD hysteresis of P-AS. An improved differential evolution algorithm and a least-squares algorithm are used to identify the static hysteresis sub-model and the dynamic linear sub-model for the Hammerstein model, respectively. Then, a hysteresis compensator based on the inverse Bouc–Wen model is designed to compensate for the static hysteresis of the P-AS. However, the inevitable modeling error presents a hurdle to the hysteresis compensation. In addition, external factors, such as environmental noise and measurement errors, affect the control accuracy. To overcome these complications, a hybrid adaptive control approach based on the hysteresis compensator is adopted to increase the control accuracy. The closed-loop system stability is analyzed with the help of the Lyapunov stability theory. Finally, experimental results indicate that the raised control approach is effective for the accurate positioning of P-AS.

A novel approach for robust model predictive control applied to switched linear systems through state and output feedback

This paper proposes a robust switched model-based predictive controller design for discrete linear systems with state constraints, inputs, and disturbances limited in norm. Modeled via linear matrix inequalities, the online and offline designs of the proposed control aim at minimizing the upper bound of the quadratic performance index for a horizon of infinite prediction associated with the state estimator and the switching rule, seeking to guarantee the robust stability for closed-loop systems. To this end, three theorems are formulated. To demonstrate the effectiveness of the control strategy, a comparative analysis is performed between the performance of the proposed model and a benchmark method. From the results, it is possible to conclude that the proposed method is promising in the scope of control of linear systems subject to switching, being more efficient than the benchmark for the stabilization and control of both numerical examples.

Safe navigation of a quadrotor UAV with uncertain dynamics and guaranteed collision avoidance using barrier Lyapunov function

In this paper, the safe autonomous motion control of a quadrotor Unmanned Aerial Vehicle (UAV) is considered, in the presence of disturbance, stationary and moving obstacles. In this regard, we directly combine an analytical control design approach, within the backstepping framework, with obstacle avoidance to solve the navigation problem. A Barrier Lyapunov Function (BLF) is incorporated into the translational control to keep the vehicle out of a safety sphere, constructed around the obstacles, while steering it toward a desired position. BLF allows the direct inclusion of the obstacle position in the control design. This is achieved for both cases of known and unknown obstacle velocities. Furthermore, the issue of arbitrary initial conditions is analytically addressed, with a preassigned exit time from the safety sphere. We also consider the case of chance-constrained collision avoidance. The proposed approach leads to a computationally efficient design, since a closed-form of the control is obtained with no need for real-time optimization. More importantly, the analytical stability of closed-loop system is guaranteed. A hierarchical control structure is designed with an adaptive model-free control for unknown attitude dynamics in the presence of disturbances. A number of numerical simulations are performed to evaluate the effectiveness of the proposed approach.

Distributed Multirate Control of Battery Energy Storage Systems for Power Allocation

With the increasing integration of intermittent energy sources into the smart grid, distributed battery energy storage systems (DBESSs) are employed to balance power generation and demand. Power allocation among DBESSs plays an important role in maintaining the stability of energy systems. So far, the control of DBESSs has focused on either continuous-time control for continuous-time battery dynamics or discrete-time control for discretized battery dynamics. However, in realistic industrial applications, DBESSs have continuous-time dynamics in nature, and their control is implemented on digital controllers. To tackle this issue, a distributed multirate control system is designed in this article for continuous-time DBESSs. It allocates power by keeping the same relative State-of-Charge (SoC) variation rate for all DBESSs. For the accurate computation of the output/input power without global information, the control strategy consists of distributed multirate estimators each for a DBESS. The operating rate of the estimation algorithm is designed multiple times higher than the sampling rate of the measurement of battery and the sampling rate of the battery controller. With the proposed multirate estimator, a smaller estimation error is achieved. The same relative SoC variation rate and the stability of closed-loop system can be guaranteed. Simulation studies are given to demonstrate the effectiveness of the proposed control strategy.

Coordinated Control of Networked Nonlinear Multiagent Systems Using Variable Horizon Learning Predictors via Cloud Edge Computing

Networked multiagent systems use network technology to realize the interconnection, intercommunication, and mutual control of things. The coordinated control problem of networked nonlinear multiagent systems via cloud edge computing is investigated in this article. A mist–fog–cloud predictive control scheme is proposed for the coordinated control of complex large-scale networked multiagent systems by making use of the advantages of cloud edge computing. This scheme actively compensates for communication delays and achieves desired coordination performance of individual agents. Variable horizon learning predictors are presented to predict the outputs of the unknown nonlinear dynamical agents within different horizons. The design of coordinated control optimizes a performance index function presented to measure the coordination between agents. The analysis on a networked nonlinear multiagent system using the mist–fog–cloud predictive control scheme results in the conditions of simultaneous consensus and stability of the entire closed-loop system. An example demonstrates the effectiveness of the proposed scheme.

Observer-Based, Robust Position Tracking in Two-Mass Drive System

Precise motion control remains one of the most important problems in modern technology. It is especially difficult in the case of two-mass systems with flexible coupling if only the motor position and velocity are measured. We propose a new methodology of control system design in this situation. The concept is founded on a robust observer design, based on a linear matrix inequality (LMI) solution. The observer cooperates with the original nonlinear controller. The presented approach allows us to solve the position tracking problem for a two-mass drive, with unknown parameters, in the presence of disturbances (for instance, nonlinear friction-like torques) acting on both ends of the flexible shaft. Under this set of assumptions, the problem was never solved previously. The closed-loop system stability is investigated, and the uniform ultimate boundedness of state estimation errors and tracking errors is proven using Lyapunov techniques. Numerical properties of the design procedure and characteristic features of the observer, controller, and closed-loop system are demonstrated by several examples.

Fault-Tolerant Control for Quadrotor Based on Fixed-Time ESO

Focusing on the actuator fault of the quadrotor unmanned aerial vehicle (QUAV), an active fault-tolerant control scheme based on fixed-time linear active disturbance rejection control is proposed. Firstly, in order to simplify the complex dynamic model, the virtual control quantity is introduced to decouple the flight control system of the QUAV. Secondly, the fixed-time extended state observer (ESO) is utilized to estimate and compensate the internal uncertainty, external disturbance and actuator fault of the QUAV in fixed time. Thirdly, a continuous output feedback controller based on fixed-time ESO is designed to keep the stability of the flight control system with actuator fault and external disturbance. Finally, the closed-loop stability of the flight control system is demonstrated by Lyapunov function. The numerical simulation is carried and the results also verify the effectiveness of the proposed control scheme.