Gain Control Design Research Articles

Leader-Following Consensus of Linear Multiagent Systems With Aperiodically Sampled Outputs: A Distributed Impulsive-Observer-Based Approach.

This article studies the leader-following consensus problem for a class of linear multiagent systems over a directed graph with aperiodically sampled outputs. First, a novel distributed impulsive-observer-based consensus protocol is designed. This protocol requires only the output measurements at sporadic time instants for the observer and control gain design. Second, by using time-varying Lyapunov function techniques, sufficient conditions for exponential stability of a class of linear impulsive systems are established; subsequently, these stability results are applied for the distributed impulsive observer design. Different from the existing related works, the impulsive observer gain designed in this work is decoupled from the graph properties. As a result, once the impulsive observer gain is designed for one network topology, it can be directly used for other network topologies, as long as the graph properties and the dynamics of local agents satisfy certain conditions. Furthermore, the resilience of the designed protocol is tested under denial of service (DoS) attacks. It is shown that the protocol is robust with respect to low-frequency DoS attacks occurring in the observer communication network. Finally, two examples illustrating the validity and effectiveness of the proposed protocol are included.

Synchronization of complex dynamical networks with saturated delayed impulsive control.

This paper considers the local exponential synchronization problem for a type of complex dynamical networks (CDNs) with both system delay and coupled delay using saturated delayed impulsive control. Based on the methods of average impulsive interval (AII), average impulsive delay (AID) and average impulsive estimation (AIE), a Razumikhin-type inequality with hybrid delayed impulses (which include delayed impulses and delay-free impulses) is derived. This inequality includes pure delayed impulsive inequalities. By utilizing the constructed inequality and the Lyapunov stability theory, the saturation nonlinearities are treated as the convex hulls, and sufficient synchronization criteria for local exponential synchronization of CDNs are presented in the framework of linear matrix inequalities (LMIs). Moreover, to enlarge the estimation of region of attraction (ROA) and the design of impulsive control gain, a convex optimization problem based on LMIs is formulated. Finally, a numerical example demonstrates the effectiveness of the obtained results.

[formula omitted] predictive control for 2-D Roesser model under multiple denial-of-service attacks

In this paper, we concentrate on H∞ predictive control issue for Roesser-type two-dimensional (2-D) system under multiple denial of service attacks (DoSs). The research will be realized through the following considerations. Firstly, a general multi-DOSs description is formulated under Roesser-type 2-D framework. Then the event-based 2-D triggered strategy is constructed to compensate the occurred multiple DoSs network attacks, which helps to save network resources and improve the network utilization. On this basis, some innovative multi-steps 2-D predictive controller is designed, and then, Roesser-type 2-D predictive control system can be obtained accordingly. For the predictive control system, we propose the detailed analysis scheme for considering H∞ predictive control issue. Furthermore, we derive the 2-D controller gain design algorithm, and the H∞ robustness analysis criterion in solvable matrix constraints. To conclude the paper, a chemical process example is given to illustrate the effectiveness and practicability of the provided method and controller design.

Event-triggered and quantised feedback stabilisation of switched networked control systems

In order to conserve network resources, this paper investigates the event-triggered control and quantised feedback stabilisation of switched networked control systems by introducing the vector quantizer technique. The state information undergoes quantisation and is transmitted to the controller after being sampled by the event-triggering technology. The designed event-triggered mechanism relies on quantised state values, and the generation of each quantised value also depends on the event-triggered condition. Addressing the asynchronous issue between the controller and the subsystem, we provide a sufficient condition for ensuring exponential stability of the closed-loop system and outline the controller gain design method by employing the multiple Lyapunov function and average dwell time methods. Besides, we demonstrate the explicit exclusion of the Zeno phenomenon in the event-triggered mechanism. Finally, the viability of our approach is demonstrated through simulation examples.

Distributed control of virtual energy storage systems for voltage regulation in low voltage distribution networks subjects to varying time delays

Distributed communication-based strategies are popular for regulating nodal voltages in distribution networks with high penetration of Photovoltaic (PV) sources. Time delays inevitably pose challenges to efficient voltage regulation and power sharing. In response, this paper presents a distributed, event-triggered voltage regulation approach that enables power sharing across virtual energy storage systems (VESS) with different parameters while accommodating diverse time delays. The process begins by determining the delay margin for the primary Volt/Watt controller in a low-voltage distribution network (LVDN), laying the foundation for stable feedback control gain design. To accommodate any arbitrary large and time-varying delays, a distributed resilient event-triggered secondary controller for VESS is designed to share voltage regulation tasks according to their capacities and state of energy (SoE) values. A mathematical analysis, grounded in the Lyapunov–Krasovskii approach, evaluates the stability and convergence of the proposed controller amidst time delays thoroughly. To validate the proposed method, simulation studies are conducted, which demonstrate the effectiveness in mitigating voltage limit violations, even with variable communication delays, and highlight balanced power sharing and SoE among VESS.

Voltage Angle Control for a BLDC Motor and Controller Gain Design

Voltage Angle Control for a BLDC Motor and Controller Gain Design

MIMO Radar Mainlobe Gain Control Design for Co-Existence With Wireless Communication Systems

MIMO Radar Mainlobe Gain Control Design for Co-Existence With Wireless Communication Systems

Model Predictive Control for a Voltage Sensorless Grid-Connected Inverter With LCL Filter Using Lumped Disturbance Observer

This paper introduces a disturbance observer-based model predictive control for a voltage sensorless grid-connected inverter (GCI), which minimizes the number of sensor measurements and eliminates the steady-state error by estimating the lumped disturbance in the presence of grid impedance variations. A full-state estimation and lumped disturbance observer are obtained based on the Luenberger observer and gradient steepest descent method, respectively. A cost function, which consists of state error, is used for controller gain design. An optimal full-state observer and controller gains are obtained by solving an optimization problem based on linear matrix inequality. The discrete-time frequency responses analysis of open-loop and closed-loop systems is presented to demonstrate the filter resonance suppression. The robustness of the proposed control against grid impedance variation is analyzed through the pole-zero map approach. Simulations and experiments are conducted for a GCI under the grid impedance variation to demonstrate the theoretical analysis and the efficacy of the proposed control schemes.

Data‐driven control for networked systems with multiple packet dropouts

AbstractThis paper investigates data‐driven control for a class of networked control systems with multiple packet dropouts and unknown system parameters. Here, multiple packet dropouts occur randomly in the controller‐to‐actuator (C/A) and sensor‐to‐controller (S/C) channels, where successive packet dropouts are limited by known upper bounds. By introducing the summation inequality, a model‐based mean‐square asymptotic stability condition is established for the closed‐loop networked control system with the potential to migrate to a data‐driven solution. Then, the data‐driven mean‐square asymptotic stability condition for the closed‐loop system is presented by merging the model‐based stability condition with noisy data‐parameterized representations. On this basis, the data‐driven controller gain design approaches for combining unknown and known input gain matrices are presented in turn. Finally, two simulation examples are provided to show the applicability of the developed approaches.

L₁-Gain Controller Design for 2-D Markov Jump Positive Systems With Directional Delays

This article is concerned with the stochastic stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain control of two-dimensional (2-D) positive Markov jump systems (PMJSs) with directional delays based on the Roesser model. First, necessary and sufficient conditions (NSCs) for the stochastic stability of the addressed system are established by constructing a deterministic “equivalent” system and applying a stochastic copositive Lyapunov function. This reveals that the stochastic stability of 2-D PMJSs with delays is affected by the size of directional delays, the transition matrix, and system matrices. Second, the exact <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain index is calculated and NSCs in the form of linear programming (LP) are established for the addressed system. Systematic methods for the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain controller design are proposed so that the closed-loop system (CLS) is positive and stochastically stable and has an optimal <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -gain performance, which is achieved using an iterative algorithm and an analytical calculation method for a single-input case. Finally, the potency and accuracy of the theoretical results are verified using two examples.

Stability of stochastic delayed multi-links complex network with semi-Markov switched topology: A time-varying hybrid aperiodically intermittent control strategy

This paper is concerned with the stability analysis of stochastic delayed multi-links complex networks with semi-Markov switched topology (SDMNST). It ought to be highlighted that a time-varying hybrid aperiodically intermittent control (THAIC) strategy, that the control gain is a sign-indefinite function and can be unbounded, is proposed. In the light of a major consideration for both stabilizing control and destabilizing input, the THAIC is capable of being manipulated to a wider range of intermittent control signals. Meanwhile, our proposed control strategy can not only deal with the problem that the intermittent control signals subject to external interferences, but also effectively avoid the possible damage of actuators caused by the sudden and rapid switching of control gain from a negative constant value to zero. The concept “average intermittent control gain” is introduced to quantify the gain of THAIC. As a generalization of the existing Halanay-type inequalities, several novel differential inequalities with time-varying and unbounded coefficients are established, based on which and Lyapunov method as well as graph theory, less conservative stability criteria of SDMNST are rigorously demonstrated. Subsequently, the theoretical results are applied to spring-mass-damper systems and numerical simulations are exploited with the design of control gain being shown.

Stabilizing Angle Rigid Formations With Prescribed Orientation and Scale

Angle rigid formations have the advantage of requiring only local bearing/direction measurements in their implementation. However, the capability of controlling the orientation and scale of these formations has not been explored. This undetermined orientation and scale can degrade the robustness of the formation against measurement noise. To maintain both advantages of requiring less sensor measurements and sustaining robustness against measurement noise, this article aims to achieve a desired angle rigid formation while simultaneously controlling its orientation and scale. In this article, we first design a formation algorithm for the first three agents to achieve a desired triangular formation with prescribed orientation and scale. Using the control gain design technique, we then design formation control algorithms for the remaining agents such that the overall desired formation can be achieved under a vertex addition operation. We present the role of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">generic</i> property from angle rigidity for the formation’s stability analysis. We also highlight that with one additional relative position measurement or two additional communication channels, the local convergence to the corresponding desired formation can be improved to a global convergence. Experiments are conducted to validate the theoretical results and the advantages are highlighted in comparison with other two formation control laws.

On l 1-gain control for 2D delayed positive systems in FM LSS models: necessary and sufficient conditions

This paper presents an -gain control design for two-dimensional (2D) delayed positive systems (PSs) in the Fornasini-Marchesini local state-space model. First, for a stable 2D delayed PS, the necessary and sufficient conditions are derived for the calculation of the exact value of the -gain. Then, the controller design is given with the aid of the singular value decomposition method, which ensures that the closed-loop system is asymptotically stable at the specified -gain level. In the end, two examples are provided to identify the validity and correctness of the results of the theory.

Robust H2-Optimal TS Fuzzy Controller Design for a Wind Energy Conversion System

In this paper, robust optimal control of an uncertain wind energy conversion system (WECS), described by a Takagi–Sugeno fuzzy model, is proposed to guarantee the maximum power trajectory tracking (MPTT). The design of the fuzzy optimal control is based on a quadratic criterion related to the maximum power tracking error. The proposed fuzzy controller allows to regulate the rectified direct current (DC) voltage of the variable-speed wind turbine by adjusting the duty cycle of a boost converter. Linear matrix inequality (LMI) conditions, ensuring the optimal H2 tracking error, are proposed for the controller gain design. Simulation as well as experimental tests are performed for efficiency evaluation of the established MPPT fuzzy control scheme under variable wind speed conditions.

Elastic Vibration Suppression Control for Multilinked Aerial Robot Using Redundant Degrees-of-Freedom of Thrust Force

Articulated aerial robots, which comprise multiple link units connected by joints, can change their shapes during flight to perform advanced aerial manipulation. The more links indicate a higher ability to handle larger objects. The critical challenge with the increase in the number of link units is the elastic vibration of the chain-like structure, which significantly hampers stable flight. Thus, the number of links is limited to four in most of our previous multilinked model. However, the redundancy in the control input (thrust force) for a model with more than four propellers (four links) can help to address the elastic vibration. Therefore, in this study, we first present the elastic vibration model due to the torsional motion of the link rod in chain-like structure, based on multi-rigid body dynamics. Subsequently, we develop a control method with an optimization-based control gain design to suppress this elastic vibration via the redundancy of a control input. Finally, we demonstrate the feasibility of the proposed methods in vibration suppression by experiments with an eight-link multilinked model that is difficult to fly with conventional control methods.

Anti-Controlling Codimension-2 Bifurcation of Discrete Dynamical Systems in 1 ∶ 2 Resonance

A set of nonlinear feedback control strategies were designed to realize the bifurcation solutions of codimensional bifurcations in discrete dynamical systems with 1∶2 resonance from the perspective of bifurcation anti-controlling. Firstly, aimed at the limitation of traditional bifurcation criteria for determination of high codimensional bifurcation points, a new explicit criterion for codimension-2 bifurcation in 1∶2 resonance was proposed. Based on this explicit criterion, the linear control gain was designed to ensure the existence of such codimension-2 bifurcation. Then, the central manifold of 1∶2 resonance was derived. Based on the normal form method, the types and stability of codimension-2 bifurcation solutions in 1∶2 resonance were analyzed through design of nonlinear control gain. Finally, an Arneodo-Coullet-Tresser mapping was taken as an example, and various bifurcation solutions with 1∶2 resonance bifurcation properties were realized by control at the specified parameter points, to further validate the theoretical analysis.

Discrete-time backstepping-state feedback approach for current control of LCL grid-tied converters

Voltage source converters connected to the grid through an LCL filter effectively attenuate the high frequency harmonics generated by the PWM modulation. However, due to the intrinsic resonant peak of this filter and due to the discretization process, the controller design is commonly a challenge and it may not guarantee robustness against abnormalities of the grid. In order to overcome these problems, this paper proposes a new discrete-time current control scheme applied to grid-tied converters based on a backstepping algorithm and state feedback controller in a multi-loop approach. The tracking of converter-side current for a given reference, which is generated by the outer loop, is performed by the backstepping algorithm. In addition, the controller gain design methodology is presented taking into account an extended model, that includes the delay resulted from the discrete-time implementation. An analysis of the gain choice effect on the system closed-loop eigenvalues is demonstrated, which allows the designer to select an appropriate set of controller gains. As outer loop, a state feedback method combined with a state-space resonant controller is used for the grid-side current tracking. In this structure, the harmonic compensation is easily preformed, in addition, the feedback gains are chosen using an optimum algorithm. The robustness of the multi-loop backstepping based control structure is improved in comparison with a full state feedback controller. Simulation and experimental results are obtained to demonstrate the effectiveness of the proposed control scheme under different test conditions, as reference changes, operating during electric faults and grid impedance variation.

Event-Triggered Output Feedback Control of Switched Nonlinear Systems With Input Saturation.

This article is concerned with the event-triggered output feedback control problem for a class of switched nonlinear strict-feedback systems subject to asymmetric input saturation. The nonlinear terms are assumed to be bounded by a continuous function of the output multiplied by unmeasured states. The hyperbolic tangent function is employed to process the error caused by the event-triggered scheme, and an indicator function of the saturation degree is used to analyze the influence generated by the asymmetric input saturation. By adopting the common Lyapunov function method and the dynamic gain control design approach, a new design procedure based on a reduced-order observer is proposed to construct an output feedback controller. It is proved by the Lyapunov analysis that the proposed event-triggered control scheme can ensure that all the signals of the closed-loop system are globally bounded. Furthermore, the output can be converged to a bounded region around the origin, and this region can be tuned to be small by adjusting the design parameters. Different from typical existing results on the switched nonlinear strict-feedback systems, the celebrated backstepping method is not employed in this article. The continuous stirred tank reactor is finally used to demonstrate the effectiveness of the proposed control scheme.

Output event triggered consensus control of nonlinear multi-agent systems with relative state constraints

The relative state constraints is inevitable in multi-agent systems(MASs) because of limited sensing capabilities of the sensors. In this paper, the consensus problem of nonlinear MASs with relative state constraints is investigated in an edge perspective. First, the consensus problem is proved to be equivalent to a stabilization problem characterized by the edge dynamics. Then the edge system is confined to a hypercube for the satisfaction of relative constraints. Finally, an output event-triggered control protocol that can exponentially stabilize the edge dynamics with constraints is proposed. Sufficient conditions on system stability are provided, the Singular triggering and the Zeno-behaviour are also excluded. A simple learning-based iterative algorithm is proposed to calculate the diagonally dominant matrix, which is crucial to the controller gain design. The effectiveness of the results is illustrated through numerical examples.

Second-order consensus in multi-agent systems with nonlinear dynamics and intermittent control

In this paper, the second-order leader-following consensus of coupled nonlinear agents with intermittent control is investigated. A subset of followers is pinned while it is assumed that the underlying digraph contains a directed spanning tree with the leader node as the root. By using multiple Lyapunov functions method and algebraic graph theory, it is proved that second-order consensus is guaranteed by choosing the control and rest durations appropriately in each time interval. This result provides high flexibility in control gain design, allowing multiple switching with different gains in arbitrarily-chosen time intervals. As a result, it not only encompasses many existing intermittent control schemes but can also manage practical situations, such as recovery from occasional control failures. Numerical simulations are also given to demonstrate our theoretical results.