Dynamic Gain Technique Research Articles

Prescribed-time fully distributed Nash equilibrium seeking of nonlinear multi-agent systems over unbalanced digraphs

This paper investigates the prescribed-time fully distributed Nash equilibrium seeking (PT-FDNES) problem for nonlinear multi-agent systems (MASs) over weight-unbalanced directed graphs (digraphs). To counterbalance unweighted communication flows caused by the unbalanced network, the temporal transformation technique is first introduced to derive a consensus-based algorithm for calculating the left eigenvector of the Laplacian matrix, based on which a prescribed-time fully distributed estimator with adaptive gains is developed to obtain the NE without requiring any global information. By utilizing this NE estimator to formulate an intermediate control law, the NE seeking problem is then effectively transformed into a local reference-tracking problem. To deal with the non-differentiability issue caused by the NE estimator and ensure the exact tracking, the dynamic gain technique and novel scaling functions are employed to derive a prescribed-time tracking controller which completely compensates for the mismatched uncertainties while reducing the computational burden. The proposed control framework enables the actions of all agents to reach the NE within a prescribed time. In addition, the obtained results are further re-designed to exhibit the robustness by introducing an improved σ-modification scheme without sacrificing the convergence performance. Numerical examples are provided to demonstrate the validity of the theoretical results.

Decentralized adaptive fault‐tolerant control for interconnected nonlinear time‐delay systems with uniform prescribed performance

AbstractIn this article, the prescribed performance tracking control problem is studied for interconnected nonlinear time‐delay systems with sensor and actuator faults. Based on the dynamic gain technique and the backstepping control method, a delay‐independent adaptive state feedback controller is designed. Besides, by embedding a smooth function into the controller, the unknown external disturbances, sensor and actuator faults are successfully compensated. Furthermore, we can deal with the asymmetric prescribed performance control with semi‐global or global requirements uniformly by selecting the initial value of the the scaling function. Based on Lyapunov theory, it is proved that the system output of each subsystem can closely track the desired signal and the boundedness of all signals in the closed‐loop systems can be ensured under the proposed control method. Finally, the effectiveness of the proposed control strategy is proved by two simulation examples.

Global adaptive event-triggered output feedback control for p-normal feedforward nonlinear systems with uncertain output function

This paper concentrates on the global adaptive event-triggered output feedback controller design for a class of p-normal feedforward nonlinear systems with uncertain output function. Due to the existence of unknown growth rate and uncertain output function, the considered uncertain nonlinear systems contain more uncertainties. To overcome this difficulty, a dynamic gain technique is introduced and an elaborate adaptive law of the gain is designed. Then, a completely time-varying event-based strategy is presented, which can effectively eliminate the effects caused by event-triggered errors. Since the presented event-triggered controller is not differentiable, a new analysis manner is developed to prove that the system is Zeno-free. Meanwhile, the closed-loop system(CLS) states are asymptotically convergent with the proposed strategy. Finally, a simulation example is given to illustrate the effectiveness of the proposed control scheme.

Dynamic-based event-triggered neural network control for p-normal interconnected time-delay systems with asymmetric constraints

A decentralized dynamic event-triggered tracking control problem is investigated for a class of p-normal interconnected time-delay nonlinear systems with asymmetric constraints. First, a new event-triggered mechanism (ETM) is constructed by designing a dynamic variable law, which effectively reduces the number of controller updates. The introduced constants provide an obvious solution for the proof of Zeno phenomenon. Second, a barrier Lyapunov function (BLF) is constructed with the help of sign functions to achieve time-varying asymmetric constraints. Meanwhile, we improve the previous neural networks (NNs) approximation scheme and dynamic gain technique in order to handle unknown interconnection functions and time-delay signals, respectively. Then, it is rigorously proved that all signals in the system are bounded, and the error signals are constrained within the time-varying asymmetric bounds. Finally, the feasibility of the scheme is verified by simulation examples.

Event-Based Output Feedback Consensus Control for Multiagent Systems With Unknown Non-Identical Control Directions

This article studies the event-triggered output feedback consensus problem for a class of high-order uncertain nonlinear multiagent systems with totally unknown non-identical control directions. Firstly, the reduced-order filters are constructed by utilizing the dynamic gain technique to compensate the system uncertainties and unmeasurable states of the followers. Based on the filter states and output information, the asymptotic output consensus result is guaranteed with the developed distributed adaptive output feedback control protocol, while the inherent issue “complexity explosion” in backstepping design is avoided. Then, to solve the interaction of multiple Nussbaum functions in a single inequality, the Nussbaum functions with different frequencies are adopted, with which the unknown directions of multiagent system are no longer limited in identical. In addition, we propose a dynamic triggering strategy with time-varying threshold parameters to reduce the updates of controller without Zeno phenomenon. Finally, simulation results are provided to illustrate the effectiveness of theoretical algorithm.

A Blow-Up Function Approach to Global Event-Triggered Prescribed Tracking Output Feedback Control of Nonlinear Systems

In this paper, global event-triggered adaptive prescribed tracking output feedback control is investigated for a class of nonlinear uncertain systems with unknown control direction. Different from the existing works, the design of the tracking error-dependent normalized function and prescribed boundary is based on our uniformly defined blow-up function rather than a specific function, and the asymmetric constraint requirements on tracking error can be achieved by appropriately selecting the blow-up function. By utilizing the Kalman filter ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -filter) and dynamic gain technique, a new reduce-order observer is proposed, which can make the estimated error exponentially converge to zero. In addition, by introducing a dynamic signal into the trigger condition, a novel event-triggered mechanism is proposed, which can extend the trigger time interval and completely counteract the event-triggered errors in terms of asymptotic stability by sacrificing part of the system transient performance. Furthermore, an adaptive controller is designed based on the backstepping method, which ensures the boundedness of the state of the closed-loop system, while regulating the tracking error meets the global prescribed performance requirements and approaches to zero asymptotically. Two examples are given to illustrate the effectiveness of the proposed control scheme.

Adaptive output feedback controller design for high-order stochastic nonlinear systems with uncertain output function

This paper concentrates on the adaptive output feedback controller design for a class of high-order stochastic nonlinear systems(SNSs) with uncertain output function. Firstly for the nominal system, a homogeneous observer and output feedback controller is put forward through adding a power integrator method. Secondly, a dynamic gain technique is adopted into the observer and controller to guarantee the convergence of original system states and boundedness of the dynamic gain in probability. Besides, the proposed controller design scheme can be also broadened to upper-triangular SNSs. Finally, two numerical examples are provided to indicate the effectiveness of the proposed method.

Adaptive output-Feedback asymptotic tracking control for a class of nonlinear systems with actuator failure

This study deals with the output-feedback asymptotic tracking control problem for a class of nonlinear strict-feedback systems with actuator loss of effectiveness failure. To handle with the output-feedback control issue in the presences of nonlinearities, a new reduced-order observer design is presented, by utilizing the dynamic gain technique, which not only eliminates the limitation that the Lipchitz coefficients are required to be known in the existing output-feedback results, but makes full use of the measurable information. Furthermore, a new failure compensation mechanism is proposed to erase the effect of actuator failure, by introducing a cubic absolute-value Lyapunov function method and a novel (σ,σf)-modification technique. Compared with the existing output-feedback failure compensation results, our proposed method can not only relax the assumption requirement on nonlinear function, i.e., the nonlinear function with respect to output y can be extended to the nonlinear one with respect to state variable χ¯i in the means of asymptotic tracking, but also avoid the issue that the estimate for actuator efficiency indicator drifts to a large value suddenly. Further, within the framework of backstepping design, a new high-gain reduced-order observer based adaptive output-feedback failure compensation control is developed. Then, with the aid of Lyapunov analysis method, it is shown that all the signals in the closed-loop system are globally bounded, and the system output can asymptotically track a given reference signal. Finally, a simulation example is given to illustrate the efficiency of the proposed techniques.

Bipartite Containment Disturbance Rejection Using Disturbance Observers

This paper mainly addresses bipartite containment control of multi-agent systems (MASs) subject to exogenous disturbances. With dynamic gain technique independent of any global information, the disturbance observer method is applied to estimate disturbances generated by heterogeneous nonlinear exosystems. Two disturbance observer-based controllers are accordingly presented via state feedback approach and output feedback approach. By means of appropriate Lyapunov method, it is shown that the bipartite containment control is realized under sufficient criteria. Finally, simulations are employed to validate the effectiveness and correctness of our proposed controllers.

Adaptive output feedback control for a class of switched stochastic nonlinear systems under event‐triggered mechanism

AbstractThis article investigates the adaptive output feedback control problem for a class of switched stochastic nonlinear systems via an event‐triggered strategy. By virtue of the dynamic gain technique, a novel event‐triggered adaptive output feedback controller is designed. It is proved that all states of the closed‐loop system are globally asymptotically stable in probability. Two examples are presented to verify the effectiveness of the proposed scheme.

Adaptive Output Feedback Control of Steer-by-Wire Systems With Event-Triggered Communication

This article addresses the event-triggered output feedback control problem for steer-by-wire (SbW) systems with uncertain nonlinearity and time-varying disturbance. First, a new framework of event-triggered control systems is proposed to eliminate the jumping phenomenon of event-based control input, in which the tradeoff between saving communication resources and attenuating jumping phenomenon can be relaxed. Then, an adaptive fuzzy logic system (FLS) is developed to approximate the uncertain nonlinearity, and an adaptive FLS-based state observer is developed to estimate the augmented SbW system state, such that the unnecessary sensors can be removed. In light of the sliding mode control technique and FLS-based state observer, an adaptive event-triggered control is proposed for SbW systems, such that controller-area-network communication resources can be saved. Much significantly, the effect of observation error and event-triggered error can be counteracted by the dynamic gain technique. Furthermore, theoretical analysis based on Lyapunov stability theory is provided to verify both the observer error of state and the tracking error of the SbW system can converge to a neighborhood of the origin in finite time. Finally, simulations and experiments are given to evaluate the effectiveness and superiority of proposed methods.

Adaptive Event-Triggered Control for Switched p-Normal Nonlinear Systems via Output Feedback.

This article studies the issue of adaptive event-triggered output-feedback control for switched p -normal nonlinear systems with the unknown homogeneous growth rate. A homogeneous output-feedback controller is first designed for nominal nonlinear systems based on adding one power integrator technique. Then, a dynamic gain technique is introduced to deal with the difficulty caused by the unknown homogeneous growth rate. With an elaborate design of the adaptive law of the dynamic gain, a novel adaptive event-triggered output-feedback controller is developed to ensure that the closed-loop system is globally asymptotically stable. Meanwhile, a new analysis way is proposed to prove that the Zeno behavior is excluded in the event-triggered control system. Finally, two examples are provided to indicate the effectiveness of the proposed control method.

Dynamic Event-Triggered Tracking Control for a Class of p-Normal Nonlinear Systems

This paper investigates the problem of dynamic event-triggered output feedback tracking control for a class of p-normal nonlinear systems with unknown growth rate. To cope with the unknown growth rate imposed on the system nonlinearities, a dynamic gain technique is introduced and a constructive coordinate transformation is given. On the other hand, an event-triggered strategy combining with the dynamic gain is proposed such that the triggering threshold can be adjusted in an adaptive manner. With the help of the proposed event-triggered strategy, a dynamic event-based output feedback controller is developed to ensure that all signals of the closed-loop system are bounded while the tracking error converges to a small neighborhood of the origin. Moreover, it is proved that the Zeno behavior is excluded in the presence of nonsmooth controller. Two examples, including an induction heater circuit system and a numerical example, are provided to indicate the effectiveness of the proposed control method.

Adaptive output feedback stabilization for switched [formula omitted]-normal nonlinear systems with unknown homogeneous growth rate

This paper investigates the problem of adaptive output feedback control for switched p-normal nonlinear systems with unknown homogeneous growth rate. A novel adaptive output feedback control scheme is first presented with the help of a dynamic gain technique, which renders the switched nonlinear systems with lower-triangular unknown homogeneous growth rate globally asymptotically stable. Then, the proposed control scheme can be extended to deal with a class of switched nonlinear systems with upper-triangular unknown homogeneous growth rate. Finally, two numerical examples are provided to verify the effectiveness of the proposed scheme.

Adaptive event‐triggered output feedback control for a class of p‐normal nonlinear systems with sensor failure

SummaryThis article investigates the problem of global adaptive output feedback control for a class of p‐normal nonlinear systems with time‐varying sensor failure and unknown growth rate via an event‐triggered strategy. Due to the existence of time‐varying sensor failure, only the system output with sensor failure is available for feedback control design. To overcome this obstacle, an adaptive reduced‐dimensional observer using only failure output is constructed. Subsequently, a novel adaptive event‐triggered controller is designed by virtual of a dynamic gain technique, under which all the states of the considered closed‐loop systems are bounded as well as the proposed event‐triggered mechanism is Zeno‐free. Finally, two examples are provided to demonstrate the validity of the presented control method.

Containment of linear multi-agent systems with disturbances generated by heterogeneous nonlinear exosystems

Abstract This paper considers containment control problem of linear multi-agent systems with exogenous disturbances generated from heterogeneous nonlinear exosystems under directed networks. Based on dynamic gain technique, a nonlinear disturbance observer is proposed to compensate for the disturbances acting on the multi-agent systems. Then, distributed containment control law is presented, and sufficient conditions are given for solving the containment problem of the linear multi-agent systems. Finally, some numerical simulations are given to demonstrate the effectiveness of the proposed disturbance observers and control protocols.

Disturbance Attenuation via Output Feedback for Nonlinear Time-Delay Systems with Input Matching Uncertainty

This paper studies the problem of output feedback disturbance attenuation for a class of uncertain nonlinear systems with input matching uncertainty and unknown multiple time-varying delays, whose nonlinearities are bounded by unmeasured states multiplying unknown polynomial-of-output growth rate. By skillfully combining extended state observer, dynamic gain technique, and Lyapunov-Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain to guarantee the boundedness of closed-loop system states and the achievement of global disturbance attenuation in the L2-gain sense.

Adaptive state feedback control for time-delay stochastic nonlinear systems based on dynamic gain method

ABSTRACTThis paper studies the adaptive state feedback control for p normal form time-delay stochastic nonlinear systems with unknown parameters by dynamic gain technique. The power order restriction is completely removed and tracking problem is further studied. Through the inductive design method, the virtual controllers are constructed in each step, and the corresponding dynamic gain is introduced to eliminate residual terms generated by the differential operator of Lyapunov–Krasovskii functional in the subsequent step, which is used to deal with the time-delay terms. The unknown parameters are addressed by the modified tuning function method. Based on the constructed adaptive controller, the boundedness of the tracking error and other state variables can be guaranteed. Especially, if the reference signal is zero, the state variables can converge to equilibrium almost surely. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.

Output feedback control for stochastic nonlinear time delay systems using dynamic gain technique

This paper investigates the output feedback control for a class of stochastic nonlinear time delay systems based on dynamic gain technique. The nonlinear terms of the stochastic system satisfy linear growth condition on unmeasured state variables with the output dependent incremental rate, which makes the studied time delay stochastic system more general than the exiting results. Firstly, the full order dynamic gain observer is constructed. Then, the linear-like controller is designed without using recursive design method. Next, the stability analysis is given and a useful corollary is obtained. Finally, a simulation is given to illustrate the effectiveness of the proposed method.

Consensus of linear multi-agent systems with exogenous disturbance generated from heterogeneous exosystems

ABSTRACTThis paper addresses the consensus tracking problem for multi-agent linear systems subject to exogenous disturbances generated from heterogeneous exosystems. For the case that the disturbances are generated from linear heterogeneous exosystems, a linear disturbance observer and distributed control law are proposed, and sufficient condition for consensus tracking is established by combining the input-to-state stability and Lyapunov analysis methods. For the case when the disturbances are generated from non-linear heterogeneous exosystems, a non-linear disturbance observer is presented to estimate such disturbance by using the dynamic gain technique; then, a distributed control law is designed, and sufficient condition is also presented for achieving consensus tracking. Two simulation examples are provided to demonstrate the effectiveness of the proposed consensus protocols.