Universal disturbance rejection for nonlinear systems in output feedback form

This note deals with global disturbance rejection via output feedback of a class of uncertain nonlinear systems subject to a class of unknown disturbances. Both the uncertainty in the system model and the uncertainty in the exosystem are tackled concurrently. The disturbances generated from an unknown linear exosystem are completely rejected. The order of the exosystem is assumed known, and the eigenvalues are distinct. The system is assumed in the format of the minimum-phase output feedback form, with no knowledge of the values of any system parameters, including the high-frequency gain. No other assumptions are needed in the control design. A new set of filters are introduced for state estimation. The stability of the internal model is exploited to design a new auxiliary error, involving both the unknown parameters of the reformatted exosystem and those of the system, which makes it possible to group all the unknown parameters in a format suitable to adaptive control design. A Nussbaum gain is introduced in adaptive control design to tackle the unknown high-frequency gain and a number of control coefficients are also made adaptive so that the disturbance rejection is global with respect to unknown frequencies in the disturbances.     

An adaptive learning regulator for uncertain minimum phase systems with undermodeled unknown exosystems

The design of an adaptive learning regulator is addressed for uncertain minimum phase linear systems (with known bounds, known upper bound on system order, known relative degree, known high frequency gain sign) and for unknown exosystems (with unknown order, uncertain frequencies). On the basis of a known bound on system uncertainties and a known bound on the modeled exosystem frequencies, a new adaptive output error feedback control algorithm is proposed which guarantees exponential convergence of both the output and the control input errors into residual bounds which decrease as the exosystem modeling error decreases. Exponential convergence of both errors to zero is obtained when the regulator exactly models all exosystem excited frequencies, while asymptotic convergence of both errors to zero is achieved when the actual exosystem is overmodeled by the regulator. The new algorithm generalizes existing learning controllers since, in the case of periodic references and/or disturbances, the knowledge of the period is not required.     

The leader-following rendezvous with connectivity preservation via a self-tuning adaptive distributed observer

This paper studies the leader-following rendezvous with connectivity preservation problem for multiple double-integrator systems subject to external disturbances via a self-tuning adaptive distributed observer approach. This approach offers two advantages over the existing approach. First, it removes the existing assumption that all the followers know the system matrix of the leader system. Second, the difficult task of calculating the observer gain is avoided by the employment of the dynamic observer gain. A rigorous analysis shows that our control law is capable of maintaining the connectivity of any initial connected communication network, and achieving the asymptotic tracking and disturbance rejection for a class of leader's signals and external disturbances, which can be the algebraic sum or multiplication of any polynomial functions with any unknown coefficients and sinusoidal functions with arbitrary unknown amplitudes, initial phases, and any frequencies.     

Fully distributed robust consensus control of multi-agent systems with heterogeneous unknown fractional-order dynamics

This paper investigates the robust consensus control problem of heterogeneous unknown nonlinear fractional-order multi-agent systems (FOMASs) without leader and with multiple leaders of bounded inputs. More specifically, FOMASs with nonidentical unknown coupling nonlinearities and external disturbances are considered in this paper, which takes the first-order MASs as its special case. Based on the σ-modification adaptive control technique, some class of discontinuous robust adaptive control protocols are proposed to solve the leaderless consensus problem and containment consensus problem, respectively. By means of the set-valued maps theory and by artfully choosing Lyapunov function, it is shown that the proposed consensus protocols are user friendly in that they are capable of compensating uncertain coupling nonlinearities, rejecting disturbances, rendering smaller control gains and thus requiring smaller amplitude on the control input while preserving global consensus convergence. All of the proposed robust adaptive consensus protocols are independent of any global and unknown information and thus are fully distributed. Some numerical simulations are provided to validate the correctness of the obtained results.     

Adaptive cooperative output regulation of nonlinear multiagent systems with arbitrarily large parametric uncertainties and an uncertain leader

This paper extends the result for cooperative output regulation problem for uncertain nonlinear multiagent systems in output feedback form in the sense that the exosystem generating leader's signal and disturbance is allowed to contain unknown parameter, and all parameters in the whole multiagent system can be arbitrarily large. Since only the information of itself and its neighbors is available, constructing a distributed control law is necessary for the asymptotic tracking of the uncertain leader's signal and the rejection of unknown external disturbances, which is also the main challenge here. A series of simulations are conducted to illustrate the efficiency and advantage of our designs together with the comparison of the design in the existing work.     

基于自适应滑模的不确定Euler-Lagrange多智能体系统抗扰动蜂拥控制

针对具有参数不确定性和未知外部扰动的Euler-Lagrange多智能体系统,设计一种基于自适应滑模控制的分布式蜂拥算法.该算法使用自适应滑模控制和自适应控制律分别补偿未知的外部扰动与模型中可线性参数化回归的不确定项,从而在实现蜂拥控制的同时,避免智能体对外部扰动先验知识的要求.理论分析表明,在多智能体达成蜂拥的同时,算法保证滑模的自适应增益有界.此外,所提出的算法同时考虑虚拟领导者追踪与基于目标区域的跟踪问题,并给出碰撞避免的条件.最后,通过算例仿真验证所提出算法的有效性.     

Coordinated control with multiple dynamic leaders for uncertain Lagrangian systems via self‐tuning adaptive distributed observer

This paper studies coordinated control of multiple Lagrangian systems with parametric uncertainties subject to external disturbances by proposing a fully distributed continuous control law based on the improved self‐tuning adaptive observer inspired by non‐identifier‐based high‐gain adaptive control technique. Under this distributed continuous control law, a group of Lagrangian systems are driven to the convex hull spanned by multiple heterogenous dynamic leaders, which can be any combination of step signals of arbitrary unknown magnitudes, ramp signals of arbitrary unknown slopes, and sinusoidal signals of arbitrary unknown amplitudes, initial phases, and any unknown frequencies. It is also worth to mention that this control law we propose, depending neither on any information of leader systems for uninformed followers, nor on external disturbances, even independent of neighbors' velocity, can achieve asymptotic tracking of multiple leaders without any additional condition instead of ensuring the ultimate boundedness of the containment error as in the literature. Copyright © 2016 John Wiley & Sons, Ltd.     

Global stabilization and disturbance suppression of a class of nonlinear systems with uncertain internal model

This paper deals with global stabilization and disturbance suppression of a class of nonlinear systems using output feedback. The disturbances generated from a unknown linear exosystem are completely compensated. The order of the exosystem is assumed known and the eigenvalues are distinct. No other assumptions are needed in the control design. This means that the proposed control design is able to completely compensate the disturbances without knowing their amplitudes, frequencies and phases, as long as the number of different frequency components in the disturbances is known. A new formulation of state estimation is introduced to ensure the global stabilization and complete disturbance suppression. Adaptive control technique is used to design an adaptive internal model based on a recently introduced formulation of unknown exosystems and the parameters in the adaptive internal model converge to the actual values, from which the unknown disturbance frequencies can be calculated. In the proposed control design, a number of control coefficients are made adaptive so that the result is global with respect to unknown frequencies in the disturbances.     

A Scalable Adaptive Approach to Multi-Vehicle Formation Control with Obstacle Avoidance

This paper deals with the problem of distributed formation tracking control and obstacle avoidance of multi-vehicle systems (MVSs) in complex obstacle-laden environments. The MVS under consideration consists of a leader vehicle with an unknown control input and a group of follower vehicles, connected via a directed interaction topology, subject to simultaneous unknown heterogeneous nonlinearities and external disturbances. The central aim is to achieve effective and collision-free formation tracking control for the nonlinear and uncertain MVS with obstacles encountered in formation maneuvering, while not demanding global information of the interaction topology. Toward this goal, a radial basis function neural network is used to model the unknown nonlinearity of vehicle dynamics in each vehicle and repulsive potentials are employed for obstacle avoidance. Furthermore, a scalable distributed adaptive formation tracking control protocol with a built-in obstacle avoidance mechanism is developed. It is proved that, with the proposed protocol, the resulting formation tracking errors are uniformly ultimately bounded and obstacle collision avoidance is guaranteed. Comprehensive simulation results are elaborated to substantiate the effectiveness and the promising collision avoidance performance of the proposed scalable adaptive formation control approach.      

Regulation of Linear Systems With Unknown Exosystems of Uncertain Order

The problem of designing an output feedback control law which exponentially achieves output regulation is considered for known stabilizable and detectable linear systems which are allowed to be non-minimum phase; output references and/or additive disturbances are both generated by a linear exosystem with unknown purely imaginary eigenvalues and uncertain order. The novelty of this note is to require only an upper bound on the exosystem order to achieve a global solution which includes exponentially convergent estimates of the exosystem unknown frequencies     

Novel distributed robust adaptive consensus protocols for linear multi-agent systems with directed graphs and external disturbances

This paper addresses the distributed consensus protocol design problem for linear multi-agent systems with directed graphs and external unmatched disturbances. Novel distributed adaptive consensus protocols are proposed to achieve leader–follower consensus for any directed graph containing a directed spanning tree with the leader as the root node and leaderless consensus for strongly connected directed graphs. It is pointed out that the adaptive protocols involve undesirable parameter drift phenomenon when bounded external disturbances exist. By using the σ modification technique, distributed robust adaptive consensus protocols are designed to guarantee the ultimate boundedness of both the consensus error and the adaptive coupling weights in the presence of external disturbances. All the adaptive protocols in this paper are fully distributed, relying on only the agent dynamics and the relative states of neighbouring agents.     

Distributed adaptive robust tracking and model matching control with actuator faults and interconnection failures

In this paper, direct adaptive-state feedback control schemes are developed to solve the robust tracking and model matching control problem for a class of distributed large scale systems with actuator faults, faulty and perturbed interconnection links, and external disturbances. The adaptation laws are proposed to update the controller parameters on-line when all the eventual faults, the upper bounds of perturbations and disturbances are assumed to be unknown. Then a class of distributed state feedback controllers is constructed to automatically compensate the fault, perturbation and disturbance effects based on the information from adaptive schemes. The proposed distributed adaptive tracking controller can ensure that the resulting adaptive closed-loop large-scale system is stable and the tracking error decreases asymptotically to zero in the presence of uncertain faults of actuators and interconnections, perturbations in interconnection channels, and disturbances. The proposed adaptive design technique is finally evaluated in the light of a simulation example.     

Global disturbance rejection of a class of nonlinear systems with unknown exosystems

An asymptotic rejection algorithm is proposed for a class of nonlinear systems that have not only additive nonlinear uncertainties but also unknown disturbances. The disturbances are generated from an unknown exosystem, and are assumed to be sinusoidal disturbances with unknown amplitude and frequency. By using the technique of backstepping and adaptive control, a nonlinear state feedback controller is designed. Under the proposed controller, the system＇s state variables asymptotically converge to zero, and the disturbances are rejected completely. The approach used is an integration of the robust stabilization technique, adaptive technique, and backstepping technique.     

Adaptive synchronisation of unknown nonlinear networked systems with prescribed performance

This paper proposes an adaptive tracking control with prescribed performance function for distributive cooperative control of highly nonlinear multi-agent systems. The use of such approach confines the tracking error within a large predefined set to a predefined smaller set. The key idea is to transform the constrained system into unconstrained one through the transformation of the output error. Agents’ dynamics are assumed unknown, and the controller is developed for a strongly connected structured network. The proposed controller allows all agents to follow the trajectory of the leader node, while satisfying the necessary dynamic requirements. The proposed approach guarantees uniform ultimate boundedness for the transformed error as well as a bounded adaptive estimate of the unknown parameters and dynamics. Simulations include two examples to validate the robustness and smoothness of the proposed controller against highly nonlinear heterogeneous multi-agent system with uncertain time-variant parameters and external disturbances.     

Adaptive robust simultaneous stabilization of multiple n-degree-of-freedom robot systems

In this paper, the adaptive robust simultaneous stabilization problem of uncertain multiple n-degree-of-freedom (n-DOF) robot systems is studied using the Hamiltonian function method, and the corresponding adaptive L2 controller is designed. First, we investigate the adaptive simultaneous stabilization problem of uncertain multiple n-DOF robot systems without external disturbance. Namely, the single uncertain n-DOF robot system is transformed into an equivalent Hamiltonian form using the unified partial derivative operator (UP-DO) and potential energy shaping method, and then a high dimensional Hamiltonian system for multiple uncertain robot systems is obtained by applying augmented dimension technology, and a single output feedback controller is designed to ensure the simultaneous stabilization for the higher dimensional Hamiltonian system. On this basis, we further study the adaptive robust simultaneous stabilization control problem for the uncertain multiple n-DOF robot systems with external disturbances, and design an adaptive robust simultaneous stabilization controller. Finally, the simulation results show that the adaptive robust simultaneous stabilization controller designed in this paper is very effective in stabilizing multi-robot systems at the same time.     

Distributed Adaptive Dynamic Surface Control for Synchronization of Uncertain Nonlinear Multi-agent Systems

In this paper a distributed adaptive dynamic surface controller is proposed for multi-agent systems under fixed directed graph topologies. The agents have uncertain nonlinear dynamics and are influenced by bounded unknown disturbances. The controller should synchronize the states of all agents with the corresponding states of the nonautonomous leader. It is proved that, with the proposed controller, the synchronization error remains bounded; and the bounds can be arbitrarily decreased by increasing the controller gains. The control rules are designed such that each agent only requires the state information of its neighbors, rendering a distributed control. The effectiveness of the proposed method is demonstrated through two simulation examples.     

Global output regulation for output feedback systems with an uncertain exosystem and its application

This paper presents the solvability conditions for the global robust output regulation problem for a class of output feedback systems with an uncertain exosystem by using output feedback control. An adaptive control technique is used to handle the unknown parameter vector in the exosystem. It is shown that this unknown parameter vector can be exactly estimated asymptotically if a controller containing a minimal internal model is employed. The effectiveness of our approach has been illustrated by an asymptotic tracking problem of a generalized fourth‐order Lorenz system. Copyright © 2009 John Wiley & Sons, Ltd.     

Distributed event-triggered output regulation of multi-agent systems

Motivated by the future use of embedded microprocessors with limited resources and limited computational resources, the distributed output regulation with event-driven strategies problem of linear multi-agent systems is considered in this paper. The main task is to design distributed feedback by employing event-triggered technique for multi-agent systems such that all agents can track an active leader, and/or distributed disturbance rejection. Both leader and disturbance are generated by some external system (exosystem). Both distributed static and dynamic feedback with event-triggered strategy are constructed here. Then, the input-to-state stability of the closed-loop multi-agent system is analysed. Finally, a numerical example is given to validate the proposed control.     

Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults

A class of unknown nonlinear systems subject to uncertain actuator faults and external disturbances will be studied in this paper with the help of fuzzy approximation theory. Using backstepping technique, a novel adaptive fuzzy control approach is proposed to accommodate the uncertain actuator faults during operation and deal with the external disturbances though the systems cannot be linearized by feedback. The considered faults are modeled as both loss of effectiveness and lock-in-place （stuck at some unknown place）. It is proved that the proposed control scheme can guarantee all signals of the closed-loop system to be semi-globally uniformly ultimately bounded and the tracking error between the system output and the reference signal converge to a small neighborhood of zero, though the nonlinear functions of the controlled system as well as the actuator faults and the external disturbances are all unknown. Simulation results demonstrate the effectiveness of the control approach.     

Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control

In this paper, the projective synchronization problem of two fractional-order different chaotic (or hyperchaotic) systems with both uncertain dynamics and external disturbances is considered. More particularly, a fuzzy adaptive control system is investigated for achieving an appropriate projective synchronization of unknown fractional-order chaotic systems. The adaptive fuzzy logic systems are used to approximate some uncertain nonlinear functions appearing in the system model. These latter are augmented by a robust control term to compensate for the unavoidable fuzzy approximation errors and external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is adopted for the design of the parameter adaptation laws and the proof of the corresponding stability as well as the asymptotic convergence of the underlying synchronization errors towards zero. The effectiveness of the proposed synchronization system is illustrated through numerical experiment results.