Search

The problem of bearing-based formation control with disturbance rejection has been studied by quite a few papers under various assumptions on the disturbances such as constant disturbances, trigonometric polynomial disturbances or bounded uniformly continuous disturbances with known bounds. In this paper, we further study the same problem with the disturbances being bounded piecewise continuous time functions. We first consider the case where the bounds of the disturbances are known. We show that the problem can be solved by a distributed static state feedback control law. Then we further consider the case where the bounds of the disturbances are unknown. We manage to solve this problem by introducing the adaptive control technique to deal with the unknown bounds of the disturbances. Our results include all the existing results on the bearing-based formation control with disturbance rejection as special cases. Moreover, we present a sufficient condition on the initial values of the closed-loop system for each case that prevents the collision. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of Nash equilibrium seeking of N -player games for high-order integrator dynamics with disturbances. Three features of our results are worth mentioning. First, our results apply to jointly strongly connected networks, which can be disconnected at every time instant. Second, our disturbances can be any bounded time function with the bound unknown, which include discontinuous disturbances that cannot be handled by the existing results. Third, in addition to two standard assumptions on the cost functions, the existing results also rely on the satisfaction of an inequality involving some Lipschitz constant of the pseudogradients of the cost functions and the smallest nonzero eigenvalue of the Laplacian of the communication graph. In contrast, our results hold without relying on the satisfaction of this inequality. To achieve our objective, we have developed an approach by integrating the distributed estimator, some nonlinear control technique, and adaptive control technique. Our design is illustrated by one example of force-actuated robots in sensor networks. [ABSTRACT FROM AUTHOR]

Recently, the distributed state estimation problem for continuous-time linear systems over jointly connected switching networks was solved. Due to the use of the generalized Barbalat's Lemma, it can only show that the estimation errors asymptotically converge to the origin. By a completely different approach, this paper further studies the distributed state estimation problem with two new features. First, the asymptotic convergence is strengthened to the exponential convergence. This strengthened result not only offers a guaranteed convergence rate, but also renders the error system total stability and thus the capability to withstand small disturbances. Second, the coupling gains of our local observers can be different from each other and thus offers greater design flexibility, while the coupling gains in the existing result were required to be identical. These two new features are achieved by establishing exponential stability for two classes of linear time-varying systems, which may have other applications. [ABSTRACT FROM AUTHOR]

This technical communique studies the robust output regulation problem of uncertain discrete-time linear systems by quantized output feedback control. We show that, under the same assumptions as those that guarantee the solvability of the robust output regulation problem by a dynamic output feedback control law, our problem is also solvable by a dynamic quantized output feedback control law as long as the quantization density is greater than certain explicitly specified lower bound. [ABSTRACT FROM AUTHOR]

This paper studies the event-triggered cooperative global robust output regulation problem for a class of nonlinear multi-agent systems via a distributed internal model design. We show that our problem can be solved practically in the sense that the ultimate bound of the tracking error can be made arbitrarily small by adjusting a design parameter in the proposed event-triggered mechanism. Our result offers a few new features. First, our control law is robust against both external disturbances and parameter uncertainties, which are allowed to belong to some arbitrarily large prescribed compact sets. Second, the nonlinear functions in our system do not need to satisfy the global Lipschitz condition. Thus our systems are general enough to include some benchmark nonlinear systems that cannot be handled by existing approaches. Finally, our control law is a specific distributed output-based event-triggered control law, which lends itself to a direct digital implementation. [ABSTRACT FROM AUTHOR]

The leader-following attitude consensus problem of multiple rigid body systems has been studied by the distributed observer approach. The key assumption in the existing results is that the communication network among the rigid body systems is static and connected. Nevertheless, this assumption is undesirable since, typically, the communication network is time-varying and disconnected from time to time due to changes of the environment or failures of some subsystems. In this paper, we will further study the leader-following attitude consensus problem of multiple rigid body systems subject to a jointly connected switching communication network. This new problem is more challenging than the existing one since a jointly connected switching communication network can be disconnected at every time instant. To overcome the difficulty, we first show that the distributed observer for a nonlinear target system subject to a jointly connected switching communication network exists. Then, we further synthesize a distributed control law utilizing this distributed observer for the multiple rigid body systems. Finally, we show that this distributed control law solves our problem through the argument of the certainty equivalence principle. [ABSTRACT FROM AUTHOR]

In this paper, we consider the event-triggered cooperative robust practical output regulation problem for a class of linear minimum-phase multi-agent systems. We first convert our problem into the cooperative robust practical stabilization problem of a well defined augmented system based on the distributed internal model approach. Then, we design a distributed event-triggered output feedback control law together with a distributed output-based event-triggered mechanism to stabilize the augmented system, which leads to the solvability of the cooperative robust practical output regulation problem of the original plant. Our distributed control law can be directly implemented in a digital platform provided that the distributed triggering mechanism can monitor the continuous-time output information from neighboring agents. [ABSTRACT FROM AUTHOR]

In this paper, we study the leader-following consensus problem for a class of uncertain nonlinear multi-agent systems under jointly connected directed switching networks. The uncertainty includes constant unbounded parameters and external disturbances. We first extend the recent result on the adaptive distributed observer from global asymptotical convergence to global exponential convergence. Then, by integrating the conventional adaptive control technique with the adaptive distributed observer, we present our solution by a distributed adaptive state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of van der Pol oscillators. [ABSTRACT FROM AUTHOR]

In this paper, we study the leader-following attitude consensus problem of multiple rigid body systems by a sampled-data distributed observer. Comparing with the continuous-time distributed observer, the sampled-data distributed observer consumes fewer communication resources and is less vulnerable to such communication failures as network congestions and packet dropouts. The sampled-data distributed observer consists of two parts. The first part is a sampled-data distributed observer for the angular velocity leader subsystem and the second part is a sampled-data distributed observer for the attitude leader subsystem. It is noted that, since the attitude leader subsystem is nonlinear, a special effort has to be made to establish the sampled-data distributed observer for the attitude leader subsystem. Moreover, we give an explicit upper bound for the sampling intervals to guarantee the validity of the sampled-data distributed observer. On the basis of the sampled-data distributed observer, we further synthesize a distributed control law to solve the leader-following consensus problem. The effectiveness of our approach is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

Recently, we studied the problem of estimating the unknown frequencies of discrete-time multi-tone sinusoidal signals. However, the result has two limitations. The first one is that the result is not global and the second one is that the algorithm works only if the constant adaptation gain of the adaptive law is sufficiently small. In this paper, by replacing the constant adaptation gain of our previous design with a time-varying adaptation gain, we overcome the two limitations in our previous result. The advantage of the new design over the existing one is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we study the leader-following attitude consensus problem for multiple rigid body systems by a distributed unit quaternion-based attitude feedback control law. The control law is based on the certainty equivalence principle and contains a distributed observer for estimating the state of the leader and an auxiliary system compensating for the unavailability of the angular velocity. It is shown that the problem is solvable under the standard assumption that each follower can access the information from the leader through a directed path. [ABSTRACT FROM AUTHOR]

This paper studies the flocking with connectivity preservation problem of multiple double integrator systems subject to a class of external disturbances. We solve the problem by a distributed dynamic position feedback control law under the standard assumptions. Our approach is a combination of the potential function technique and observer design. Our result also includes some existing results as special cases. [ABSTRACT FROM AUTHOR]

A standard assumption on the existence of the distributed observer or adaptive distributed observer for a linear leader system over jointly connected switching networks is that none of the eigenvalues of the system matrix of the leader system have positive real parts. In this paper, after establishing a stability result for a class of linear periodic switched systems, we present sufficient conditions for the existence of both the distributed observer and the adaptive distributed observer for general linear leader systems over periodic jointly connected switching networks. As an application of the distributed observer, we solve the cooperative output regulation problem for linear multi-agent systems with general linear leader systems over periodic jointly connected switching networks. A numerical example is provided to illustrate our design. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the leader-following consensus problem for a multiple rigid spacecraft system whose attitude is represented by the unit quaternion. Most results on this problem rely on the assumption that every follower can access the state of the leader and are obtained via a decentralized control manner. By developing a nonlinear distributed observer for the leader system, we can solve this problem via a distributed control scheme under the mild assumptions that the state of the leader can reach every follower through a path and that the communication between followers is bidirectional. Moreover, our result can accommodate a class of desired angular velocities generated by a marginally stable linear autonomous system. [Copyright &y& Elsevier]

Abstract: In this paper, we study the cooperative semi-global robust output regulation problem for a class of minimum phase nonlinear uncertain multi-agent systems. This problem is a generalization of the leader-following tracking problem in the sense that it further addresses such issues as disturbance rejection, robustness with respect to parameter uncertainties. To solve this problem, we first introduce a type of distributed internal model that converts the cooperative semi-global robust output regulation problem into a cooperative semi-global robust stabilization problem of the so-called augmented system. We then solve the semi-global stabilization problem via distributed dynamic output control law by utilizing and combining a block semi-global backstepping technique, a simultaneous high gain feedback control technique, and a distributed high gain observer technique. [Copyright &y& Elsevier]

Abstract: In this paper, we study the cooperative global output regulation problem for a class of heterogeneous second order nonlinear uncertain multi-agent systems. We first introduce a type of distributed internal model that converts the cooperative global output regulation problem into the global robust stabilization problem of the so-called augmented multi-agent system. Then we further globally stabilize this augmented multi-agent system via a distributed state feedback control law, thus leading to the solution of the original problem. A special case of our result leads to the solution of the global leader-following consensus problem for the second order nonlinear multi-agent systems without satisfying the global Lipschitz condition. [Copyright &y& Elsevier]

Abstract: This paper generalizes our recent results on global robust output regulation of output feedback systems with integral input-to-state stable (iISS) inverse dynamics in two aspects. First, we consider the general relative degree case instead of the unity relative degree case. For this purpose, the one step approach proposed previously has to be generalized to a recursive approach. Second, we allow the exosystem to be uncertain. For this purpose, we need to introduce an adaptive control technique to estimate the unknown parameter vector in the exosystem. A convergence analysis of the estimated parameter vector will also be given. [Copyright &y& Elsevier]

Abstract: This paper studies a leader-following rendezvous problem for a double integrator multi-agent system where the leader system can generate a class of signals such as ramp signal and sinusoidal signals with arbitrary amplitudes and initial phases. Motivated by some techniques in output regulation theory, we propose a dynamic distributed state feedback control protocol that is able to maintain the connectivity of an initially connected communication network, and, at the same time, achieve the objective of the asymptotic tracking of all followers to the leader regardless of external disturbances. [Copyright &y& Elsevier]

Abstract: In this paper, we study both the leaderless consensus problem and the leader-following consensus problem for linear discrete-time multi-agent systems under switching network topology. Under the assumption that the system matrix is marginally stable, we show that these two consensus problems can be solved via the state feedback protocols, provided that the dynamic graph is jointly connected. Our result will contain several existing results as special cases. The proof is based on the stability analysis of a class of linear discrete-time switched systems which may have some independent interest. [Copyright &y& Elsevier]

Abstract: In this paper, we study the global robust stabilization problem of strict feedforward systems subject to input unmodeled dynamics. We present a recursive design method for a nested saturation controller which globally stabilizes the closed-loop system in the presence of input unmodeled dynamics. One of the difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable. We overcome this difficulty by employing a special version of the small gain theorem to address the local stability, and, respectively, the asymptotic small gain theorem to establish the global convergence property, of the closed-loop system. An example is given to show that a redesign of the controller is required to guarantee the global robust asymptotic stability in the presence of the input unmodeled dynamics. [Copyright &y& Elsevier]

Abstract: In this note, we investigate the possibility of simplifying the connectivity verification for multi-agent systems with proximity graphs and the linear feedback protocol. A Lyapunov-like approach is developed for analyzing the monotonicity of the largest edge length in the network. Based on this approach, we provide an initial-connectivity-based sufficient condition for dynamic connectivity. In particular, when each initial node degree is not less than three fourth of the graph order, initial network connectivity implies dynamic connectivity. [Copyright &y& Elsevier]

Abstract: This paper presents the solvability conditions for the global robust output regulation problem for lower triangular nonlinear systems assuming the control direction is unknown. The approach used is an integration of the robust stabilization technique and Nussbaum gain technique. [Copyright &y& Elsevier]

Abstract: The global robust stabilization problem of cascaded systems with dynamic uncertainty has been approached by the small gain theorem. This method, however, does not produce an explicit Lyapunov function for the closed-loop system. In this paper, we develop a Lyapunov''s direct method based recursive approach to solving the global robust stabilization problem for the mentioned systems. This method also produces an explicit Lyapunov function for the closed-loop system which is a superposition of those of individual subsystems. This Lyapunov function is indispensable when the adaptive control of the same class of systems is further considered. [Copyright &y& Elsevier]

Abstract: For over a decade, the solvability of the nonlinear robust output regulation problem relies on the assumption that the exosystem is linear and neutrally stable. Thus, the only exogenous signal that can be accommodated by the existing theory is a combination of finitely many step functions and sinusoidal functions. In this paper, we will show that it is possible to find controllers that can admit exogenous signals produced by nonlinear exosystems. An example with the well known van der Pol oscillator as the exosystem is given to illustrate our approach. [Copyright &y& Elsevier]

A procedure is developed for the design of adaptive neural network controller for a class of SISO uncertain nonlinear systems in pure-feedback form. The design procedure is a combination of adaptive backstepping and neural network based design techniques. It is shown that, under appropriate assumptions, the solution of the closed-loop system is uniformly ultimately bounded. [Copyright &y& Elsevier]

While the estimation problem of the unknown frequencies for a continuous-time multi-tone sinusoidal signal was thoroughly solved in the early 2000s, the discrete-time version of this problem was studied only recently via a nonlinear control approach. In this paper, we present a simpler approach to the estimation problem of the unknown frequencies for a discrete-time multi-tone sinusoidal signal. Our approach only involves the design of two linear filters together with a linear adaptation law. As a result, the implementation of our two linear filters is easier than that of nonlinear ones. Moreover, the linear form of our filters lends itself to the establishment of the exponential convergence of the estimated frequencies to their actual values. In addition, we obtain an interesting exponential stability result for a class of discrete-time linear time-varying systems that can be viewed as a discrete-time counterpart of a well-known stability result arising from continuous-time adaptive identification. [ABSTRACT FROM AUTHOR]

The adaptive distributed observer approach has been an effective tool for synthesizing a distributed control law for solving various control problems of leader–follower multiagent systems. However, the existing adaptive distributed observer needs to make use of the full state of the leader system. This assumption not only precludes many practical applications in which only the output of the leader system is available, but also leads to a high dimension observer. In this communique, we propose an adaptive distributed output observer which only makes use of the output of the leader system, and is thus more practical than the state based adaptive distributed observer. Moreover, the dimension and the information exchange among agents of the proposed adaptive distributed output observer can be significantly smaller than those of the state based adaptive distributed output observer. [ABSTRACT FROM AUTHOR]

In this paper, we study the output regulation problem for linear systems by the aperiodic sampled-data control approach. Suppose the problem is solvable by a continuous-time static state feedback control law and a continuous-time dynamic output feedback control law. Then, we first show that, if the exogenous signal is constant, then the output regulation problem is solvable exactly by both the sampled-data static state feedback control law and the sampled-data dynamic output feedback control law. If the exogenous signal is time-varying with bounded derivative, then we further show that the problem is solvable practically by both the sampled-data static state feedback control law and the sampled-data dynamic output feedback control law. [ABSTRACT FROM AUTHOR]

In this paper, we study the cooperative robust output regulation problem for a class of nonlinear multi-agent systems subject to a nonlinear leader system. We first establish a result on the existence of a distributed observer for a class of nonlinear leader systems. Then, we convert the cooperative robust output regulation problem into a robust stabilization problem of an augmented system composed of the given multi-agent system and the distributed internal model. Finally, we stabilize this augmented system by a decentralized output feedback control law, which together with the distributed observer and the distributed internal model, constitutes an overall distributed output feedback control law to solve the cooperative robust output regulation problem of the given multi-agent system. An example with the well-known Van der Pol system as the leader system is used to illustrate our design. [ABSTRACT FROM AUTHOR]

Abstract This paper proposes a novel Krasovskii–LaSalle theorem for discrete-time switched linear time-invariant systems. The result is utilized to guarantee exponential convergence of both leaderless and leader-following consensus of discrete-time multi-agent systems under jointly connected switching network topology. Different from the continuous-time multi-agent systems under switching networks, where the magnitude of the dwell time of switching signals is irrelevant, in the discrete-time case, this value is critical for consensus reaching. A special index, called the constrained controllability index, is defined. This index can be easily calculated and provide a tighter lower bound of the dwell time when compared to those given in the literature. With our novel method, the controllability condition on the system matrix is relaxed to the stabilizability condition, and the proposed results not only expand the existing discussions to balanced switching networks but also cover some unbalanced networks. Finally, numerical examples and simulations are provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: The parameter convergence of nonlinear adaptive control systems is an important yet not well addressed issue. In this paper, using the global robust output regulation problem of output feedback systems with unknown exosystems as a platform, we will show that the well known persistency of excitation (PE) condition still guarantees the convergence of the estimated parameter vector to the true parameter vector. Moreover, the PE condition will be satisfied if the internal model is minimal in certain sense. [Copyright &y& Elsevier]

The cooperative output regulation problem of linear multi-agent systems using distributed observer approach has been solved under the assumption that each follower knows the system matrix of the leader system. To remove this assumption, in this paper, a distributed control scheme utilizing the adaptive distributed observer has been proposed, which consists of three steps. First, an adaptive distributed observer is designed to estimate both the system matrix and the state of the leader system. Second, an adaptive algorithm is developed to calculate the solutions of the regulator equations online. Third, both adaptive state feedback and adaptive measurement output feedback controllers are synthesized to solve the cooperative output regulation problem without the assumption that each follower knows the system matrix of the leader system. [ABSTRACT FROM AUTHOR]