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Summary: The problem of practical predefined‐time tracking control is con sidered for high‐order strict‐feedback nonlinear systems subject to unknown mismatched disturbances. The exact bound of the mismatched disturbances is unknown in this study. A novel adaptive predefined‐time tracking control strategy based on backstepping is proposed by applying a predefined time stability theory. Using the designed tracking controller, all signals are bounded, and a user‐defined bound on the tracking error is ensured in a predefined interval, independent of initial states. The estimation parameters associated with the upper bound of the disturbances are updated adaptively, making the system robust to the disturbances. Simulation studies are conducted to illustrate the performance of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Summary: In this article, we consider the event‐triggered cascade high‐gain observer (ETCHGO) for a class of nonlinear systems. By cascading lower dimensional observers, we design a cascade high‐gain observer together with a Zeno‐free event‐triggered mechanism to estimate the state of the plant. We show that the ETCHGO has the same steady‐state performance as the continuous‐time cascade high‐gain observer, that is, there is a finite time after which the estimation error will not exceed the given threshold, and moreover, the finite time and the threshold can be made sufficiently small by adjusting some design parameters. We also investigate an ETCHGO with saturation, which will reduce the peaking value while maintaining the steady‐state estimation performance. Furthermore, we use the ETCHGO with saturation to solve the output feedback stabilization problem for a class of nonlinear systems. An example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the adaptive fuzzy formation control of multiple autonomous agents with prioritized missions. For a platoon of autonomous agents in an unknown environment containing multiple obstacles, formation control is investigated, where each agent is modeled by a second-order nonlinear system under unknown external disturbance in the Brunovsky form. We introduce the systematic procedure of null-space-based projection to convert the prioritized multimission control problem into a behavioral control problem. Then, we further develop a class of nonlinear-fast-terminal-sliding-mode-based adaptive control strategies that combine the fuzzy logic systems by jointly considering both kinematic and dynamic levels of the agents. The proposed controllers can guarantee each individual agent to achieve the predesigned desired pattern and drive the entire systems to achieve the prescribed missions. A simulation example with five agents demonstrates the effectiveness of the algorithm. Finally, the strategies are experimentally validated using a platoon of Pioneer 3AT and 3DX mobile robots. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we study the event‐triggered global robust practical output regulation problem for a class of nonlinear systems in output feedback form with any relative degree. Our approach consists of the following three steps. First, we design an internal model and an observer to form the so‐called extended augmented system. Second, we convert the original problem into the event‐triggered global robust practical stabilization problem of the extended augmented system. Third, we design an output‐based event‐triggered control law and a Zeno‐free output‐based event‐triggered mechanism to solve the stabilization problem, which, in turn, leads to the solvability of the original problem. Finally, we apply our result to the controlled hyperchaotic Lorenz systems. [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]

The global robust output regulation problem of nonlinear systems in output feedback form has been studied via a linear internal model. In this paper, we study the same problem using a class of nonlinear internal models. An advantage of nonlinear internal models is that it exists even when the system contains nonpolynomial nonlinearity and the exosystem is nonlinear. Thus, the result of this paper applies to a larger class of nonlinear systems and a larger class of exosystems. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The surface-mounted permanent-magnet synchronous motor is a two-input, two-output nonlinear system. The multi-input, multi-output nature of the system has posed some specific challenges to various control methods. Recently, the robust output regulation problem of the system subject to a known neutrally stable exosystem was studied. The problem came down to a global robust stabilization problem of an augmented system composed of the original plant and an internal model. In this paper, we will further study the robust output regulation problem of the system subject to an unknown neutrally stable exosystem. Like in the case where the exosystem is known, the current problem can be solved by globally stabilizing an augmented system. But unlike in the case where the exosystem is known, the augmented system takes a much more complicated form because of uncertainty in the exosystem than the case where the exosystem is known. In particular, the dynamic uncertainty in the current augmented system contains linearly parameterized uncertainty, and hence is not input-to-state stable. By utilizing some dynamic coordinate transformation technique, and combining some robust control and adaptive control techniques, we will solve the problem via a recursive approach. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

SUMMARY The asymptotic rejection of spacecraft systems under multi-tone sinusoidal disturbances has been studied recently for the case where the frequencies of the disturbance are known. In this paper, we further consider the case where the frequencies of the disturbance are unknown. We show that this case can be solved by an adaptive regulation technique. We also present some analysis on the convergence issue of the estimated frequencies to unknown frequencies. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

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: In this paper, we study the cooperative global adaptive output regulation problem for a class of nonlinear uncertain multi-agent systems subject to an uncertain leader system. In comparison with the case where the leader system is known exactly, we need to combine adaptive control and robust control techniques to deal with the unknown parameters in the leader system. By employing a distributed internal model for the multi-agent system, we first convert the problem into a global adaptive robust stabilization problem of a distributed augmented system. Then we further solve the global adaptive stabilization problem of the augmented system by a distributed adaptive control law. Finally, we show that the unknown parameters in the leader system can be exactly estimated provided that the distributed internal model is of minimal order. [Copyright &y& Elsevier]

SUMMARY In this paper, we study the global robust output regulation problem for a class of multivariable nonlinear systems. The problem is first converted into a stabilization problem of an augmented system composed of the original plant and an internal model. The augmented system is a multi-input system containing both dynamic uncertainty and time-varying static uncertainty. By decomposing the multi-input control problem into several single-input control problems, we will solve the problem by solving several single-input control problems via a recursive approach utilizing the changing supply function technique. The theoretical result is applied to the speed tracking control and load torque disturbance rejection problem of a surface-mounted permanent magnet synchronous motor. Copyright © 2011 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: The spherical inverted pendulum is a two-input, two-output non-minimum phase nonlinear system. Recently, the output regulation problem of the spherical inverted pendulum was studied in . It is known that the solvability of the output regulation problem depends on the solvability of the regulator equations which are a set of nonlinear partial differential equations. Since the exact solution of the regulator equations associated with the spherical inverted pendulum is not available due to the complexity of the equations, the paper tried a polynomial approximation of the solution of the regulator equations. In this paper, we first show that the solution of the regulator equations associated with the spherical inverted pendulum exist and then find an approximate solution to the output regulation problem of the spherical inverted pendulum via a neural network approximation approach. We also make some comparison between the method in this paper and the method in . [Copyright &y& Elsevier]

In this article, we consider a speed tracking and load torque disturbance rejection problem of PM synchronous motor by internal model design. The problem is first formulated as a global robust output regulation problem of a special class of multivariable systems. Then the output regulation problem is further converted into a global stabilisation problem of an augmented system composed of the original plant and an internal model. As the augmented system does not take any known special form, we have developed a specific tool to deal with the stabilisation problem. In particular, a generalised changing supply function technique applicable to non-input-to-state stable (ISS) systems is developed. This technique, in conjunction with a particular nonlinear internal model, leads to an effective solution to the problem. [ABSTRACT FROM AUTHOR]

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: 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]

The dynamic surface control (DSC) technique was developed recently by Swaroop et at This technique simplified the backstepping design for the control of nonlinear systems in strict-feedback form by overcoming the problem of "explosion of complexity?' It was later extended to adaptive backstepping design for nonlinear systems with linearly parameterized uncertainty. In this paper, by incorporating this design technique into a neural network based adaptive control design framework, we have developed a backstepping based control design for a class of nonlinear systems in strict-feedback form with arbitrary uncertainty. Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing method. In addition, a stability analysis is given which shows that our control law can guarantee the uniformly ultimate boundedness of the solution of the closed-loop system, and make the tracking error arbitrarily small. [ABSTRACT FROM AUTHOR]

Global robust stabilization of nonlinear cascaded systems is a challenging problem when the zero-dynamics is not exponentially stable. Recently, some recursive procedure has been developed for handling this problem utilizing the small gain theorem. However, the success of the procedure depends on the satisfaction of some conditions which arise at each step of the recursion. In this paper, we will show that, for the important class of cascaded polynomial systems, the solvability conditions can be made satisfied by appropriately implementing the recursive procedure. This result leads to an explicit construction of the control law. [Copyright &y& Elsevier]

Addresses the output regulation problem for the class of singular nonlinear systems. Generalized version of the center manifold theorem applied to singular nonlinear systems; Conditions necessary for the solvability of the output regulation.

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: 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]