Systems In Lower Triangular Form Research Articles

Event-triggered impulsive control of lower-triangular large-scale nonlinear systems based on gain scaling technique

This paper investigates the event-triggered impulsive control problem for a class of large-scale nonlinear systems in lower-triangular form. Based on gain scaling technique and impulsive control theory, a novel decentralized event-triggered impulsive control strategy is first put forward by introducing a static scaling gain, where no control input exists between two consecutive triggering points. Moreover, when the large uncertainties exist in system nonlinearities, we further develop a new control strategy by introducing a time-varying scaling gain. It is proved that the proposed closed-loop control strategies exclude the Zeno behavior without sacrificing the global convergence of system states. Compared with the existing results, it is the first time to apply impulsive control to lower-triangular large-scale nonlinear systems, and the advantages of event-triggered impulsive control and gain scaling technique are subtly combined in the proposed control strategies. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed schemes.

Adaptive decentralized stabilization of infinite networks of interconnected nonlinear systems with uncontrollable linearization

We solve the problem of decentralized adaptive stabilization for infinite networks of interconnected nonlinear systems in lower-triangular form with power integrators with uncontrollable linearization and with uncertainties in the last equation in which the control input appears. The feedback law is adaptive and continuous but not necessarily smooth, and the decentralized adaptive backstepping algorithm is based on small gain approach and on suitable gain assignment for each node of the infinite network.

Event-triggered decentralised control for large-scale systems with actuator failures

ABSTRACT This paper investigates the trajectory tracking problem for large-scale nonlinear systems in lower triangular form by employing the technology of static gain. For one thing, in the interest of improving the fault tolerance of the concerned system, a novel adaptive compensation method is considered in the tracking strategy for dealing with actuator failures. For another, in order to alleviate the communication burden and maintain satisfactory systems performance, the control method for handling event-triggered input is also added in the tracking strategy. Besides, this paper also proves that the designed strategy can achieve the control goal for large-scale nonlinear systems with bounded disturbance. The simulation example of the machine feed system is given to verify the validity of the proposed strategy.

A note on applications of a trajectory-based small-gain theorem to decentralized stabilization of switching networks with generalized dead zones

We propose a method for uniform decentralized stabilitzation for a class of large-scale networks of nonlinear switched systems in lower-triangular form with unknown arbitrary switchings. In contrast to the class of networks with the same structure of interconnections that was considered in [1], the dynamics of each subsystem of our network satisfies more general conditions and its input–output maps are not necessarily right invertible, for instance, they can have dead zones. Another difference from [1] is that the current result is proved by a different approach. Instead of using a small-gain theorem in terms of ISS Lyapunov functions as in [1], we use the trajectory-based small-gain theorem for switched systems proved in [2].

Robust containment control for a class of heterogeneous uncertain nonlinear multi-agent systems in lower triangular form

This paper studies the robust containment control problem for a class of nonlinear multi-agent systems in lower triangular form with parameter uncertainty. The agents are heterogenous with the particularity that the dynamics of the leaders are totally different from those of the followers. The interconnection topology is described by a general directed graph. Based on the distributed internal model, the robust containment control problem is first converted into the stabilisation problem for an augmented network. A distributed state feedback control is then proposed to solve the stabilisation problem of the subsequent augmented network by the block backstepping technique. Under the proposed control, all the followers' outputs will converge to the convex hull spanned by the leaders.

Adaptive low-power high-gain observers for lower-triangular systems with input-dependent Lipschitz constant

We combine the low-power high-gain observer recently proposed in Astolfi and Marconi (2015) with the updated-gain technique used in Andrieu et al. (2009). The resulting adaptive low-power high-gain observer inherits the advantages of both techniques and can be used to address the state-estimation problem for Lipschitz systems in lower triangular form with nonlinearities having a Lipschitz constant that depends on a known external input.

Neural Networks-Based Adaptive Exponential Quasi-Passification and Output Tracking Control for Uncertain Switched Nonlinear Systems

In this paper, we mainly study the adaptive exponential quasi-passivity and adaptive tracking control of lower triangular uncertain switched nonlinear systems, even though the adaptive output tracking control problem of individual subsystem is unsolvable. First, the exponential quasipassivity concept is proposed to describe the energy changing of the overall switched nonlinear systems without the exponential quasi-passivity property of all the subsystems. Then, for switched nonlinear systems, the semiglobally uniformly ultimate boundedness is achieved by using exponential quasipassivity. Second, this result is applied to solve adaptive tracking control problem uncertain switched nonlinear systems in lower-triangular form. A new adaptive tracking control technique is developed by combining quasi-passification methods with adaptive backstepping techniques. The unknown nonlinear functions are approximated by the radial basis function neural networks. In contrast to the existing results, the multiple storage functions method reduces the conservativeness caused by a common Lyapunov function for all subsystems. Finally, the effectiveness of the proposed method is verified by an example.

Relative-output-based consensus for nonlinear multi-agent systems with unknown measurement sensitivities

In this paper, the consensus problem is investigated for a class of nonlinear multi-agent systems in lower triangular form through dynamic output feedback control. Each agent can only access to the uncertain relative output information from other agents under directed communication. The presence of unknown measurement sensitivities causes the relative output can not be used to construct the observer for each agent directly. For the sake of overcoming this difficulty, a dual-domination gain method is applied to dominate the nonlinear terms and the unknown measurement sensitivities. Then, a new dynamic output feedback consensus prtocol is presented to drive the multi-agent systems to consensus. The upper bound of the unknown measurements sensitivities is also given. At last, we provide two numerical simulation examples to verify the effectiveness of our proposed methods.

Adaptive Neural Backstepping Control Design for A Class of Nonsmooth Nonlinear Systems

This paper investigates the problems of backstepping control for a class of nonsmooth nonlinear systems. With the help of set-valued functions (or maps) and set-valued derivatives, a new Lyapunov criterion is developed for nonsmooth systems. The concept of semi-globally uniformly ultimately bounded (SGUUB) stability that is widely used for smooth nonlinear systems in lower triangular form is, for the first time, applied to the nonsmooth case, and such a concept provides a theory foundation for the subsequent backstepping control design. Then, two types of continuous controllers are designed based on the backstepping technique and adaptive neural network (NN) algorithm. In the light of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent model. Then, the first type of controller can be efficiently designed by using the traditional backstepping technique. On the other hand, when the unknown uncertainty is taken into account in the equivalent systems, another type of controller is designed based on adaptive NN control strategy. It is proved that in both cases, all the closed-loop signals are SGUUB by using our proposed controllers. Finally, a numerical example with two types of controllers is supplied to show the availability of the provided control schemes.

Morphing aircraft control based on switched nonlinear systems and adaptive dynamic programming

This paper investigates the control problem of a morphing aircraft with variable sweep wings based on switched nonlinear systems and adaptive dynamic programming (ADP). The longitudinal altitude motion of the morphing aircraft is first modeled as switched nonlinear systems in lower triangular form. Then, the designed controller is comprised of the basic part and supplementary part. For the basic part, the backstepping technique is applied and a modified dynamic surface is introduced to overcome the ‘explosion of complexity’ problem. Disturbance observers inspired from the idea of extended state observer are designed to obtain the estimations of the internal uncertainties and external disturbances. The common virtual control laws of the backstepping method are developed by the disturbance observers and radial basis function neural networks. On the other hand, for the supplementary part, an ADP approach with the name of action-dependent heuristic dynamic programming is used to further decrease the altitude tracking error, which generates an additional control input by observing the differences between the actual and desired values in the backstepping design. Finally, comparative simulations are conducted to demonstrate the improved control performance of the proposed approach.

Prescribed performance control of morphing aircraft based on switched nonlinear systems and reinforcement learning

The prescribed performance control of a morphing aircraft with variable sweep wings is investigated based on switched nonlinear systems and reinforcement learning. Switched nonlinear systems in lower triangular form are first adopted to describe the longitudinal altitude motion, and an error transformation is applied to handle the prescribed performance bound. Then, the designed controller is divided into the basic part and supplementary part. For the basic part, the backstepping method with involvement of the modified dynamic surface control technique is utilized to avoid the “explosion of complexity” problem. Improved disturbance observers inspired from the idea of extended state observer are then designed to estimate the disturbances and combined with radial basis function neural networks to develop the common virtual control laws. Moreover, by using the error variables defined in the backstepping design, the reinforcement learning–based supplementary part controller is devised with the critic-action neural network structure, which can adjust its parameters online and further decrease the altitude tracking error. It is proved that all signals of the closed-loop system are uniformly ultimately bounded, and the prescribed performance bound for convergence of the altitude tracking error can be satisfied. Finally, comparative simulations demonstrate the effectiveness of the proposed control approach.

Event-triggered output-feedback tracking of a class of nonlinear systems with unknown time delays

A single function approximation (SFA) approach for event-triggered output-feedback tracker design is presented for uncertain nonlinear time-delay systems in lower-triangular form. Contrary to the existing event-triggered output-feedback control methods dependent on multiple function approximators in the presence of lower-triangular nonlinearities, the proposed SFA approach provides the following advantages: (i) the simple observer structure independent of function approximators; (ii) one event-triggering condition based on only a tracking error; and (iii) the simple control scheme using one function approximator. Thus, the structural simplicity is allowed for implementing the observer and the event-triggering law in the sensor part and the adaptive tracker in the control part. Under the proposed SFA-based event-triggered control scheme, it is shown that the boundedness of closed-loop signals and the existence of a minimum inter-event time are guaranteed regardless of unknown time-delay nonlinearities and unmeasurable state variables.

Disturbance rejection control of morphing aircraft based on switched nonlinear systems

The problem of disturbance rejection control for the longitudinal dynamics of a morphing aircraft is investigated based on switched nonlinear systems. A disturbance observer with nonlinear gains composed of two distinct linear regions is first designed, which adopts the idea of the extended state observer to provide the estimations of disturbances and can reduce the peaking value problem. To achieve disturbance rejection via the designed disturbance observer, two separate controllers are then designed for the velocity and altitude subsystem of the longitudinal motion model, where the altitude subsystem is modeled as switched nonlinear systems in lower triangular form and the backstepping design technique is applied. Furthermore, a modified dynamic surface is introduced at each step of the backstepping method to avoid the ‘explosion of complexity’ problem. It is proven rigorously that all signals of the closed-loop system remain bounded by the developed control scheme. Finally, comparative simulations validate the effectiveness of the proposed approach.

Neural Networks-Based Adaptive Finite-Time Fault-Tolerant Control for a Class of Strict-Feedback Switched Nonlinear Systems.

This paper concentrates upon the problem of finite-time fault-tolerant control for a class of switched nonlinear systems in lower-triangular form under arbitrary switching signals. Both loss of effectiveness and bias fault in actuator are taken into account. The method developed extends the traditional finite-time convergence from nonswitched lower-triangular nonlinear systems to switched version by designing appropriate controller and adaptive laws. In contrast to the previous results, it is the first time to handle the fault tolerant problem for switched system while the finite-time stability is also necessary. Meanwhile, there exist unknown internal dynamics in the switched system, which are identified by the radial basis function neural networks. It is proved that under the presented control strategy, the system output tracks the reference signal in the sense of finite-time stability. Finally, an illustrative simulation on a resistor-capacitor-inductor circuit is proposed to further demonstrate the effectiveness of the theoretical result.

Adaptive Output-Feedback Controller Design for Switched Nonlinear Stochastic Systems With a Modified Average Dwell-Time Method

This paper considers the problem of adaptive fuzzy backstepping-based output-feedback controller design for a class of uncertain switched nonlinear stochastic systems in lower-triangular form without the measurements of the system states. By combining fuzzy logic systems’ universal approximation ability and dynamic surface control technique in the adaptive backstepping recursive design with a modified average dwell-time scheme, a new adaptive fuzzy control approach is presented for the switched system. More specifically, a switched observer is constructed to reduce the conservativeness aroused by the employ of a common observer, and individual coordinate transformations for subsystems are given up by adopting a common coordinate transformation of all subsystems. It is proved that the overall closed-loop system is stable in the sense of semi-globally uniformly ultimately bounded in mean square, and the output of the switched system converges to a small neighborhood of the origin with appropriate choice of design parameters. Finally, simulation studies are provided to demonstrate the validity of the proposed control method.

Minimal-Approximation-Based Distributed Consensus Tracking of a Class of Uncertain Nonlinear Multiagent Systems With Unknown Control Directions.

A minimal-approximation-based distributed adaptive consensus tracking approach is presented for strict-feedback multiagent systems with unknown heterogeneous nonlinearities and control directions under a directed network. Existing approximation-based consensus results for uncertain nonlinear multiagent systems in lower-triangular form have used multiple function approximators in each local controller to approximate unmatched nonlinearities of each follower. Thus, as the follower's order increases, the number of the approximators used in its local controller increases. However, the proposed approach employs only one function approximator to construct the local controller of each follower regardless of the order of the follower. The recursive design methodology using a new error transformation is derived for the proposed minimal-approximation-based design. Furthermore, a bounding lemma on parameters of Nussbaum functions is presented to handle the unknown control direction problem in the minimal-approximation-based distributed consensus tracking framework and the stability of the overall closed-loop system is rigorously analyzed in the Lyapunov sense.

Approximation-based disturbance observer approach for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched disturbances

ABSTRACTThis paper presents an approximation-based nonlinear disturbance observer (NDO) methodology for adaptive tracking of uncertain pure-feedback nonlinear systems with unmatched external disturbances. Compared with existing control results using NDO for nonlinear systems in lower-triangular form, the major contribution of this study is to develop an NDO-based control framework in the presence of non-affine nonlinearities and disturbances unmatched in the control input. An approximation-based NDO scheme is designed to attenuate the effect of compounded disturbance terms consisting of external disturbances, approximation errors and control coefficient nonlinearities. The function approximation technique using neural networks is employed to estimate the unknown nonlinearities derived from the recursive design procedure. Based on the designed NDO scheme, an adaptive dynamic surface control system is constructed to ensure that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a neighbourhood of the origin. Simulation examples including a mechanical system are provided to show the effectiveness of the proposed theoretical result.

Cooperative Global Robust Output Regulation for Nonlinear Uncertain Multi-Agent Systems in Lower Triangular Form

In this paper, we study the cooperative global robust output regulation problem for a class of lower triangular nonlinear uncertain multi-agent systems. We first introduce a type of distributed internal model to convert the cooperative global robust output regulation problem into a global robust stabilization problem of a so-called augmented multi-agent system which is in the block lower triangular form. We then further show that, under a set of standard assumptions, the augmented multi-agent system can be globally stabilized via a distributed state feedback control law by developing a block backstepping technique. A special case of the main result of this paper leads to the solution of the leader-following global robust consensus problem for a class of nonlinear uncertain multi-agent systems.

State‐constrained robust stabilisation for a class of high‐order switched non‐linear systems

This study deals with the problem of robust stabilisation for a class of state-constrained high-order uncertain switched non-linear systems in lower triangular form. Bounded state-feedback controllers are designed to assure that asymptotic stabilisation is achieved in a domain without violation of the state constraint, and all closed-loop signals are bounded, when an appropriate requirement on the initial condition is imposed. Simulation results are provided to show the efficiency of the developed method.

Fuzzy Adaptive Control Design and Discretization for a Class of Nonlinear Uncertain Systems.

In this paper, tracking control problems are investigated for a class of uncertain nonlinear systems in lower triangular form. First, a state-feedback controller is designed by using adaptive backstepping technique and the universal approximation ability of fuzzy logic systems. During the design procedure, a developed method with less computation is proposed by constructing one maximum adaptive parameter. Furthermore, adaptive controllers with nonsymmetric dead-zone are also designed for the systems. Then, a sampled-data control scheme is presented to discretize the obtained continuous-time controller by using the forward Euler method. It is shown that both proposed continuous and discrete controllers can ensure that the system output tracks the target signal with a small bounded error and the other closed-loop signals remain bounded. Two simulation examples are presented to verify the effectiveness and applicability of the proposed new design techniques.