Showing papers in "International Journal of Robust and Nonlinear Control in 2018"

Performance analysis of 2‐DOF tracking control for a class of nonlinear uncertain systems with discontinuous disturbances

Abstract: Summary In this paper, the tracking control problem is considered for a class of uncertain nonlinear systems with infinite discontinuous points in the external disturbance. The extended state observer–based 2-degree-of-freedom control is used with one degree to estimate and cancel the “total disturbance” and the other to force the closed-loop system to have desired characteristics. The tracking error between the state vector and its ideal trajectory in the entire transient process is adequately discussed to illuminate the performance of resulting control systems. The quantitative analysis shows that the tracking error can be small enough by tuning the bandwidth of the extended state observer. Moreover, the necessary and sufficient condition for the tracking error and the estimation error of the “total disturbance” to converge to zero is presented. The simulation results of a motion test demonstrate that the desired performance of the control system can be achieved despite discontinuous disturbance and nonlinear uncertainties.

Event-triggered adaptive backstepping control for parametric strict-feedback nonlinear systems

Abstract: Summary This paper proposes a novel adaptive backstepping control method for parametric strict-feedback nonlinear systems with event-sampled state and input vectors via impulsive dynamical systems tools. In the design procedure, both the parameter estimator and the controller are aperiodically updated only at the event-sampled instants. An adaptive event sampling condition is designed to determine the event sampling instants. A positive lower bound on the minimal intersample time is provided to avoid Zeno behavior. The closed-loop stability of the adaptive event-triggered control system is rigorously proved via Lyapunov analysis for both the continuous and jump dynamics. Compared with the periodic updates in the traditional adaptive backstepping design, the proposed method can reduce the computation and the transmission cost. The effectiveness of the proposed method is illustrated using 2 simulation examples.

Guaranteed‐cost consensus for multiagent networks with Lipschitz nonlinear dynamics and switching topologies

Abstract: Guaranteed-cost consensus for high-order nonlinear multi-agent networks with switching topologies is investigated. By constructing a time-varying nonsingular matrix with a specific structure, the whole dynamics of multi-agent networks is decomposed into the consensus and disagreement parts with nonlinear terms, which is the key challenge to be dealt with. An explicit expression of the consensus dynamics, which contains the nonlinear term, is given and its initial state is determined. Furthermore, by the structure property of the time-varying nonsingular transformation matrix and the Lipschitz condition, the impacts of the nonlinear term on the disagreement dynamics are linearized and the gain matrix of the consensus protocol is determined on the basis of the Riccati equation. Moreover, an approach to minimize the guaranteed cost is given in terms of linear matrix inequalities. Finally, the numerical simulation is shown to demonstrate the effectiveness of theoretical results.

A game theory approach for cooperative control to improve data quality and false data detection in WSN

Abstract: New solutions are required for the management of heterogeneous distributed sensor networks in order to address the problem of data quality and false data detection in wireless sensor networks (WSNs). In this paper, we present a nonlinear cooperative control algorithm based on game theory. Here, a new model is proposed for the automatic processing and management of information in heterogeneous distributed WSNs. We apply our algorithm to a case study with the aim of improving the quality of temperature data collected from indoor surfaces by a WSN. Unlike the classic unsupervised methods, in the proposed algorithm, it is not necessary to define the number of clusters beforehand. Once the game reaches the game equilibrium, the resulting number of clusters can be used as input for the unsupervised classification analysis. Anomalous temperature values are corrected according to their neighborhood, without modifying the temperature clusters.

Sampled‐data consensus of nonlinear multiagent systems subject to cyber attacks

Abstract: Summary This paper is concerned with the sampled-data consensus problem for a class of nonlinear multiagent systems subject to cyber attacks. The considered attacks are assumed to be recoverable, which destroy the connectivity of the network topology with directed spanning tree. In light of the designed sampled-data control protocol, a more general switched system is proposed to model both the cyber attacks and the sampled-data mechanism within a unified framework. Then, by using the contradiction methods, the solution of a class of differential equations is provided to deal with the technical challenge resulting from the switching and sampling issues. Furthermore, in terms of such a solution combined with the constructed piecewise Lyapunov function, sufficient conditions are derived under which the nonlinear multiagent systems subject to attacks achieve the consensus exponentially. The relationship between the attack frequency and the sampling period is also revealed through the obtained conditions. Finally, simulations are given to show the effectiveness of the proposed results.

Multivariable finite‐time output feedback trajectory tracking control of quadrotor helicopters

Abstract: Summary A continuous multivariable output feedback control scheme is developed for trajectory tracking and attitude stabilization of quadrotor helicopters. The whole closed-loop system is composed by position loop and attitude loop. The homogeneous technique is used to design finite-time stabilizing controller and observer in each loop. The virtual control is introduced in position loop to ensure that the real control is smooth enough such that it can be tracked by attitude loop. The finite-time stability of the closed-loop system is guaranteed through homogeneity and Lyapunov analysis. Finally, the efficiency of the proposed algorithm is illustrated by numerical simulations.

Controllability of multiagent systems based on path and cycle graphs

Abstract: Summary This paper studies the controllability of multiagent systems based on path and cycle graphs. For paths or cycles, sufficient and necessary conditions are presented for determining the locations of leaders under which the controllability can be realized. Specifically, the controllability of a path is shown to be determined by a set generated only from its odd factors, and the controllability of a cycle is determined by whether the distance between 2 leaders belongs to a set generated from its even (odd) factors when the number of its nodes is even (odd). For both graphs, the dimension of the controllable subspace is also derived. Moreover, the technique used in the derivation of the above results is further used to get sufficient and necessary conditions for several different types of graphs generated from path and cycle topologies. These types of graphs can be regarded as typical topologies in the study of multiagent controllability, and accordingly the obtained results have meaningful enlightenment for the research in this field.

Adaptive dynamic surface asymptotic tracking for a class of uncertain nonlinear systems

Abstract: Summary This paper contributes to dynamic surface asymptotic tracking for a class of uncertain nonlinear systems in strict-feedback form. By utilizing the nonlinear filters with a positive time-varying integral function, an adaptive state feedback controller is explicitly designed via a dynamic surface approach, where the compensating term with the estimate of an unknown bound is introduced to eliminate the effect raised by the boundary layer error at each step. Compared with the existing results in the literature, the proposed control scheme not only avoids the issue of “explosion of complexity” inherent in the backstepping procedure but also holds the asymptotic output tracking. Finally, simulation results are presented to verify the effectiveness of the proposed methodology.

Input‐to‐state exponents and related ISS for delayed discrete‐time systems with application to impulsive effects

Abstract: Summary This paper aims to investigate the input-to-state exponents (IS-e) and the related input-to-state stability (ISS) for delayed discrete-time systems (DDSs). By using the method of variation of parameters and introducing notions of uniform and weak uniform M-matrix, the estimates for 3 kinds of IS-e are derived for time-varying DDSs. The exponential ISS conditions with parts suitable for infinite delays are thus established, by which the difference from the time-invariant case is shown. The exponential stability of a time-varying DDS with zero external input cannot guarantee its ISS. Moreover, based on the IS-e estimates for DDSs, the exponential ISS under events criteria for DDSs with impulsive effects are obtained. The results are then applied in 1 example to test synchronization in the sense of ISS for a delayed discrete-time network, where the impulsive control is designed to stabilize such an asynchronous network to the synchronization.

Reliable sliding mode finite-time control for discrete-time singular Markovian jump systems with sensor fault and randomly occurring nonlinearities

Abstract: Summary This paper focuses on the problem of finite-time H∞ control for one family of discrete-time uncertain singular Markovian jump systems with sensor fault and randomly occurring nonlinearities through a sliding mode approach. The failure of sensor is described as a general and practical continuous fault model. Nonlinear disturbance satisfies the Lipschitz condition and occurs in a probabilistic way. Firstly, based on the state estimator, the discrete-time close-loop error system can be constructed and sufficient criteria are provided to guarantee the augment system is sliding mode finite-time boundedness and sliding mode H∞ finite-time boundedness. The sliding mode control law is synthesized to guarantee the reachability of the sliding surface in a short time interval, and the gain matrices of state feedback controller and state estimator are achieved by solving a feasibility problem in terms of linear matrix inequalities through a decoupling technique. Finally, numerical examples are given to illustrate the effectiveness of the proposed method.

Distributed impulsive synchronization of Lur'e dynamical networks via parameter variation methods

Abstract: Summary This paper is devoted to investigating the exponential synchronization of coupled Lur'e dynamical networks with multiple time-varying delays and stochastic disturbance. The problem studied in this paper could be regarded as a kind of leader-following synchronization issue. As the networks may suffer from certain impulsive disturbance, an effective distributed impulsive control protocol is proposed to synchronize the stochastic Lur'e dynamical networks. According to the comparison principle, the average impulsive interval, and the extended formula for the variation of parameters, sufficient conditions are derived for successful achievement of the network synchronization with consideration to different functions of impulsive effects. Furthermore, the exponential convergence rate is obtained based on the impulsive solution equation. In addition, finally, some numerical simulations are given to illustrate the validity of the control scheme and the theoretical analysis.

Dynamic modeling and vibration control for a nonlinear 3-dimensional flexible manipulator

Abstract: In the previous chapters, modeling and vibration control of the flexible mechanical systems are restricted to one dimensional space, and only transverse deformation is taken into account. However, flexible systems may move in a three-dimensional (3D) space in practical applications. The control performance will be affected if the coupling effects between motions in three directions are ignored. In spatial and industrial environment, flexible manipulators have been widely used due to their advantages such as light weight, fast motion and low energy consumption [3, 7]. For dynamic analysis, the flexible manipulator system is regarded as a distributed parameter system (DPS) which is mathematically represented by partial differential equations (PDEs) and ordinary differential equations (ODEs) [2, 5, 8], however, these works are only considered in one dimensional space. To improve accuracy and reliability analysis, modeling and control of the flexible manipulator system in a 3D space is necessary. Therefore, several works have been done in dynamics modeling and control design when the coupling effect are taken into account.

Distributed event‐triggered consensus control with fully continuous communication free for general linear multi‐agent systems under directed graph

Abstract: Summary This paper considers the distributed event-triggered consensus problem for multi-agent systems with general linear dynamics under a directed graph. We propose a novel distributed event-triggered consensus controller with state-dependent threshold for each agent to achieve consensus. In this strategy, continuous communication in both controller update and triggering condition monitoring is not required, which means the proposed strategy is fully continuous communication free. Each agent only needs to monitor its own state continuously to determine if the event is triggered. Additionally, the approach shown here provides consensus with guaranteed positive inter-event time intervals. Therefore, there is no Zeno behavior under the proposed consensus control algorithm. Finally, numerical simulations are given to illustrate the theoretical results.

Mixed H2∕H∞ control of hidden Markov jump systems

Abstract: Summary In this work, we study the mixed H2/H∞ control for Markov jump linear systems with hidden Markov parameters. The hidden Markov process is denoted by (θ(k),θ^(k)), where the nonobservable component θ(k) represents the mode of operation of the system, whereas θ^(k) represents the observable component provided by a detector. The goal is to obtain design techniques for mixed H2/H∞ control problems, with the controllers depending only on the estimate θ^(k), for problems formulated in 3 different forms: (i) minimizing an upper bound on the H2 norm subject to a given restriction on the H∞ norm; (ii) minimizing an upper bound on the H∞ norm, while limiting the H2 norm; and (iii) minimizing a weighted combination of upper bounds of both the H2 and H∞ norms. We propose also new conditions for synthesizing robust controllers under parametric uncertainty in the detector probabilities and in the transition probabilities. The so-called cluster case for the mixed H2/H∞ control problem is also analyzed under the detector approach. The results are illustrated by means of 2 numerical examples.

Structured H∞‐control of infinite‐dimensional systems

Abstract: We develop a novel frequency-based H∞-control method for a large class of infinite-dimensional Linear-TimeInvariant systems in transfer function form. A major benefit of our approach is that reduction or identification techniques are not needed, which avoids typical distortions. Our method allows to exploit both, state-space or transfer function models, but also input/output frequency response data when only such are available. We aim at the design of practically useful H∞-controllers of any convenient structure and size. We use a non-smooth trust-region bundle method to compute arbitrarily structured locally optimal H∞-controllers for a frequency sampled approximation of the underlying infinite-dimensional H∞-problem in such a way that (i) exponential stability in closed-loop is guaranteed, and (ii) the optimal H∞-value of the approximation differs from the true infinite-dimensional value only by a prior user-specified tolerance. We demonstrate the versatility and practicality of our method on a variety of infinite-dimensional H∞-synthesis problems, including distributed and boundary control of PDEs, control of dead time and delay systems, and using a rich testing set.

Dual-rate sampled-data stabilization for active suspension system of electric vehicle

Abstract: Summary In this paper, we consider the dual-rate sampled-data state-feedback control problem for an active suspension system of an electric vehicle. In the active suspension system, there exist 2 accelerometers to measure the heave acceleration of the sprung mass and the vertical acceleration of the unsprung mass, respectively. When the 2 accelerations are measured by sampled data under different sampling periods, the difficulty arising from the dual-rate sampled data makes the active suspension stabilization problem challenging but interesting. In this paper, a linear hybrid stabilizer is proposed, which is implemented using dual-rate sampled-data state feedback. In order to deal with the more difficult stabilization problem under different triggering time instants, a coordinate transformation is proposed. A useful technical theorem is proposed in the stability analysis to show that the proposed hybrid controller can guarantee the states of the active suspension system being asymptotically stabilized or at least bounded to arbitrarily small domains. The experiment result is similar to the simulation result and indicates that the proposed active suspension controlling system is effective.

Formation control for a class of nonlinear multiagent systems using model-free adaptive iterative learning

Abstract: Summary In this paper, the problem of formation control is considered for a class of unknown nonaffine nonlinear multiagent systems under a repeatable operation environment. To achieve the formation objective, the unknown nonlinear agent's dynamic is first transformed into a compact form dynamic linearization model along the iteration axis. Then, a distributed model-free adaptive iterative learning control scheme is designed to ensure that all agents can keep their desired deviations from the reference trajectory over the whole time interval. The main results are given for the multiagent systems with fixed communication topologies and the extension to the switching topologies case is also discussed. The feature of this design is that formation control can be solved only depending on the input/output data of each agent. An example is given to demonstrate the effectiveness of the proposed method.