Showing papers in "International Journal of Robust and Nonlinear Control in 2014"

High-gain observers in nonlinear feedback control

Abstract: In this document, we present the main ideas and results concerning high-gain observers and some of their applications in control. The introduction gives a brief history of the topic. Then, a motivating second-order example is used to illustrate the key features of high-gain observers and their use in feedback control. This is followed by a general presentation of high-gain-observer theory in a unified framework that accounts for modeling uncertainty, as well as measurement noise. The paper concludes by discussing the use of high-gain observers in the robust control of minimum-phase nonlinear systems.

Distributed consensus of multi-agent systems with general linear node dynamics and intermittent communications

Abstract: SUMMARY Without assuming that the mobile agents can communicate with their neighbors all the time, the consensus problem of multi-agent systems with general linear node dynamics and a fixed directed topology is investigated. To achieve consensus, a new class of distributed protocols designed based only on the intermittent relative information are presented. By using tools from matrix analysis and switching systems theory, it is theoretically shown that the consensus in multi-agent systems with a periodic intermittent communication and directed topology containing a spanning tree can be cast into the stability of a set of low-dimensional switching systems. It is proved that there exists a protocol guaranteeing consensus if each agent is stabilizable and the communication rate is larger than a threshold value. Furthermore, a multi-step intermittent consensus protocol design procedure is provided. The consensus algorithm is then extended to solve the formation control problem of linear multi-agent systems with intermittent communication constraints as well as the consensus tracking problem with switching directed topologies. Finally, some numerical simulations are provided to verify the effectiveness of the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.

Distance-based undirected formations of single-integrator and double-integrator modeled agents in n-dimensional space

Abstract: SUMMARY We study the local asymptotic stability of undirected formations of single-integrator and double-integrator modeled agents based on interagent distance control. First, we show that n-dimensional undirected formations of single-integrator modeled agents are locally asymptotically stable under a gradient control law. The stability analysis in this paper reveals that the local asymptotic stability does not require the infinitesimal rigidity of the formations. Second, on the basis of the topological equivalence of a dissipative Hamiltonian system and a gradient system, we show that the local asymptotic stability of undirected formations of double-integrator modeled agents in n-dimensional space is achieved under a gradient-like control law. Simulation results support the validity of the stability analysis. Copyright © 2013 John Wiley & Sons, Ltd.

Finite-time formation control of multiple nonholonomic mobile robots

Abstract: SUMMARY This paper considers finite-time formation control problem for a group of nonholonomic mobile robots. The desired formation trajectory is represented by a virtual dynamic leader whose states are available to only a subset of the followers and the followers have only local interaction. First of all, a continuous distributed finite-time observer is proposed for each follower to estimate the leader's states in a finite time. Then, a continuous distributed cooperative finite-time tracking control law is designed for each mobile robot. Rigorous proof shows that the group of mobile robots converge to the desired geometric formation pattern in finite time. At the same time, all the robots can track the desired formation trajectory in finite time. Simulation example illustrates the effectiveness of our method. Copyright © 2012 John Wiley & Sons, Ltd.

Stochastic stability of semi‐Markovian jump systems with mode‐dependent delays

Abstract: SUMMARY Semi-Markovian jump systems, due to the relaxed conditions on the stochastic process, and its transition rates are time varying, can be used to describe a larger class of dynamical systems than conventional full Markovian jump systems. In this paper, the problem of stochastic stability for a class of semi-Markovian systems with mode-dependent time-variant delays is investigated. By Lyapunov function approach, together with a piecewise analysis method, a sufficient condition is proposed to guarantee the stochastic stability of the underlying systems. As more time-delay information is used, our results are much less conservative than some existing ones in literature. Finally, two examples are given to show the effectiveness and advantages of the proposed techniques. Copyright © 2013 John Wiley & Sons, Ltd.

Adaptive neural tracking control for a class of stochastic nonlinear systems

Abstract: SUMMARY This paper investigates the problem of adaptive neural control design for a class of single-input single-output strict-feedback stochastic nonlinear systems whose output is an known linear function. The radial basis function neural networks are used to approximate the nonlinearities, and adaptive backstepping technique is employed to construct controllers. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. The salient property of the proposed scheme is that only one adaptive parameter is needed to be tuned online. So, the computational burden is considerably alleviated. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.

Finite‐time stability of switched positive linear systems

Abstract: SUMMARY This brief paper addresses the finite-time stability problem of switched positive linear systems. First, the concept of finite-time stability is extended to positive linear systems and switched positive linear systems. Then, by using the state transition matrix of the system and copositive Lyapunov function, we present a necessary and sufficient condition and a sufficient condition for finite-time stability of positive linear systems. Furthermore, two sufficient conditions for finite-time stability of switched positive linear systems are given by using the common copositive Lyapunov function and multiple copositive Lyapunov functions, a class of switching signals with average dwell time is designed to stabilize the system, and a computational method for vector functions used to construct the Lyapunov function of systems is proposed. Finally, a concrete application is provided to demonstrate the effectiveness of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.

Multi‐surface sliding control for fast finite‐time leader–follower consensus with high order SISO uncertain nonlinear agents

Abstract: SUMMARY In this paper, multi surface sliding cooperative control scheme is presented and new multiple sliding surfaces are proposed. It is proven that, for the setup that each agent is described by a chain of integrators, where the last integrator is perturbed by a bounded disturbance, leader–follower consensus can be achieved on these sliding surfaces if the communication graph has a directed spanning tree. Also, sliding variables can be driven to the sliding surfaces in fast finite time by the nonsmooth control law. The fast finite-time Lyapunov stability theorem, the terminal sliding control technique, and the adding a power integrator design approach are used in our proposed control. Simulation results demonstrate the effectiveness of the proposed scheme. Copyright © 2013 John Wiley & Sons, Ltd.

Interval observers for discrete-time systems

Abstract: Interval observers are constructed for discrete-time systems. First, time-invariant interval observers are proposed for a family of nonlinear systems. Second, it is shown that, for any time-invariant exponentially stable discrete-time linear system with additive disturbances, time-varying exponentially stable discrete-time interval observers can be constructed. The latter result relies on the design of time-varying changes of coordinates, which transform a linear system into a nonnegative one. Copyright © 2013 John Wiley & Sons, Ltd.

Online adaptive algorithm for optimal control with integral reinforcement learning

Abstract: SUMMARY In this paper, we introduce an online algorithm that uses integral reinforcement knowledge for learning the continuous-time optimal control solution for nonlinear systems with infinite horizon costs and partial knowledge of the system dynamics. This algorithm is a data-based approach to the solution of the Hamilton–Jacobi–Bellman equation, and it does not require explicit knowledge on the system's drift dynamics. A novel adaptive control algorithm is given that is based on policy iteration and implemented using an actor/critic structure having two adaptive approximator structures. Both actor and critic approximation networks are adapted simultaneously. A persistence of excitation condition is required to guarantee convergence of the critic to the actual optimal value function. Novel adaptive control tuning algorithms are given for both critic and actor networks, with extra terms in the actor tuning law being required to guarantee closed loop dynamical stability. The approximate convergence to the optimal controller is proven, and stability of the system is also guaranteed. Simulation examples support the theoretical result. Copyright © 2013 John Wiley & Sons, Ltd.

Group consensus control for double‐integrator dynamic multiagent systems with fixed communication topology

Abstract: SUMMARY The problem of group consensus is investigated in this paper, where all agents possess double-integrator dynamics. Two different kinds of consensus protocols are proposed for networks with fixed communication topology to reach group consensus for the agents’ positions and velocities. Convergence analysis is discussed, and necessary and/or sufficient conditions are presented for multiagent systems to achieve group consensus. The first protocol leads to dynamic consensus where positions of all agents reach time-varying consensus values. By applying the second protocol, both the agents’ positions and their velocities reach constant consensus values. That is, static consensus is achieved. Simulation examples are given to show the effectiveness of the theoretical results.Copyright © 2012 John Wiley & Sons, Ltd.

Sliding mode control and active disturbance rejection control to the stabilization of one-dimensional Schrödinger equation subject to boundary control matched disturbance

Abstract: SUMMARY In this paper, we are concerned with the boundary stabilization of a one-dimensional anti-stable Schrodinger equation subject to boundary control matched disturbance. We apply both the sliding mode control (SMC) and the active disturbance rejection control (ADRC) to deal with the disturbance. By the SMC approach, the disturbance is supposed to be bounded only. The existence and uniqueness of the solution for the closed-loop system is proved and the ‘reaching condition’ is obtained. Considering the SMC usually requires the large control gain and may exhibit chattering behavior, we develop the ADRC to attenuate the disturbance for which the derivative is also supposed to be bounded. Compared with the SMC, the advantage of the ADRC is not only using the continuous control but also giving an online estimation of the disturbance. It is shown that the resulting closed-loop system can reach any arbitrary given vicinity of zero as time goes to infinity and high gain tuning parameter goes to zero. Copyright © 2013 John Wiley & Sons, Ltd.

Output synchronization for heterogeneous networks of introspective right-invertible agents

Abstract: In this paper, we consider the output synchronization problem for heterogeneous networks of right-invertible linear agents. We assume that all the agents are introspective, meaning that they have access to their own local measurements. Under this assumption, we then propose a decentralized control scheme for solving the output synchronization problem for a set of network topologies. The proposed scheme can also be applied to solve the output formation problem with arbitrary formation vectors. We also consider the regulation of output synchronization problem, where the output of each agent has to track an a priori specified reference trajectory, generated by an exosystem. In this case, we assume that the root agent has access to its own output relative to the reference trajectory.

Adaptive iterative learning control for coordination of second-order multi-agent systems

Abstract: SUMMARY In this paper, an efficient framework is proposed to the consensus and formation control of distributed multi-agent systems with second-order dynamics and unknown time-varying parameters, by means of an adaptive iterative learning control approach. Under the assumption that the acceleration of the leader is unknown to any follower agents, a new adaptive auxiliary control and the distributed adaptive iterative learning protocols are designed. Then, all follower agents track the leader uniformly on [0,T] for consensus problem and keep the desired distance from the leader and achieve velocity consensus uniformly on [0,T] for the formation problem, respectively. The distributed multi-agent coordinations performance is analyzed based on the Lyapunov stability theory. Finally, simulation examples are given to illustrate the effectiveness of the proposed protocols in this paper.Copyright © 2013 John Wiley & Sons, Ltd.

Robust fault reconstruction for linear parameter varying systems using sliding mode observers

Abstract: SUMMARY This paper presents a robust fault detection and isolation scheme using a sliding mode observer based on a linear parameter varying system, with fault reconstruction capability Both actuator and sensor fault reconstruction schemes are considered that possess robustness against a certain class of uncertainty and corrupted measurements For actuator fault reconstruction, the input distribution matrix (associated with the actuators being monitored) is factorized into fixed and varying components LMIs are used to design the key observer parameters in order to minimize the effect of uncertainty and measurement corruption on the fault reconstruction signal The faults are reconstructed using the output error injection signal associated with the nonlinear term of the sliding mode observer For sensor fault reconstruction, the idea is to reformulate the problem into an actuator fault reconstruction scenario so that the same design procedure can be applied This is achieved by augmenting the original system with the filtered sensors being monitored Simulations using a full nonlinear model of a large transport aircraft are presented and show good fault reconstruction performance Copyright © 2013 John Wiley & Sons, Ltd

Active actuator fault-tolerant control of a wind turbine benchmark model

Abstract: SUMMARY This paper describes the design of an active fault-tolerant control scheme that is applied to the actuator of a wind turbine benchmark. The methodology is based on adaptive filters obtained via the nonlinear geometric approach, which allows to obtain interesting decoupling property with respect to uncertainty affecting the wind turbine system. The controller accommodation scheme exploits the on-line estimate of the actuator fault signal generated by the adaptive filters. The nonlinearity of the wind turbine model is described by the mapping to the power conversion ratio from tip-speed ratio and blade pitch angles. This mapping represents the aerodynamic uncertainty, and usually is not known in analytical form, but in general represented by approximated two-dimensional maps (i.e. look-up tables). Therefore, this paper suggests a scheme to estimate this power conversion ratio in an analytical form by means of a two-dimensional polynomial, which is subsequently used for designing the active fault-tolerant control scheme. The wind turbine power generating unit of a grid is considered as a benchmark to show the design procedure, including the aspects of the nonlinear disturbance decoupling method, as well as the viability of the proposed approach. Extensive simulations of the benchmark process are practical tools for assessing experimentally the features of the developed actuator fault-tolerant control scheme, in the presence of modelling and measurement errors. Comparisons with different fault-tolerant schemes serve to highlight the advantages and drawbacks of the proposed methodology. Copyright © 2013 John Wiley & Sons, Ltd.

State estimation for two-dimensional complex networks with randomly occurring nonlinearities and randomly varying sensor delays

Abstract: SUMMARY This paper is concerned with the state estimation problem for two-dimensional (2D) complex networks with randomly occurring nonlinearities and randomly varying sensor delays. To describe the fact that measurement delays may occur in a probabilistic way, the randomly varying sensor delays are introduced in the delayed sensor measurements. The randomly occurring nonlinearity, on the other hand, is included to account for the phenomenon of nonlinear disturbances appearing in a random fashion that is governed by a Bernoulli distributed white sequence with known conditional probability. The stochastic Brownian motions are also considered, which enter into not only the coupling terms of the complex networks but also the measurements of the output systems. Through available actual network measurements, a state estimator is designed to estimate the true states of the considered 2D complex networks. By utilizing an energy-like function, the Kronecker product and some stochastic analysis techniques, several sufficient criteria are established in terms of matrix inequalities under which the 2D estimation error dynamics is globally asymptotically stable in the mean square. Furthermore, the explicit expression of the estimator gains is also characterized. Finally, a numerical example is provided to demonstrate the effectiveness of the design method proposed in this paper. Copyright © 2012 John Wiley & Sons, Ltd.

Distributed filtering in sensor networks with randomly occurring saturations and successive packet dropouts

Abstract: SUMMARY This paper is concerned with the distributed filtering problem for a class of nonlinear systems with randomly occurring sensor saturations (ROSS) and successive packet dropouts in sensor networks. The issue of ROSS is brought up to account for the random nature of sensor saturations in a networked environment of sensors, and accordingly, a novel sensor model is proposed to describe both the ROSS and successive packet dropouts within a unified framework. Two sets of Bernoulli distributed white sequences are introduced to govern the random occurrences of the sensor saturations and successive packet dropouts. Through available output measurements from not only the individual sensor but also its neighboring sensors, a sufficient condition is established for the desired distributed filter to ensure that the filtering dynamics is exponentially mean-square stable and the prescribed performance constraint is satisfied. The solution of the distributed filter gains is characterized by solving an auxiliary convex optimization problem. Finally, a simulation example is provided to show the effectiveness of the proposed filtering scheme. Copyright © 2013 John Wiley & Sons, Ltd.

An efficient online trajectory generating method for underactuated crane systems

Abstract: SUMMARY In this paper, a trajectory planning approach is proposed for underactuated overhead cranes. Different from existing trajectory planning methods, the presented approach generates trajectory commands online without the necessity of iterative optimization, which is convenient for practical implementation. We demonstrate the performance of the proposed method, including swing elimination and precise trolley positioning, with rigorous Lyapunov-based mathematical analysis. Both numerical simulation and experimental results suggest that the presented method is feasible and efficient for practical applications. Copyright © 2013 John Wiley & Sons, Ltd.

Formation control for multi-agent systems through an iterative learning design approach

Abstract: SUMMARY This paper deals with formation control problems for multi-agent systems by using iterative learning control (ILC) design approaches. Distributed formation ILC algorithms are presented to enable all agents in directed graphs to achieve the desired relative formations perfectly over a finite-time interval. It is shown that not only asymptotic stability but also monotonic convergence of multi-agent formation ILC can be accomplished, and the convergence conditions in terms of linear matrix inequalities can be simultaneously established. The derived results are also applicable to multi-agent systems that are subject to stochastic disturbances and model uncertainties. Furthermore, the feasibility of convergence conditions and the effect of communication delays are discussed for the proposed multi-agent formation ILC algorithms. Simulation results are given for uncertain multi-agent systems to verify the theoretical study. Copyright © 2012 John Wiley & Sons, Ltd.

A new result on the delay‐dependent stability of discrete systems with time‐varying delays

Abstract: SUMMARY This paper proposes an improvement to the delay-dependent stability of discrete systems with time-varying delays. The approach is based on the observation that the positive definiteness of a chosen Lyapunov–Krasovskii functional does not necessarily require all the involved symmetric matrices to be positive definite, which has been overlooked in the literature. The derived delay-dependent stability conditions are in terms of linear matrix inequalities. It is theoretically proved that our results are less conservative than the corresponding ones obtained by requiring the positive definiteness of all the symmetric matrices in a chosen Lyapunov–Krasovskii functional. The importance of the present approach is that a great number of delay-dependent analysis and synthesis results obtained by the aforementioned requirement in the literature can be improved by the present approach without introducing any new decision variables. Copyright © 2013 John Wiley & Sons, Ltd.

Second‐order consensus for directed multi‐agent systems with sampled data

Abstract: SUMMARY This paper deals with the consensus problem of second-order multi-agent systems with sampled data. Because of the unavailable velocity information, consensus problem is studied only by using the sampled position information. The final consensus states of multi-agent system are given. And a necessary and sufficient consensus condition is provided, which depends on the parameters of sampling interval, eigenvalues of Laplacian matrix, and coupling strengths. Then, the case that both the sampled position and velocity information can be obtained is discussed. On the basis of introducing a time-varying piecewise-continuous delay and proposing a novel time-dependent Lyapunov functional, the sufficient consensus condition is presented, and the upper bound of sampling interval can be estimated. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright © 2013 John Wiley & Sons, Ltd.

IQC-synthesis with general dynamic multipliers

Abstract: SUMMARY Analogously to the existing μ-synthesis tools, we propose an alternative algorithm for the systematic design of robust controllers based on an iteration of standard nominal controller synthesis and integral quadratic constraint (IQC) analysis with general dynamic multipliers. The suggested algorithm enables us to perform robust controller synthesis for a significantly larger class of uncertainties if compared with the existing methods. Indeed, while the classical approaches are restricted to the use of real/complex time invariant or arbitrarily fast time-varying parametric uncertainties, the IQC framework also offers, for example, the possibility to efficiently handle sector-bounded and slope restricted nonlinearities or time-varying parametric uncertainties and uncertain time-varying time-delays, both with bounds on the rate-of-variation. Secondly, in contrast to the classical approaches, the proposed techniques completely avoid gridding and curve-fitting. We present new insights that allow us to reformulate the robust IQC analysis LMIs into a standard quadratic performance problem. This enables us to generate suitable initial conditions for each subsequent iteration step. Depending on the size of the problem, this can significantly speed up the synthesis process. The results are illustrated by means of two numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.

Composite hierarchical anti-disturbance control for nonlinear systems with DOBC and fuzzy control

Abstract: SUMMARY Anti-disturbance control and estimation problem is introduced for a class of nonlinear system subject to disturbances. The adaptive disturbance observers are constructed separately from the controller design to estimate the disturbance with partial known information. By integrating disturbance-observer-based control with fuzzy control, a novel type of composite hierarchical anti-disturbance control scheme is presented for a class of nonlinear system with unknown nonlinear dynamics. Simulations for a flight control system are given to demonstrate the effectiveness of the results compared with the previous schemes.Copyright © 2012 John Wiley & Sons, Ltd.

Cooperative robust output regulation of a class of heterogeneous linear uncertain multi-agent systems†

Abstract: SUMMARY The cooperative output regulation of a linear multi-agent system can be viewed as a generalization of the leader-following consensus problem and was studied recently for the case where the system uncertain parameters vary in a sufficiently small neighborhood of their nominal value. This case was handled by the internal model design which converts the problem into a simultaneous eigenvalue placement problem of an augmented multi-agent system. In this paper, we further consider the cooperative robust output regulation problem for a class of minimum phase linear multi-agent systems in the sense that the controller allows the system uncertain parameters to vary in an arbitrarily prescribed compact subset. For this purpose, we introduce a new type of internal model that allows the cooperative robust output regulation problem of the given plant to be converted into a robust stabilization problem of an augmented multi-agent system. We then solve our problem by combining a simultaneous high-gain state feedback control technique and a distributed high-gain observer technique. A special case of our result leads to the solution of the leader-following robust consensus problem for a class of uncertain multi-agent systems. Copyright © 2013 John Wiley & Sons, Ltd.

A barrier composite energy function approach for robot manipulators under alignment condition with position constraints

Abstract: SUMMARY In this work, we propose an iterative learning control scheme with a novel barrier composite energy function approach to deal with position constrained robotic manipulators with uncertainties under alignment condition. The classical assumption of initial resetting condition is removed. Through rigorous analysis, we show that uniform convergence is guaranteed for joint position and velocity tracking error. By introducing a novel tan-type barrier Lyapunov function into barrier composite energy function and keeping it bounded in closed-loop analysis, the constraint on joint position vector will not be violated. A simulation study has further demonstrated the efficacy of the proposed scheme. Copyright © 2013 John Wiley & Sons, Ltd.

Output feedback control for a class of stochastic high-order nonlinear systems with time-varying delays

Abstract: SUMMARY This paper discusses the problem of output feedback stabilization for a more general class of stochastic high-order nonlinear systems with time-varying delays. On the basis of a subtle homogeneous observer and controller construction, and the homogeneous domination approach, the closed-loop system is globally asymptotically stable in probability, by choosing an appropriate Lyapunov–Krasovskii functional. An example is given to illustrate the effectiveness of the proposed design procedure. Copyright © 2013 John Wiley & Sons, Ltd.

Observer-based consensus of second-order multi-agent system with fixed and stochastically switching topology via sampled data

Abstract: SUMMARY This paper addresses the distributed observer-based consensus problem of second-order multi-agent systems via sampled data. Firstly, for the case of fixed topology, a velocity-independent distributed control law is proposed by designing a distributed observer to estimate the unavailable velocity, then a sufficient and necessary condition of consensus on design parameters and sampling period is obtained by using the matrix analysis method. Secondly, for the case of stochastically switching topology, a sufficient and necessary condition of mean square consensus is also proposed and proven, and an algorithm is provided to design the parameters in the consensus protocol. Two simulation examples are given to illustrate the effectiveness of the proposed consensus algorithms. Copyright © 2012 John Wiley & Sons, Ltd.

On adaptive sliding mode control without switching gain overestimation

Abstract: SUMMARY This paper presents some further results on adaptive sliding mode control (ASMC) for a class of nonlinear systems with bounded uncertain parameters. Given a large initial tracking error, current ASMC design generally produces an unnecessarily large switching gain, consequently leading to a serious chattering problem or a large-amplitude control jump for the continuous counterpart. To solve such an overadaptation problem, the switching gain adaptation mechanism is first analyzed in this paper, and the adaptation induced by the initial tracking error is suggested to be removed. Then, by exploiting the global sliding mode feature of time-varying sliding mode control and integral sliding mode control, we present two effective methodologies for ASMC design. The proposed ASMC algorithms ensure that there is no overestimation of the switching gain and the system response is not slowed down when a small switching gain is generated. The validity of the proposed methods is verified by both theoretical analysis and simulation results. Copyright © 2012 John Wiley & Sons, Ltd.