Showing papers in "International Journal of Robust and Nonlinear Control in 2012"

Consensus in multi-agent systems with communication constraints

Abstract: The problem of second-order consensus is investigated in this paper for a class of multi-agent systems with a fixed directed topology and communication constraints where each agent is assumed to share information only with its neighbors on some disconnected time intervals. A novel consensus protocol designed based on synchronous intermittent local information feedback is proposed to coordinate the states of agents to converge to second-order consensus under a fixed strongly connected topology, which is then extended to the case where the communication topology contains a directed spanning tree. By using tools from algebraic graph theory and Lyapunov control approach, it is proved that second-order consensus can be reached if the general algebraic connectivity of the communication topology is larger than a threshold value and the mobile agents communicate with their neighbors frequently enough as the network evolves. Finally, a numerical example is simulated to verify the theoretical analysis. Copyright © 2011 John Wiley & Sons, Ltd.

Model Predictive Control approach for guidance of spacecraft rendezvous and proximity maneuvering

Abstract: SUMMARY Traditionally, rendezvous and proximity maneuvers have been performed using open-loop maneuver planning techniques and ad hoc error corrections. In this paper, a Model Predictive Control (MPC) approach is applied to spacecraft rendezvous and proximity maneuvering problems in the orbital plane. We demonstrate that various constraints arising in these maneuvers can be effectively handled with the MPC approach. These include constraints on thrust magnitude, constraints on spacecraft positioning within Line-of-Sight cone while approaching the docking port on a target platform, and constraints on approach velocity to match the velocity of the docking port. The two cases of a nonrotating and a rotating (tumbling) platform are treated separately, and trajectories are evaluated in terms of maneuver time and fuel consumption. For the case when the platform is not rotating and the docking port position is fixed with respect to the chosen frame, an explicit offline solution of the MPC optimization problem is shown to be possible; this explicit solution has a form of a piecewise affine control law suitable for online implementation without an on-board optimizer. In the case of a fast rotating platform, it is, however, shown that the prediction of the platform rotation is necessary to successfully accomplish the maneuvers and to reduce fuel consumption. Finally, the proposed approach is applied to debris avoidance maneuvers with the debris in the spacecraft rendezvous path. The significance of this paper is in demonstrating that Model Predictive Control can be an effective feedback control approach to satisfy various maneuver requirements, reduce fuel consumption, and provide robustness to disturbances. Copyright © 2012 John Wiley & Sons, Ltd.

Robust ℋ︁∞ PID control for multivariable networked control systems with disturbance/noise attenuation

Abstract: In this paper, we study the design problem of PID controllers for networked control systems (NCSs) with polyhedral uncertainties. The load disturbance and measurement noise are both taken into account in the modeling to better reflect the practical scenario. By using a novel technique, the design problem of PID controllers is converted into a design problem of output feedback controllers. Our goal of this paper is two-fold: (1) To design the robust PID tracking controllers for practical models; (2) To develop the robust ℋ∞ PID control such that load and reference disturbances can be attenuated with a prescribed level. Sufficient conditions are derived by employing advanced techniques for achieving delay dependence. The proposed controller can be readily designed based on iterative suboptimal algorithms. Finally, four examples are presented to show the effectiveness of the proposed methods. Copyright © 2011 John Wiley & Sons, Ltd.

Online solution of nonlinear two-player zero-sum games using synchronous policy iteration

Abstract: SUMMARY The two-player zero-sum (ZS) game problem provides the solution to the bounded L2-gain problem and so is important for robust control. However, its solution depends on solving a design Hamilton–Jacobi–Isaacs (HJI) equation, which is generally intractable for nonlinear systems. In this paper, we present an online adaptive learning algorithm based on policy iteration to solve the continuous-time two-player ZS game with infinite horizon cost for nonlinear systems with known dynamics. That is, the algorithm learns online in real time an approximate local solution to the game HJI equation. This method finds, in real time, suitable approximations of the optimal value and the saddle point feedback control policy and disturbance policy, while also guaranteeing closed-loop stability. The adaptive algorithm is implemented as an actor/critic/disturbance structure that involves simultaneous continuous-time adaptation of critic, actor, and disturbance neural networks. We call this online gaming algorithm ‘synchronous’ ZS game policy iteration. A persistence of excitation condition is shown to guarantee convergence of the critic to the actual optimal value function. Novel tuning algorithms are given for critic, actor, and disturbance networks. The convergence to the optimal saddle point solution is proven, and stability of the system is also guaranteed. Simulation examples show the effectiveness of the new algorithm in solving the HJI equation online for a linear system and a complex nonlinear system. Copyright © 2011 John Wiley & Sons, Ltd.

Global control of nonlinear systems with uncertain output function using homogeneous domination approach

Abstract: SUMMARY This paper addresses the problem of using output feedback to globally control a class of nonlinear systems whose output functions are not precisely known. First, for the nominal linear system, we design a homogeneous state compensator without requiring precise information of the output function, and construct a nonlinear stabilizer with adjustable coefficients by using the generalized adding a power integrator technique. Then based on the homogeneous domination approach, a scaling gain is introduced into the proposed output feedback controller, which can be used by tuning the scaling gain to solve: (i) the problem of global output feedback stabilization for a class of upper-triangular systems; and (ii) the problem of global practical output tracking for a class of lower-triangular systems. Copyright © 2011 John Wiley & Sons, Ltd.

Cooperative control of dynamically decoupled systems via distributed model predictive control

Abstract: SUMMARY In this paper, we propose a general framework for distributed model predictive control of discrete-time nonlinear systems with decoupled dynamics but subject to coupled constraints and a common cooperative task. To ensure recursive feasibility and convergence to the desired cooperative goal, the systems optimize a local cost function in a sequential order, whereas only neighbor-to-neighbor communication is allowed. In contrast to most of the existing distributed model predictive control schemes in the literature, we do not necessarily consider the stabilization of an a priori known set point. Instead, also other cooperative control tasks such as consensus and synchronization problems can be handled within the proposed framework. In particular, one of our main contributions is to show how for the latter case the terminal cost functions and the terminal region can be suitably defined and computed. Furthermore, we illustrate our results with simulation examples. Copyright © 2012 John Wiley & Sons, Ltd.

Networked-based stabilization via discontinuous Lyapunov functionals

Abstract: SUMMARY This paper presents a new stability and L2-gain analysis of linear Networked Control Systems (NCS). The new method is inspired by discontinuous Lyapunov functions that were introduced by Naghshtabrizitextitet al. (Syst. Control Lett. 2008; 57:378–385; Proceedings 26th American Control Conference, New York, U.S.A., July 2007) in the framework of impulsive system representation. Most of the existing works on the stability of NCS (in the framework of time delay approach) are reduced to some Lyapunov-based analysis of systems with uncertain and bounded time-varying delays. This analysis via time-independent Lyapunov functionals does not take advantage of the sawtooth evolution of the delays induced by sample-and-hold. The latter drawback was removed by Fridman (Automatica 2010; 46:421–427), where time-dependent Lyapunov functionals for sampled-data systems were introduced. This led to essentially less conservative results. The objective of the present paper is to extend the time-dependent Lyapunov functional approach to NCS, where variable sampling intervals, data packet dropouts, and variable network-induced delays are taken into account. The Lyapunov functionals in this paper depend on time and on the upper bound of the network-induced delay, and these functionals do not grow along the input update times. The new analysis is applied to the state-feedback and to a novel network-based static output-feedback H∞ control problems. Numerical examples show that the novel discontinuous terms in Lyapunov functionals essentially improve the results. Copyright © 2011 John Wiley & Sons, Ltd.

State‐feedback stabilization for a class of stochastic time‐delay nonlinear systems

Abstract: SUMMARY This paper investigates the problem of state-feedback stabilization for a class of lower-triangular stochastic time-delay nonlinear systems without controllable linearization. By extending the adding-a-power-integrator technique to the stochastic time-delay systems, a state-feedback controller is explicitly constructed such that the origin of closed-loop system is globally asymptotically stable in probability. The main design difficulty is to deal with the uncontrollable linearization and the nonsmooth system perturbation, which, under some appropriate assumptions, can be solved by using the adding-a-power-integrator technique. Two simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this paper.Copyright © 2011 John Wiley & Sons, Ltd.

Optimization of airborne wind energy generators

Abstract: This paper presents novel results related to an innovative airborne wind energy technology, named Kitenergy, for the conversion of high-altitude wind energy into electricity. The research activities carried out in the last five years, including theoretical analyses, numerical simulations, and experimental tests, indicate that Kitenergy could bring forth a revolution in wind energy generation, providing renewable energy in large quantities at a lower cost than fossil energy. This work investigates three important theoretical aspects: the evaluation of the performance achieved by the employed control law, the optimization of the generator operating cycle, and the possibility to generate continuously a constant and maximal power output. These issues are tackled through the combined use of modeling, control, and optimization methods that result to be key technologies for a significant breakthrough in renewable energy generation.

Gain-scheduled dynamic output feedback control for discrete-time LPV systems

Abstract: SUMMARY This paper presents synthesis conditions for the design of gain-scheduled dynamic output feedback controllers for discrete-time linear parameter-varying systems The state-space matrix representation of the plant and of the controller can have a homogeneous polynomial dependency of arbitrary degree on the scheduling parameter As an immediate extension, conditions for the synthesis of a multiobjective ℋ∞ and ℋ2 gain-scheduled dynamic feedback controller are also provided The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real-time If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results The geometric properties of the uncertainty domain are exploited to derive finite sets of linear matrix inequalities based on the existence of a homogeneous polynomially parameter-dependent Lyapunov function An application of the control design to a realistic engineering problem illustrates the benefits of the proposed approach Copyright © 2011 John Wiley & Sons, Ltd

A delay-dependent bounded real lemma for singular LPV systems with time-variant delay

Abstract: SUMMARY This paper is concerned with establishing a delay-dependent bounded real lemma (BRL) for singular linear parameter-varying (LPV) systems with time-variant delay. In terms of linear matrix inequality, a delay-dependent BRL is presented to ensure singular time-delay LPV systems to be admissible and satisfy a prescribed H∞ performance level. The BRL is obtained based on the construction of a parameter-dependent Lyapunov–Krasovskii functional. The effectiveness of the proposed approach is shown by several numerical examples. Copyright © 2011 John Wiley & Sons, Ltd.

Flocking of multi-agent dynamical systems with intermittent nonlinear velocity measurements

Abstract: SUMMARY In this paper, the problem of flocking control in networks of multiple dynamical agents with intermittent nonlinear velocity measurements is studied. A new flocking algorithm is proposed to guarantee the states of the velocity variables of all the dynamical agents to converge to consensus while ensuring collision avoidance of the whole group, where each agent is assumed to obtain some nonlinear measurements of the relative velocity between itself and its neighbors only on a sequence of non-overlapping time intervals. The results are then extended to the scenario of flocking with a nonlinearly dynamical virtual leader, where only a small fraction of agents are informed and each informed agent can obtain intermittent nonlinear measurements of the relative velocity between itself and the virtual leader. Theoretical analysis shows that the achieved flocking in systems with or without a virtual leader is robust against the time spans of the agent speed-sensors. Finally, some numerical simulations are provided to illustrate the effectiveness of the new design. Copyright © 2011 John Wiley & Sons, Ltd.

Integral partitioning approach to robust stabilization for uncertain distributed time-delay systems

Abstract: SUMMARY In this paper, the problems of robust delay-dependent stability analysis and stabilization are investigated for distributed delay systems with linear fractional uncertainties. By introducing an integral partitioning technique, a new form of Lyapunov functional is constructed and improved distributed delay-dependent stability conditions are established in terms of linear matrix inequalities. Based on the criterion, a design algorithm for a state-feedback controller is proposed. Following similar lines, we extend these results to uncertain distributed delay systems. The results developed in this paper can tolerate larger allowable delay than existing ones in the literature, which is illustrated by several examples. Copyright © 2011 John Wiley & Sons, Ltd.

Delay-dependent exponential H ∞ filtering for discrete-time switched delay systems

Abstract: This chapter is concerned with the problems of delay-dependent exponential H ∞ filtering and model reduction for discrete-time switched delay systems under average dwell time (ADT) switching signals. First, by introducing a proper factor to construct a novel Lyapunov-Krasovskii function and using ADT approach, sufficient conditions for the solvability of exponential H ∞ filtering problem, dependent on the upper and lower bounds of the time-varying delay, are obtained in terms of linear matrix inequalities (LMIs). The second objective is to construct a reduced-order model, which ensures that the resulting error system under switching signal with ADT is exponentially stable with an H ∞ norm bound. A weighting factor α is introduced to present sufficient conditions on the existence of reduced-order model in terms of strict LMIs, which lessen the computation complexity. Two numerical examples are presented to demonstrate the effectiveness of the developed results.

Controllability of switching networks of multi‐agent systems

Abstract: SUMMARY This paper addresses the controllability of a switching network of multi-agent systems with a leader obeying nearest-neighbor communication rules. The leader is a particular agent acting as an external input to control other member agents. Some computationally efficient sufficient conditions for such multi-agent systems to be controllable are derived. The results show that a multi-agent system can be controllable even if each of its subsystem is not controllable, by appropriately selecting one of the agents as the leader and suitably designing the neighbor-interaction rules via a switching topology. The fixed topology case is analyzed and new controllability conditions and formula of inputs for the desired formation of the network are presented. The controllability of a switching network of multi-agent systems in the presence of communication delay is also investigated. Examples with numerical simulations are given to illustrate the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.

Positive state-bounding observer for positive interval continuous-time systems with time delay

Abstract: SUMMARY This paper is concerned with the problem of positive observer synthesis for positive systems with both interval parameter uncertainties and time delay. Conventional observers may no longer be applicable for such kind of systems due to the positivity constraint on the observers, and they only provide an estimate of the system state in an asymptotic way. A pair of positive observers with state-bounding feature is proposed to estimate the state of positive systems at all times in this paper. A necessary and sufficient condition for the existence of desired observers is first established, and the observer matrices can be obtained easily through the solutions of a set of linear matrix inequalities (LMIs). Then, to reduce the error signal between the system state and its estimates, an iterative LMI algorithm is developed to compute the optimized state-bounding observer matrices. Finally, a numerical example is presented to show the effectiveness and applicability of the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.

H ∞ sliding mode observer design for a class of nonlinear discrete time-delay systems: A delay-fractioning approach

Abstract: In this paper, the H ∞ sliding mode observer (SMO) design problem is investigated for a class of nonlinear discrete time-delay systems. The nonlinear descriptions quantify the maximum possible derivations from a linear model, and the system states are allowed to be immeasurable. Attention is focused on the design of a discrete-time SMO such that the asymptotic stability as well as the H ∞ performance requirement of the error dynamics can be guaranteed in the presence of nonlinearities, time delay and external disturbances. Firstly, a discrete-time discontinuous switched term is proposed to make sure that the reaching condition holds. Then, by constructing a new Lyapunov-Krasovskii functional based on the idea of 'delay fractioning' and by introducing some appropriate free-weighting matrices, a sufficient condition is established to guarantee the desired performance of the error dynamics in the specified sliding mode surface by solving a minimization problem. Finally, an illustrative example is given to show the effectiveness of the designed SMO design scheme. Copyright © 2011 John Wiley & Sons, Ltd. Copyright © 2011 John Wiley & Sons, Ltd.

Optimal tracking performance of MIMO discrete‐time systems with communication constraints

Abstract: SUMMARY The optimal tracking problem for multiple-input multiple-output linear-time-invariant discrete-time systems with communication constraints in the feedback path is studied in this paper. The tracking performance is measured by the energy of the error signal between the output of the plant and the reference signal. The objective is to obtain an optimal tracking performance, attainable by all possible stabilizing compensators. It is shown that the optimal tracking performance consists of two parts, one depends on the nonminimum phase zeros and zero direction of the given plant, as well as the reference input signal direction, and the other depends on the nonminimum phase zeros, unstable poles, and pole direction of the given plant, as well as the bandwidth and additive white Gaussian noise of the communication channel. It is also shown that, if the constraint of the communication channel does not exist, the optimal tracking performance reduces to the existing tracking performance of the control system without communication constraints. A typical example is given to illustrate the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.

Distributed state estimation for uncertain Markov-type sensor networks with mode-dependent distributed delays

Abstract: This the post-print version of the Article The official published version can be accessed from the link below - Copyright @ 2012 John Wiley & Sons, Ltd

Stability analysis and control synthesis of switched impulsive systems

Abstract: SUMMARY In this paper, we investigate the stability analysis problem of switched impulsive nonlinear systems and several stabilization problems of switched discrete-time linear systems are studied First, sufficient conditions ensuring globally uniformly asymptotically stability of switched nonlinear impulsive system under arbitrary and DDT (dynamical dwell time which defines the length of the time interval between two successive switchings) switching are derived, respectively In the DDT switching case, we first consider the switched system composed by stable subsystems, then we extend the results to the case where not all subsystems are stable The stabilizations of switched discrete-time linear system under arbitrary switching, DDT switching and asynchronous switching are investigated respectively Based on the stability analysis results, the control synthesis consists of controller design for each subsystem and state impulsive jumping generators design at switching instant With the aid of the state impulsive jumping generators at switching instant, the ‘energy’ produced by switching can be minimized, which leads to less conservative results Several numerical examples are given to illustrate the proposed results within this paper Copyright © 2011 John Wiley & Sons, Ltd

Cooperative control of multiple surface vessels with discrete-time periodic communications

Abstract: SUMMARY This paper addresses the problem of cooperative path-following of networked autonomous surface vessels with discrete-time periodic communications. The objective is to steer a group of autonomous vehicles along given spatial paths, while holding a desired inter-vehicle formation pattern. For a given class of marine vessels, we show how Lyapunov-based techniques, graph theory, and results from networked control systems can be brought together to yield a decentralized control structure where the dynamics of the cooperating vessels and the constraints imposed by the topology of the inter-vehicle communication network are explicitly taken into account. Cooperation is achieved by adjusting the speed of each vessel along its path according to information exchanged periodically on the positions of a subset of the other vessels, as determined by the communications topology adopted. The closed-loop system that is obtained by putting together the path-following and cooperation strategies takes an interconnected feedback form where both systems are input-to-state stable with respect to the outputs of each other. Using a small-gain theorem, stability and convergence of the overall system are guaranteed for adequate choices of the controller gains. Copyright © 2011 John Wiley & Sons, Ltd.

Active fault-tolerant control of sampled-data nonlinear distributed parameter systems

Abstract: SUMMARY This work presents an integrated fault detection and fault-tolerant control architecture for spatially distributed systems described by highly dissipative systems of nonlinear partial differential equations with actuator faults and sampled measurements. The architecture consists of a family of nonlinear feedback controllers, observer-based fault detection filters that account for the discrete measurement sampling, and a switching law that reconfigures the control actuators following fault detection. An approximate finite-dimensional model that captures the dominant dynamics of the infinite-dimensional system is embedded in the control system to provide the controller and fault detection filter with estimates of the measured output between sampling instances. The model state is then updated using the actual measurements whenever they become available from the sensors. By analyzing the behavior of the estimation error between sampling times and exploiting the stability properties of the compensated model, a sufficient condition for the stability of the sampled-data nonlinear closed-loop system is derived in terms of the sampling rate, the model accuracy, the controller design parameters, and the spatial placement of the control actuators. This characterization is used as the basis for deriving appropriate rules for fault detection and actuator reconfiguration. Singular perturbation techniques are used to analyze the implementation of the developed architecture on the infinite-dimensional system. The results are demonstrated through an application to the problem of stabilizing the zero solution of the Kuramoto–Sivashinsky equation. Copyright © 2011 John Wiley & Sons, Ltd.

Path‐following control for small fixed‐wing unmanned aerial vehicles under wind disturbances

Abstract: SUMMARY This paper presents an alternative method of designing a guidance controller for a small unmanned aerial vehicle (UAV) so as to perform path following under wind disturbances. The wind effects acting on UAVs need to be taken into account and eventually eliminated. To solve this problem, we adopted a disturbance observer-based control approach. The wind information is first estimated by a nonlinear disturbance observer, then it is incorporated into the nominal path following controller to formulate a composite controller that is able to compensate wind influences. The globally asymptotic stability of the composite controller is illustrated through theoretical analysis, whereas its performance is evaluated by various simulations including the one with software-in-the-loop. Initial flight tests using a small fixed-wing UAV are carried out to demonstrate its actual performance. Copyright © 2012 John Wiley & Sons, Ltd.

Exponential l2−l∞ output tracking control for discrete-time switched system with time-varying delay

Abstract: SUMMARY The problem of exponential l2−l∞ output tracking control is considered in this paper for discrete-time switched systems with time-varying delay. The exponential l2−l∞ performance index is first introduced to study this problem for discrete-time switched systems. By resorting to the average dwell time approach and Lyapunov–Krasovskii functional technology, some new delay-dependent criteria guaranteeing exponential stability are developed. In addition, the corresponding solvability conditions using cone complement linearization method for the desired exponential l2−l∞ output tracking controller is established. A numerical example is provided to demonstrate the effectiveness of the obtained results. Copyright © 2011 John Wiley & Sons, Ltd.

Razumikhin‐type theorems on general decay stability and robustness for stochastic functional differential equations

Abstract: SUMMARY This paper establishes Razumikhin-type theorems on general decay stability for stochastic functional differential equations. This improves existing stochastic Razumikhin-type theorems and can make us examine the stability with general decay rate in the sense of the pth moment and almost sure. These stabilities may be specialized as the exponential stability and the polynomial stability. When the almost sure stability is examined, the conditions of this paper may defy the linear growth condition for the drift term, which implies that the theorems of this paper can work for some cases to which the existing results cannot be applied. This paper also examines some sufficient criteria under which this stability is robust. To illustrate applications of our results clearly, this paper also gives two examples and examines the exponential stability and the polynomial stability, respectively. Copyright © 2011 John Wiley & Sons, Ltd.

Consensus strategy for a class of multi‐agents with discrete second‐order dynamics

Abstract: SUMMARY This paper investigates consensus strategies for a group of agents with discrete second-order dynamics under directed communication topology. Consensus analysis for both the fixed topology and time-varying topology cases is systematically performed by employing a novel graph theoretic methodology as well as the classical nonnegative matrix theory. Furthermore, it is shown that the necessary and sufficient condition for the agents under fixed communication topology to reach consensus is that the communication topology has a spanning tree; and sufficient conditions for the agents to reach consensus when allowing for the dynamically changing communication topologies are also given. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed results. Copyright © 2011 John Wiley & Sons, Ltd.

Adaptive dynamic surface control for pure-feedback systems

Abstract: SUMMARY This paper proposes a novel dynamic surface control algorithm for a class of uncertain nonlinear systems in completely non-affine pure-feedback form. Instead of using the mean value theorem, we construct an affine variable at each design step, and then neural network is employed to deduce a virtual control signal or an actual control signal. As a result, the unknown control directions and singularity problem raised by the mean value theorem is circumvented. The proposed scheme is able to overcome the explosion of complexity inherent in backstepping control and guarantee the tracking performance by introducing an initialization technique based on a surface error modification. Simulation results are presented to demonstrate the efficiency of the proposed scheme. Copyright © 2011 John Wiley & Sons, Ltd.

Adaptive output feedback control of uncertain nonlinear systems based on dynamic surface control technique

Abstract: SUMMARY An adaptive output feedback control approach is studied for a class of uncertain nonlinear systems in the parametric output feedback form. Unlike the previous works on the adaptive output feedback control, the problem of ‘explosion of complexity’ of the controller in the conventional backstepping design is overcome in this paper by introducing the dynamic surface control (DSC) technique. In the previous schemes for the DSC technique, the time derivative for the virtual controllers is assumed to be bounded. In this paper, this assumption is removed. It can be proven that the resulting closed-loop system is stable in the sense that all the signals are semi-global uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set. A simulation example is given to verify the effectiveness of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.