Showing papers in "International Journal of Robust and Nonlinear Control in 2010"

Composite disturbance-observer-based control and H∞ control for complex continuous models

Abstract: A novel type of control scheme combining the disturbance-observer-based control (DOBC) with H∞ control is proposed for a class of complex continuous models with disturbances. The disturbances are supposed to include two parts. One part in the input channel is generated by an exogenous system with uncertainty, which can represent the harmonic signals with modeling perturbations. The other part is supposed to have the bounded H2-norm. Parametric uncertainties exist both in concerned plant and in exogenous subsystem. The disturbance observers based on regional pole placement and D-stability theory are designed and integrated with conventional H∞ control laws. The new composite DOBC and H∞ control scheme is applied to complex continuous models for the case with known and unknown nonlinearity, respectively. Then the first type of disturbances can be estimated and rejected, and the second type can be attenuated; simultaneously, the desired dynamic performances can be guaranteed. Simulations for a flight control system are given to demonstrate the effectiveness of the results and compare the proposed results with the previous schemes. Copyright © 2009 John Wiley & Sons, Ltd.

Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction in a sampled-data setting

Abstract: This paper studies the convergence of two coordination algorithms for double-integrator dynamics under fixed undirected/ directed interaction in a sampled-data setting. The first algorithm guarantees that a team of vehicles achieves coordination on their positions with a zero final velocity while the second algorithm guarantees that a team of vehicles achieves coordination on their positions with a constant final velocity. We show necessary and sufficient conditions on the sampling period, the control gain, and the communication graph such that coordination is achieved using these two algorithms under, respectively, an undirected interaction topology and a directed interaction topology. Tools like matrix theory, bilinear transformation, and Cauchy theorem are used for convergence analysis. Coordination equilibria for both algorithms are also given. Simulation results are presented as a proof of concept. Copyright © 2009 John Wiley & Sons, Ltd.

Quantized average consensus via dynamic coding/decoding schemes

Abstract: In the average consensus a set of linear systems has to be driven to the same final state, which corresponds to the average of their initial states. This mathematical problem can be seen as the simplest example of coordination task. In fact it can be used to model both the control of multiple autonomous vehicles which all have to be driven to the centroid of the initial positions, and to model the decentralized estimation of a quantity from multiple measure coming from distributed sensors. This contribution presents a consensus strategy in which the systems can exchange information among themselves according to a fixed strongly connected digital communication network. Beside the decentralized computational aspects induced by the choice of the communication network, we here have also to face the quantization effects due to the digital links. We here present and discuss two different encoding/decoding strategies with theoretical and simulation results on their performance. Copyright © 2009 John Wiley & Sons, Ltd.

Necessary and sufficient conditions for solving consensus problems of double-integrator dynamics via sampled control

Abstract: In this paper, consensus problems of double-integrator dynamics via sampled control are investigated. The sampled control protocol is induced from continuous-time linear consensus protocol by using periodic sampling technology and zero-order hold circuit. With the obtained sampled control protocol, the continuous-time multi-agent system is equivalently transformed into a linear discrete-time system. Necessary and sufficient conditions are given to guarantee that all the agents asymptotically travel with zero relative positions and common velocities. Furthermore, consensus problem with continuous-time consensus protocol is re-analyzed. A necessary and sufficient condition is also obtained which is consistent with the special case when the sampling period tends to zero. The effectiveness of these algorithms is demonstrated through simulations. Copyright © 2009 John Wiley & Sons, Ltd.

H∞ filtering for singular Markovian jump systems with time delay

Abstract: The problem of H∞ filtering is considered for singular Markovian jump systems with time delay. In terms of linear matrix inequality (LMI) approach, a delay-dependent bounded real lemma (BRL) is proposed for the considered system to be stochastically admissible while achieving the prescribed H∞ performance condition. Based on the BRL and under partial knowledge of the jump rates of the Markov process, both delay-dependent and delay-independent sufficient conditions that guarantee the existence of the desired filter are presented. The explicit expression of the desired filter gains is also characterized by solving a set of strict LMIs. Some numerical examples are given to demonstrate the effectiveness of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.

Sliding mode control approaches to the robust regulation of linear multivariable fractional‐order dynamics

Abstract: Sliding mode control approaches are developed to stabilize a class of linear uncertain fractional-order dynamics. After making a suitable transformation that simplifies the sliding manifold design, two sliding mode control schemes are presented. The first one is based on the conventional discontinuous first-order sliding mode control technique. The second scheme is based on the chattering-free second-order sliding mode approach that leads to the same robust performance but using a continuous control action. Simple controller tuning formulas are constructively developed along the paper by Lyapunov analysis. The simulation results confirm the expected performance. Copyright © 2010 John Wiley & Sons, Ltd.

Performance analysis of reset control systems

Abstract: In this paper we present a general linear matrix inequality-based analysis method to determine the performance of a SISO reset control system in both the ℒ2 gain and ℋ2 sense. In particular, we derive convex optimization problems in terms of LMIs to compute an upperbound on the ℒ2 gain performance and the ℋ2 norm, using dissipativity theory with piecewise quadratic Lyapunov functions. The results are applicable to for all LTI plants and linear-based reset controllers, thereby generalizing the available results in the literature. Furthermore, we provide simple though convincing examples to illustrate the accuracy of our proposed ℒ2 gain and ℋ2 norm calculations and show that, for an input constrained ℋ2 problem, reset control can outperform a linear controller designed by a common nonlinear optimization method. Copyright © 2009 John Wiley & Sons, Ltd.

Stabilization of linear systems with input delay and saturation—A parametric Lyapunov equation approach

Abstract: This paper studies the problem of stabilizing a linear system with delayed and saturating feedback. It is known that the eigenstructure assignment-based low-gain feedback law (globally) stabilizes a linear system in the presence of arbitrarily large delay in its input, and semi-globally stabilizes it when the input is also subject to saturation, as long as all its open-loop poles are located in the closed left-half plane. Based on a recently developed parametric Lyapunov equation-based low-gain feedback design method, this paper presents alternative, but simpler and more elegant, feedback laws that solve these problems. The advantages of this new approach include its simplicity, the capability of giving explicit conditions to guarantee the stability of the closed-loop system, and the ease in scheduling the low-gain parameter on line to achieve global stabilization in the presence of actuator saturation. Copyright © 2009 John Wiley & Sons, Ltd.

Trajectory‐keeping in satellite formation flying via robust periodic learning control

Abstract: This paper proposes an iterative learning control (ILC) scheme to ensure trajectory-keeping in satellite formation flying. Since satellites rotate the earth periodically, position-dependent disturbances can be considered time-periodic disturbances. This observation motivates the idea of repetitively compensating for external disturbances such as solar radiation, magnetic field, air drag, and gravity forces in an iterative, orbit-to-orbit manner. It is shown that robust ILC can be effectively utilized for satellite trajectory tracking, thus enabling time-variant formation flying between the leader- and follower-satellites. The validity of the results is illustrated through computational simulations. Copyright © 2009 John Wiley & Sons, Ltd.

Fault-tolerant adaptive control allocation schemes for overactuated systems

Abstract: This paper presents a fault-tolerant adaptive control allocation scheme for overactuated systems subject to loss of effectiveness actuator faults. The main idea is to use an ‘ad hoc’ online parameters estimator, coupled with a control allocation algorithm, in order to perform online control reconfiguration whenever necessary. Time-windowed and recursive versions of the algorithm are proposed for nonlinear discrete-time systems and their properties analyzed. Two final examples have been considered to show the effectiveness of the proposed scheme. The first considers a simple linear system with redundant actuators and it is mainly used to exemplify the main properties and potentialities of the scheme. In the second, a realistic marine vessel scenario under propeller and thruster faults is treated in full details. Copyright © 2010 John Wiley & Sons, Ltd.

Consensus problem of high‐order multi‐agent systems with external disturbances: An H∞ analysis approach

Abstract: This paper is devoted to the output consensus problem of directed networks of multiple high-order agents with external disturbances, and proposes a distributed protocol using the neighbors' measured outputs. By defining an appropriate controlled output and conducting a model transformation in two steps, consensus performance analysis of the multi-agent system under the proposed protocol is transformed into a normal H∞ problem. Then using H∞ theory of linear systems, conditions are derived to ensure the consensus performance with a prescribed H∞ index for networks with fixed and switching topologies, respectively. A numerical example of the formation control application is included to validate the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.

Cooperative control of multiple surface vessels in the presence of ocean currents and parametric model uncertainty

Abstract: This paper addresses the problem of cooperative path-following of multiple autonomous vehicles. Stated briefly, the problem consists of steering a group of vehicles along specified paths while keeping a desired spatial formation. For a given class of autonomous surface vessels, it is shown how Lyapunov-based techniques and graph theory can be brought together to design a decentralized control structure, where the vehicle dynamics and the constraints imposed by the topology of the inter-vehicle communication network are explicitly taken into account. To achieve path-following for each vehicle, a nonlinear adaptive controller is designed that yields convergence of the trajectories of the closed-loop system to the path in the presence of constant unknown ocean currents and parametric model uncertainty. The controller derived implicitly compensates for the effect of the ocean current without the need for direct measurements of its velocity. Vehicle cooperation is achieved by adjusting the speed of each vehicle along its path according to information exchanged on the positions of a subset of the other vehicles, as determined by the communication topology adopted. Global stability and convergence of the closed-loop system are guaranteed. Illustrative examples are presented and discussed. Copyright © 2009 John Wiley & Sons, Ltd.

Flight control of a rotary wing UAV using backstepping

Abstract: This paper presents a novel application of backstepping controller for autonomous landing of a rotary wing UAV (RUAV). This application, which holds good for the full flight envelope control, is an extension of a backstepping algorithm for general rigid body velocity control. The nonlinear RUAV model used in this paper includes the flapping and servo dynamics. The backstepping‐based controller takes advantage of the ‘decoupling’ of the translation and rotation dynamics of the rigid body, resulting in a two‐step procedure to obtain the RUAV control inputs. The first step is to compute desired thrusts and flapping angles to achieve the commanded position and the second step is to compute control inputs, which achieve the desired thrusts and flapping angles. This paper presents a detailed analysis of the inclusion of a flapping angle correction term in control. The performance of the proposed algorithm is tested using a high‐fidelity RUAV simulation model. The RUAV simulation model is based on miniature rotorcraft parameters. The closed‐loop response of the rotorcraft indicates that the desired position is achieved after a short transient. The Eagle RUAV control inputs, obtained using high‐fidelity simulation results, clearly demonstrate that this algorithm can be implemented on practical RUAVs.

Stability analysis for networked control systems based on average dwell time method

Abstract: This paper studies the problem of the exponential stability of networked control systems (NCSs) with large delay periods, which often appear in the transmission of NCSs. Some new concepts about large delay periods are introduced, and a method based on switching is employed. The maximum allowable transfer interval is obtained such that the considered system is exponentially stable. The criteria obtained contain existing results without considering a large delay period as a special case. An example is given to show the effectiveness of the proposed criteria. Copyright © 2009 John Wiley & Sons, Ltd.

ℋ︁∞ sliding mode observers for uncertain nonlinear Lipschitz systems with fault estimation synthesis

Abstract: This paper presents a scheme to design robust sliding mode observers(SMO) with ℋ∞ performance for uncertain nonlinear Lipschitz systems where both faults and disturbances are considered. We study the necessary conditions to achieve insensitivity of the proposed sliding mode observer to the unknown input(fault). The objective is to derive a sufficient condition using linear matrix inequality(LMI) optimization for minimizing the ℋ∞ gain between the estimation error and disturbances, while at the same time the design method guarantees that the solution of the LMI optimization satisfies the so-called structural matching condition. The sliding motion affects only a part of the system through a novel reduced-order sliding mode controller. Furthermore, the so-called equivalent control concept is discussed for fault estimation. Finally, a numerical example of MCK chaos demonstrates the high performance of the results compared with a pure SMO. Copyright © 2010 John Wiley & Sons, Ltd.

H∞ filtering for singular systems with time‐varying delay

Abstract: This paper is concerned with the delay-dependent H∞ filtering problem for singular systems with time-varying delay in a range. In terms of linear matrix inequality approach, the delay-range-dependent bounded real lemmas are proposed, which guarantee the considered system to be regular, impulse free and exponentially stable while satisfying a prescribed H∞ performance level. The sufficient conditions are proposed for the existence of linear H∞ filter. Numerical examples are given to demonstrate the effectiveness and the benefits of the proposed methods. Copyright © 2009 John Wiley & Sons, Ltd.

Anti-windup synthesis for nonlinear dynamic inversion control schemes

Abstract: A general anti-windup (AW) compensation scheme is provided for a class of input constrained feedback-linearizable nonlinear systems. The controller considered is an inner-loop nonlinear dynamic inversion controller, augmented with an outer-loop linear controller, of arbitrary structure. For open-loop globally exponentially stable plants, it is shown that (i) there always exists a globally stabilizing AW compensator corresponding to a nonlinear generalization of the Internal-Model-Control (IMC) AW solution; (ii) important operator theoretic parallels exist between the AW design scheme for linear control and the suggested AW design scheme for nonlinear affine plants and (iii) a more attractive AW compensator may be obtained by using a nonlinear state-feedback term, which plays a role similar to the linear state-feedback term in linear coprime factor-based AW compensation. The results are demonstrated on a dual-tank simulation example. Copyright © 2009 John Wiley & Sons, Ltd.

Consensus of multiple double‐integrator agents with intermittent measurement

Abstract: This paper is concerned with consensus problems in directed networks of multiple agents with double-integrator dynamics. It is assumed that each agent adjusts its state based on the information of its states relative to its neighbors at discrete times and the interaction topology among agents is time-varying. Both synchronous and asynchronous cases are considered. The synchrony means that each agent's update times, at which it obtains new control signals, are the same as the others', and the asynchrony implies that each agent's update times are independent of the others'. In the synchronous case, the consensus problem is proved to be equivalent to the asymptotic stability problem of a discrete-time switched system. By analyzing the asymptotic stability of the discrete-time switched system, it is shown that consensus can be reached if the update time intervals are small sufficiently, and an allowable upper bound of update time intervals is obtained. In the asynchronous case, the consensus problem is transformed into the global asymptotic stability problem of a continuous-time switched system with time-varying delays. In virtue of a linear matrix inequality method, it is proved that consensus can be reached if the delays are small enough, and an admissible upper bound of delays is derived. Simulations are provided to illustrate the effectiveness of the theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.

Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delay

Abstract: This paper is concerned with delay-dependent exponential stability for stochastic Markovian jump systems with nonlinearity and time-varying delay. An improved exponential stability criterion for stochastic Markovian jump systems with nonlinearity and time-varying delay is proposed without ignoring any terms by considering the relationship among the time-varying delay, its upper bound and their difference, and using both Ito's differential formula and Lyapunov stability theory. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.

Global set stabilization of the spacecraft attitude control problem based on quaternion

Abstract: In this paper, we develop a global set stabilization method for the attitude control problem of spacecraft system based on quaternion. The control law that uses both optimal control and finite-time control techniques can globally stabilize the attitude of spacecraft system to a set of equilibria. First, for the kinematic subsystem, we design a virtual optimal angular velocity. To obtain the global minimum of the performance index, this optimal angular velocity is only discontinuous in initial values. It can be regarded as a combination of open loop control and closed loop control. Then for the dynamic subsystem, we design a finite-time control law that can force the angular velocity to track the virtual optimal angular velocity. It is proved that the closed loop system satisfies global set stability in the absence of disturbances. In the presence of disturbances, the system trajectory will converge to a neighborhood of the equilibrium set. Rigorous analysis shows that by introducing finite-time control techniques, the closed loop system possesses a better disturbance rejection property. The control method is more natural and energy-efficient. The effectiveness of the proposed method is demonstrated by simulation results. Copyright © 2009 John Wiley & Sons, Ltd.

Deployment algorithms for a power‐constrained mobile sensor network

Abstract: This paper presents distributed coverage algorithms for mobile sensor networks in which agents have limited power to move. Rather than making use of a constrained optimization technique, our approach accounts for power constraints by assigning non-homogeneously time-varying regions to each robot. This leads to novel partitions of the environment into limited-range, generalized Voronoi regions. The motion control algorithms are then designed to ascend the gradient of several types of locational optimization functions. In particular, the objective functions reflect the global energy available to the group and different coverage criteria. As we discuss in the paper, this has an effect on limiting each agent's velocity to save energy and balance its expenditure across the network. Copyright © 2009 John Wiley & Sons, Ltd.

Quantized feedback control for linear uncertain systems

Abstract: This paper studies robust control problems under the setting of quantized feedback. We consider both the static and dynamic logarithmic quantizers. In the static quantization case, the quantizer has an infinite number of levels, and the design problem is to find the minimal quantization density required to achieve a given control objective. In the dynamic quantization case, the problem is to minimize the number of quantization levels to achieve a given control objective. We present a number of results for different controller-quantizer configurations. These results are developed using the so-called sector bound approach for quantized feedback control, which was initiated by the authors previously for systems without uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.

Stability conditions for integral delay systems

Abstract: In this paper we consider a special class of integral delay systems arising in several stability problems of time-delay systems. For these integral systems we derive stability and robust stability conditions in terms of Lyapunov–Krasovskii functionals. More explicitly, after providing the stability conditions we compute quadratic functionals and apply them to derive exponential estimates for solutions, and robust stability conditions for perturbed integral delay systems. Copyright © 2008 John Wiley & Sons, Ltd.

New results of stability analysis for systems with time‐varying delay

Abstract: This paper studies the problem of stability analysis for continuous-time systems with time-varying delay. By developing a delay decomposition approach, the information of the delayed plant states can be taken into full consideration, and new delay-dependent sufficient stability criteria are obtained in terms of linear matrix inequalities. The merits of the proposed results lie in their less conservatism, which are realized by choosing different Lyapunov matrices in the decomposed integral intervals and estimating the upper bound of some cross term more exactly. Numerical examples are given to illustrate the effectiveness and less conservatism of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.

Consensus‐based distributed sensor calibration and least‐square parameter identification in WSNs

Abstract: In this paper we study the problem of estimating the channel parameters for a generic wireless sensor network (WSN) in a completely distributed manner, using consensus algorithms. Specifically, we first propose a distributed strategy to minimize the effects of unknown constant offsets in the reading of the radio strength signal indicator due to uncalibrated sensors. Then we show how the computation of the optimal wireless channels parameters, which are the solution of a global least-square optimization problem, can be obtained with a consensus-based algorithm. The proposed algorithms are general algorithms for sensor calibration and distributed least-square parameter identification, and do not require any knowledge either on the global topology of the network nor the total number of nodes. Finally, we apply these algorithms to experimental data collected from an indoor WSN. Copyright © 2009 John Wiley & Sons, Ltd.

Robust MIMO disturbance observer analysis and design with application to active car steering

Abstract: A multi-input–multi-output extension of the well-known two control degrees-of-freedom disturbance observer architecture that decouples the problem into single-input–single-output disturbance observer loops is presented in this paper. Robust design based on mapping D-stability and the frequency domain specifications of weighted sensitivity minimization and phase margin bound to a chosen controller parameter space is presented as a part of the proposed design approach. The effect of the choice of disturbance observer Q filter on performance is explained with a numerical example. This is followed by the use of structured singular values in the robustness analysis of disturbance observer controlled systems subject to structured, real parametric and mixed uncertainty in the plant. A design and simulation study based on a four wheel active car steering control example is used to illustrate the methods presented in the paper. Copyright © 2009 John Wiley & Sons, Ltd.

Asymptotic stabilization of high‐order feedforward systems with delays in the input

Abstract: This paper deals with the state feedback controller design for a class of high-order feedforward (upper-triangular) nonlinear systems with delayed inputs. The uncertainties in the systems are assumed to be dominated by higher-order nonlinearities multiplying by a constant growth rate. The designed controller, which is a continuous but not smooth feedback, could achieve global asymptotical stability. Based on the appropriate state transformation of time-delay systems, the problem of controller design can be converted into the problem of finding a parameter, which can be obtained by appraising the nonlinear terms of the systems. The nonlinear systems considered here are more general than conventional feedforward systems and they could be viewed as generalized feedforward systems. Two examples are given to show the effectiveness of the proposed design procedure. Copyright © 2009 John Wiley & Sons, Ltd.

Decentralized adaptive fuzzy sliding mode control for reconfigurable modular manipulators

Abstract: A stable decentralized adaptive fuzzy sliding mode control scheme is proposed for reconfigurable modular manipulators to satisfy the concept of modular software. For the development of the decentralized control, the dynamics of reconfigurable modular manipulators is represented as a set of interconnected subsystems. A first-order Takagi–Sugeno fuzzy logic system is introduced to approximate the unknown dynamics of subsystem by using adaptive algorithm. The effect of interconnection term and fuzzy approximation error is removed by employing an adaptive sliding mode controller. All adaptive algorithms in the subsystem controller are derived from the sense of Lyapunov stability analysis, so that resulting closed-loop system is stable and the trajectory tracking performance is guaranteed. The simulation results are presented to show the effectiveness of the proposed decentralized control scheme. Copyright © 2009 John Wiley & Sons, Ltd.

Distributed Moving Horizon Estimation for Nonlinear Constrained Systems

Abstract: In this paper we consider a nonlinear constrained system observed by a sensor network and propose a distributed state estimation scheme based on Moving Horizon Estimation (MHE). In order to embrace the case where the whole system state cannot be reconstructed from data available to individual sensors, we resort to the notion of MHE-detectability for nonlinear systems, and add to the MHE problems solved by each sensor a consensus term for propagating information about estimates through the network. Under some suitable assumptions we prove convergence to zero and stability of the state estimation error provided by any sensor.