Showing papers in "International Journal of Robust and Nonlinear Control in 2011"

Attitude stabilization of rigid spacecraft with finite‐time convergence

Abstract: The problem of attitude control for a spacecraft model which is nonlinear in dynamics with inertia uncertainty and external disturbance is investigated in this paper. Two sliding mode controllers are proposed to force the state variables of the closed-loop system to converge to the origin in finite time. Specially, the second control design consists of the estimation of the uncertainty and disturbance by adaptive method and thus it achieves the decrease of undesired chattering effectively. Also, simulation results are presented to illustrate the effectiveness of the control strategies. Copyright © 2010 John Wiley & Sons, Ltd.

Nonsingular fast terminal sliding-mode control for nonlinear dynamical systems

Abstract: This paper investigates fast finite-time control of nonlinear dynamics using terminal sliding-mode (TSM) scheme. Some new norms of fast TSM strategies are proposed, and a faster convergence rate is established in comparison with the conventional fast TSM. A novel concept of nonsingular fast TSM, which is able to avoid the possible singularity during the control phase, is adopted in the robust high-precision control of uncertain nonlinear systems. Numerical simulation on a two-link rigid robot manipulator demonstrates the effectiveness of the proposed algorithm. Copyright © 2010 John Wiley & Sons, Ltd.

Stability and stabilization of Boolean networks

Abstract: The stability of Boolean networks and the stabilization of Boolean control networks are investigated. Using semi-tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean (control) network can be converted to a discrete time linear (bilinear) dynamics, called the algebraic form of the Boolean (control) network. Then the stability can be revealed by analyzing the transition matrix of the corresponding discrete time system. Main results consist of two parts: (i) Using logic coordinate transformation, the known sufficient condition based on incidence matrix has been improved. It can also be used in stabilizer design. (ii) Based on algebraic form, necessary and sufficient conditions for stability and stabilization, respectively, are obtained. Copyright © 2010 John Wiley & Sons, Ltd.

Discrete‐time control for switched positive systems with application to mitigating viral escape

Abstract: This paper has been motivated by the problem of viral mutation in HIV infection. Under simplifying assumptions, viral mutation treatment dynamics can be viewed as a positive switched linear system. Using linear co-positive Lyapunov functions, results for the synthesis of stabilizing, guaranteed performance and optimal control laws for switched linear systems are presented. These results are then applied to a simplified human immunodeficiency viral mutation model. The optimal switching control law is compared with the law obtained through an easily computable guaranteed cost function. Simulation results show the effectiveness of these methods. Copyright © 2010 John Wiley & Sons, Ltd.

Tube-based robust nonlinear model predictive control

Abstract: This paper extends tube-based model predictive control of linear systems to achieve robust control of nonlinear systems subject to additive disturbances. A central or reference trajectory is determined by solving a nominal optimal control problem. The local linear controller, employed in tube-based robust control of linear systems, is replaced by an ancillary model predictive controller that forces the trajectories of the disturbed system to lie in a tube whose center is the reference trajectory thereby enabling robust control of uncertain nonlinear systems to be achieved. Copyright © 2011 John Wiley & Sons, Ltd.

Cooperative adaptive control for synchronization of second‐order systems with unknown nonlinearities

Abstract: This paper studies synchronization to a desired trajectory for multi-agent systems with second-order integrator dynamics and unknown nonlinearities and disturbances. The agents can have different dynamics and the treatment is for directed graphs with fixed communication topologies. The command generator or leader node dynamics is also nonlinear and unknown. Cooperative tracking adaptive controllers are designed based on each node maintaining a neural network parametric approximator and suitably tuning it to guarantee stability and performance. A Lyapunov-based proof shows the ultimate boundedness of the tracking error. A simulation example with nodes having second-order Lagrangian dynamics verifies the performance of the cooperative tracking adaptive controller. Copyright © 2010 John Wiley & Sons, Ltd.

Neural network-based adaptive dynamic surface control of uncertain nonlinear pure-feedback systems

Abstract: In this paper, by incorporating the dynamic surface control technique into a neural network-based adaptive control design framework, we have developed a backstepping-based control design for a class of nonlinear systems in pure-feedback form with arbitrary uncertainty. The circular design problem which may exist in pure-feedback systems is overcome. In addition, our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping-based methods. A stability analysis is given, which shows that our control law can guarantee the semi-global uniformly ultimate boundedness of the solution of the closed-loop system, and makes the tracking error arbitrarily small. Moreover, the proposed control design scheme can also be directly applied to the strict-feedback nonlinear systems with arbitrary uncertainty. Copyright © 2010 John Wiley & Sons, Ltd.

Consensus of second‐order multi‐agent systems with exogenous disturbances

Abstract: In this paper, the consensus of second-order multi-agent dynamical systems with exogenous disturbances is studied. A pinning control strategy is designed for a part of agents of the multi-agent systems without disturbances, and this pinning control can bring multiple agents' states to reaching an expected consensus track. Under the influence of the disturbances, disturbance observers-based control (DOBC) is developed for disturbances generated by an exogenous system to estimate the disturbances. Asymptotical consensus of the multi-agent systems with disturbances under the composite controller can be achieved for fixed and switching topologies. Finally, by applying an example of multi-agent systems with switching topologies and exogenous disturbances, the consensus of multi-agent systems is reached under the DOBC with the designed parameters. Copyright © 2010 John Wiley & Sons, Ltd.

Design of UDE-based controllers from their two-degree-of-freedom nature

Abstract: The control algorithm based on the uncertainty and disturbance estimator (UDE) is a robust control strategy and has received wide attention in recent years. In this paper, the two-degree-of-freedom nature of UDE-based controllers is revealed. The set-point tracking response is determined by the reference model, whereas the disturbance response and robustness are determined by the error feedback gain and the filter introduced to estimate the uncertainty and disturbances. It is also revealed that the error dynamics of the system is determined by two filters, of which one is determined by the error feedback gain and the other is determined by the filter introduced to estimate the uncertainty and disturbances. The design of these two filters are decoupled in the frequency domain. Moreover, after introducing the UDE-based control, the Laplace transform can be applied to some time-varying systems for analysis and design because all the time-varying parts are lumped into a signal. It has been shown that, in addition to the known advantages over the time-delay control, the UDE-based control also brings better performance than the time-delay control under the same conditions. Design examples and simulation results are given to demonstrate the findings. Copyright © 2010 John Wiley & Sons, Ltd.

Adaptive NN output-feedback decentralized stabilization for a class of large-scale stochastic nonlinear strict-feedback systems

Abstract: In this paper, the decentralized adaptive neural network (NN) output-feedback stabilization problem is investigated for a class of large-scale stochastic nonlinear strict-feedback systems, which interact through their outputs. The nonlinear interconnections are assumed to be bounded by some unknown nonlinear functions of the system outputs. In each subsystem, only a NN is employed to compensate for all unknown upper bounding functions, which depend on its own output. Therefore, the controller design for each subsystem only need its own information and is more simplified than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the whole closed-loop system can be proved to be stable in probability by constructing an overall state-quartic and parameter-quadratic Lyapunov function. The simulation results demonstrate the effectiveness of the proposed control scheme. Copyright © 2010 John Wiley & Sons, Ltd.

Linear temporal logic vehicle routing with applications to multi‐UAV mission planning

Abstract: Missions with high combinatorial complexity involving several logical and temporal constraints often arise in cooperative control of multiple Uninhabited Aerial Vehicles. In this paper, we propose a new class of problems that generalizes the standard Vehicle Routing Problem (VRP) by addressing complex tasks and constraints on the mission, called the ‘mission specifications’, expressed in a high-level specification language. In the generalized problem setup, these mission specifications are naturally specified using the Linear Temporal Logic language LTL−X. Using a novel systematic procedure, the LTL−X specification is converted to a set of constraints suitable to a Mixed-Integer Linear Programming (MILP) formulation, which in turn can be incorporated into two widely-used MILP formulations of the standard VRP. Solving the resulting MILP provides an optimal plan that satisfies the given mission specification. The paper also presents two mission planning applications. Copyright © 2011 John Wiley & Sons, Ltd.

Constructing consensus controllers for networks with identical general linear agents

Abstract: We use a high-gain methodology to construct linear decentralized controllers for consensus, in networks with identical but general multi-input linear time-invariant (LTI) agents and quitegeneral time-invariant and time-varying observation topologies.

Global stabilization of a class of upper-triangular systems with unbounded or uncontrollable linearizations

Abstract: In this paper, we consider the problem of global stabilization for a class of upper-triangular systems which have unbounded or uncontrollable linearizations around the origin. The explicit formula of the control law is designed in two steps: First, we use the generalized adding a power integrator technique to design a homogeneous controller which locally stabilizes the upper-triangular systems. Then, we integrate a series of nested saturation functions with the homogeneous controller and adjust the saturation level to ensure global asymptotic stability of the closed-loop systems. Owing to the versatility of the generalized adding a power integrator technique, our controller not only can be used to stabilize more general upper-triangular systems by relaxing the current conditions used in existing results, but also is able to lead to a stronger result of finite-time stabilization under appropriate conditions. Copyright © 2010 John Wiley & Sons, Ltd.

Robust control of uncertain nonlinear systems with state delays based on an uncertainty and disturbance estimator

Abstract: In this article, one linear and one nonlinear robust control strategies are proposed for uncertain nonlinear continuous-time systems with disturbances and state delays. The approaches are based on the uncertainty and disturbance estimator (UDE) introduced in 2004. In the case of a linear controller, the terms containing the nonlinear functions and time delays are treated as additional disturbances to the system. In the case of a nonlinear controller, both known and unknown delay scenarios are considered. In the case of an unknown time delay, the terms containing the delay are treated as additional disturbances to the system. The algorithms provide excellent tracking and disturbance rejection performance. Simulations are given to show the effectiveness of the strategies, first via a simple example and second via an application to a continuous stirred tank reactor system. Copyright © 2010 John Wiley & Sons, Ltd.

Stabilization of networked control systems with nonuniform random sampling periods

Abstract: In this paper, a new linear delayed delta operator switched system model is proposed to describe networked control systems with packets dropout and network-induced delays. The plant is a continuous-time system, which is sampled by time-varying random sampling periods. A general delta domain Lyapunov stability criterion is given for delta operator switched systems with time delays. Sufficient conditions for asymptotic stability of closed-loop networked control systems with both packets dropout and network-induced delays are presented in terms of linear matrix inequalities (LMIs). A verification theorem is given to show the solvability of the stabilization conditions by solving a class of finite LMIs. Both the case of data packets arrive instantly and the case of invariant sampling periods in delta operator systems are given, respectively. Three numerical examples are given to illustrate the effectiveness and potential of the developed techniques. Copyright © 2010 John Wiley & Sons, Ltd.

Coordination of discrete-time multi-agent systems via relative output feedback

Abstract: This paper investigates the joint effects of agent dynamic and network topology on the consensusability of linear discrete-time multi-agent systems via relative output feedback. An observer-based distributed control protocol is proposed. A necessary and sufficient condition for consensusability under this control protocol is given, which explicitly reveals how the intrinsic entropy rate of the agent dynamic and the eigenratio of the undirected communication graph affect consensusability. As a special case, multi-agent systems with discrete-time double integrator dynamics are discussed where a simple control protocol directly using two-step relative position feedback is provided to reach a consensus. Finally, the result is extended to solve the formation and formation-based tracking problems. The theoretical results are illustrated by simulations. Copyright © 2010 John Wiley & Sons, Ltd.

Small gain problem in coupled differential‐difference equations, time‐varying delays, and direct Lyapunov method

Abstract: This article presents a Lyapunov–Krasovskii formulation of scaled small gain problem for systems described by coupled differential-difference equations. This problem includes H∞ problem with block-diagonal uncertainty as a special case. A discretization may be applied to reduce the conditions into linear matrix inequalities. As an application, the stability problem of systems with time-varying delays is transformed into the scaled small gain problem through a process of either one-term approximation or two-term approximation. The cases of time-varying delays with and without derivative upper-bound are compared. Finally, it is shown that similar conditions can also be obtained by a direct Lyapunov–Krasovskii functional method for coupled differential-functional equations. Numerical examples are presented to illustrate the effectiveness of the method in tackling systems with time-varying delays. Copyright © 2010 John Wiley & Sons, Ltd.

Filtering of discrete‐time Markov jump linear systems with uncertain transition probabilities

Abstract: This article addresses the filtering design problem for discrete-time Markov jump linear systems (MJLS) under the assumption that the transition probabilities are not completely known. We present the methods to determine ℋ2- and ℋ∞-norm bounded filters for MJLS whose transition probability matrices have uncertainties in a convex polytope and establish an equivalence with the ones with partly unknown elements. The proposed design, based on linear matrix inequalities, allows different assumptions on Markov mode availability to the filter and on system parameter uncertainties to be taken into account. Under mode-dependent assumption and internal model knowledge, observer-based filters can be obtained and it is shown theoretically that our method outperforms some available ones in the literature to date. Numerical examples illustrate this claim. Copyright © 2010 John Wiley & Sons, Ltd.

Analytical and numerical Lyapunov functions for SISO linear control systems with first‐order reset elements

Abstract: In this paper we provide analytical and numerical Lyapunov functions that prove stability and performance of a First-order Reset Element (FORE) in feedback interconnection with a SISO linear plant. The Lyapunov functions also allow to establish finite gain ℒ2 stability from a disturbance input acting at the input of the plant to the plant output. ℒ2 stability is established by giving a bound on the corresponding ℒ2 gains. The proof of stability and performance is carried out by showing that the Lyapunov functions constructed here satisfy the sufficient conditions in the main results of Nesic et al. (Automatica 2008; 44(8):2019–2026). In the paper we also point out and illustrate via a counterexample an analysis subtlety overlooked in the preliminary results of Zaccarian et al. (American Control Conference, Portland, OR, U.S.A., 2005). Copyright © 2010 John Wiley & Sons, Ltd.

Decay rate constrained stabilization of positive systems using static output feedback

Abstract: This paper investigates the stabilization problem by means of a static output feedback control for positive systems with/without interval uncertainties. The designed closed-loop system is ensured to be positive and stable with a prescribed decay rate. Necessary and sufficient conditions for the existence of such controllers are established in terms of linear matrix inequalities together with a matrix equality constraint. Furthermore, the desired static output feedback controllers can be derived directly via the cone complementarity linearization techniques. Finally, an illustrative example is presented to show the validity of results obtained in this paper

Robust finite-time stability of impulsive dynamical linear systems subject to norm-bounded uncertainties

Abstract: Robust finite-time stability (FTS) for a class of uncertain hybrid systems is tackled for the first time in this paper. In particular, uncertain impulsive dynamical linear systems (U-IDLS) are considered. U-IDLS exhibit jumps in the state trajectory that can be either time-driven (time-dependent IDLS) or driven by specific state values (state-dependent IDLS). Furthermore, U-IDLS may exhibit uncertainties both in the linear dynamic and in the jump equation. In this paper, sufficient conditions for FTS of IDLS are provided. These results require the solution of feasibility problems involving differential-difference linear matrix inequalities (D/DLMIs), which can be numerically solved in an efficient way, as illustrated in the proposed examples. Copyright © 2010 John Wiley & Sons, Ltd.

Delay-dependent robust H∞ controller synthesis for discrete singular delay systems

Abstract: In this paper, the problems of delay-dependent robust stability analysis, robust stabilization and robust H∞ control are investigated for uncertain discrete-time singular systems with state delay. First, by making use of the delay partitioning technique, a new delay-dependent criterion is given to ensure the nominal system to be regular, causal and stable. This new criterion is further extended to singular systems with both delay and parameter uncertainties. Then, without the assumption that the considered systems being regular and causal, robust controllers are designed for discrete-time singular time-delay systems such that the closed-loop systems have the characteristics of regularity, causality and asymptotic stability. Moreover, the problem of robust H∞ control is solved following a similar line. The obtained results are dependent not only on the delay, but also on the partitioning size and the conservatism is non-increasing with reducing partitioning size. These results are shown, via extensive numerical examples, to be much less conservative than the existing results in the literature. Copyright © 2010 John Wiley & Sons, Ltd.

H∞ filtering for uncertain time‐varying systems with multiple randomly occurred nonlinearities and successive packet dropouts

Abstract: This paper is concerned with the robust H∞ finite-horizon filtering problem for discrete time-varying stochastic systems with multiple randomly occurred sector-nonlinearities (MROSNs) and successive packet dropouts. MROSNs are proposed to model a class of sector-like nonlinearities that occur according to the multiple Bernoulli distributed white sequences with a known conditional probability. Different from traditional approaches, in this paper, a time-varying filter is designed directly for the addressed system without resorting to the augmentation of system states and measurement, which helps reduce the filter order. A new H∞ filtering technique is developed by means of a set of recursive linear matrix inequalities that depend on not only the current available state estimate but also the previous measurement, therefore ensuring a better accuracy. Finally, two illustrative examples are used to demonstrate the effectiveness and applicability of the proposed filter design scheme. Copyright © 2010 John Wiley & Sons, Ltd.

Sampled-data H∞ filtering for stochastic genetic regulatory networks

Abstract: SUMMARY This paper is concerned with the sampled-data Hinfty filtering problem for a class of stochastic genetic regulatory networks with both extrinsic and intrinsic disturbances. The extrinsic disturbance and intrinsic noises are described, respectively, by an unknown signal with finite energy and a set of scalar Brownian motions. The expression levels of the mRNA and protein of the considered genetic regulatory network are sampled and then transmitted to the filter in order to estimate the states of the genetic network under consideration. The corresponding filtering error dynamics is then represented by means of a system with time-varying delay. By constructing a simple yet practical Lyapunov functional that reflects all the information about the system complexity, sufficient conditions are established so as to guarantee both the exponential mean-square stability and the H∞ performance for the filtering error dynamics. It is shown that the desired sampled-data H∞ filter exists if certain matrix inequalities are solvable where the solvability can be readily checked by using the available software. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper. Copyright © 2011 John Wiley & Sons, Ltd.

A new discretized Lyapunov–Krasovskii functional for stability analysis and control design of time-delayed TS fuzzy systems

Abstract: This paper proposes a new Lyapunov–Krasovskii functional to cope with stability analysis and control design for time-delay nonlinear systems modeled in the Takagi–Sugeno (TS) fuzzy form. The delay-dependent conditions are formulated as linear matrix inequalities (LMIs), solvable through several numerical tools. By using the Gu's discretization technique and by employing an appropriated fuzzy functional, less conservative conditions are obtained. Numerical results illustrate the efficiency of the proposed methods. Copyright © 2010 John Wiley & Sons, Ltd.

Close target reconnaissance with guaranteed collision avoidance

Abstract: This manuscript considers the problem of close target reconnaissance by a group of autonomous agents. The overall close target reconnaissance (CTR) involves subtasks of avoiding inter-agent collisions, reaching a close vicinity of a specific target position, and forming an equilateral polygon formation around the target. The agents performing the task fly at a constant speed to mimic the velocity behavior of small fixed-wing unmanned aerial vehicles (UAV). A decentralized control scheme is developed for this overall task and the finite-time convergence of the system under the proposed control law is established. Furthermore, it is guaranteed that no collision occurs among the agent. The relevant analysis and simulation test results are provided. Copyright © 2010 John Wiley & Sons, Ltd.

Observer-based tracking control for switched linear systems with time-varying delay

Abstract: The issue of observer-based tracking control for switched linear systems with time-varying delay is investigated in this paper. The possibility of designing switching control laws based on measured output is considered when the states are not available. Hysteresis based switching method and single Lyapunov-Krasovskii functional method are utilized to the stability analysis and controller design. By introducing the descriptor system method, the consideration of mixed mode is avoided since can be seen as state variable, and thus it is not necessary to substitute everywhere by the right-hand part of the system. The variation-of-constants formula is used to overcome the difficulties caused by the estimation error and exotic disturbance. Free weighting matrix scheme facilitates us to the stability analysis and control synthesis, and the numerical example shows the effectiveness of the proposed design methods. Copyright © 2010 John Wiley & Sons, Ltd.

Leader-following control for multiple inertial agents

Abstract: This paper investigates distributed controller design problem for a leader-follower network in the presence of communication delays. Two main contributions are made in this work. First, the second-order controlled consensus scheme for the weakly connected communication graph topology is proposed. A necessary and sufficient condition is given under which the exponential consensus is achieved. Meanwhile, the relationship among the agents' inertias, the allowable delay bound, the communication topology, the consensus convergence rate, and the control gains is unveiled. Second, the robustness performances of the distributed control scheme with respect to the communication failures and delays are provided. It is shown that if the communication failure rate and the topology switching frequency, respectively, satisfy the given bounds, the exponential second-order controlled consensus can be achieved under a bounded delay. Numerical examples are given to illustrate the theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.

Tracking control design for a wave equation with dynamic boundary conditions modeling a piezoelectric stack actuator

Abstract: This paper is concerned with the design of an asymptotically stabilizing tracking controller for an undamped wave equation modeling a piezoelectric stack actuator. For this, flatness-based methods for trajectory planning and feedforward control are combined with dynamic feedback control involving a Luenberger-type observer within the two degrees-of-freedom control concept. The asymptotic stability of the closed-loop system is verified using Lyapunov's stability theory and LaSalle's invariance principle. Thereby, a separation theorem is introduced for bounded perturbations of infinitesimal generators of asymptotically stable C0-semigroups. Finally, the tracking performance is illustrated in simulation scenarios. Copyright © 2010 John Wiley & Sons, Ltd.

Robust adaptive control for greenhouse climate using neural networks

Abstract: This paper presents a general framework for robust adaptive neural network (NN)-based feedback linearization controller design for greenhouse climate system. The controller is based on the well-known feedback linearization, combined with radial basis functions NNs, which allows the feedback linearization technique to be used in an adaptive way. In addition, a robust sliding mode control is incorporated to deal with the bounded disturbances and the approximation errors of NNs. As a result, an inherently nonlinear robust adaptive control law is obtained, which not only provides fast and accurate tracking of varying set-points, but also guarantees asymptotic tracking even if there are inherent approximation errors. Copyright © 2010 John Wiley & Sons, Ltd.