Showing papers in "International Journal of Robust and Nonlinear Control in 2017"

Bipartite consensus of multi-agent systems over signed graphs: State feedback and output feedback control approaches

Abstract: Summary This paper studies bipartite consensus problems for continuous-time multi-agent system over signed directed graphs. We consider general linear agents and design both state feedback and dynamic output feedback control laws for the agents to achieve bipartite consensus. Via establishing an equivalence between bipartite consensus problems and the conventional consensus problems under both state feedback and output feedback control approaches, we make direct application of existing state feedback and output feedback consensus algorithms to solve bipartite consensus problems. Moreover, we propose a systematical approach to design bipartite consensus control laws. Copyright © 2016 John Wiley & Sons, Ltd.

Event-triggered H∞ control for a class of nonlinear networked control systems using novel integral inequalities

Abstract: Summary This paper is concerned with event-triggered H∞ control for a class of nonlinear networked control systems. An event-triggered transmission scheme is introduced to select ‘necessary’ sampled data packets to be transmitted so that precious communication resources can be saved significantly. Under the event-triggered transmission scheme, the closed-loop system is modeled as a system with an interval time-varying delay. Two novel integral inequalities are established to provide a tight estimation on the derivative of the Lyapunov–Krasovskii functional. As a result, a novel sufficient condition on the existence of desired event-triggered H∞ controllers is derived in terms of solutions to a set of linear matrix inequalities. No parameters need to be tuned when controllers are designed. The proposed method is then applied to the robust stabilization of a class of nonlinear networked control systems, and some linear matrix inequality-based conditions are formulated to design both event-triggered and time-triggered H∞ controllers. Finally, two numerical examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Observer-based leader-following consensus of uncertain nonlinear multi-agent systems

Abstract: Summary In this paper, the leader-following consensus problem of uncertain high-order nonlinear multi-agent systems on directed graph with a fixed topology is studied, where it is assumed that the relative states of a follower and its neighbors are immeasurable and only the relative outputs are available. Nonlinear adaptive observers are firstly proposed for each follower to estimate the states of it and its neighbors, and an observer-based distributed adaptive control scheme is constructed to guarantee that all followers asymptotically synchronize to a leader with tracking errors being semi-globally uniform ultimate bounded. On the basis of algebraic graph theory and Lyapunov theory, the closed-loop system stability analysis is conducted. Finally, numerical simulations are presented to illustrate the effectiveness and potential of the proposed new design techniques. Copyright © 2017 John Wiley & Sons, Ltd.

Event‐triggered optimal tracking control of nonlinear systems

Abstract: Summary We propose a novel event-triggered optimal tracking control algorithm for nonlinear systems with an infinite horizon discounted cost. The problem is formulated by appropriately augmenting the system and the reference dynamics and then using ideas from reinforcement learning to provide a solution. Namely, a critic network is used to estimate the optimal cost while an actor network is used to approximate the optimal event-triggered controller. Because the actor network updates only when an event occurs, we shall use a zero-order hold along with appropriate tuning laws to encounter for this behavior. Because we have dynamics that evolve in continuous and discrete time, we write the closed-loop system as an impulsive model and prove asymptotic stability of the equilibrium point and Zeno behavior exclusion. Simulation results of a helicopter, a one-link rigid robot under gravitation field, and a controlled Van-der-Pol oscillator are presented to show the efficacy of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

On optimal predefined-time stabilization

Abstract: Summary This paper addresses the problem of optimal predefined-time stability. Predefined-time stable systems are a class of fixed-time stable dynamical systems for which the minimum bound of the settling-time function can be defined a priori as an explicit parameter of the system. Sufficient conditions for a controller to solve the optimal predefined-time stabilization problem for a given nonlinear system are provided. These conditions involve a Lyapunov function that satisfies a certain differential inequality for guaranteeing predefined-time stability. It also satisfies the steady-state Hamilton–Jacobi–Bellman equation for ensuring optimality. Furthermore, for nonlinear affine systems and a certain class of performance index, a family of optimal predefined-time stabilizing controllers is derived. This class of controllers is applied to optimize the sliding manifold reaching phase in predefined time, considering both the unperturbed and perturbed cases. For the perturbed case, the idea of integral sliding mode control is jointly used to ensure robustness. Finally, as a study case, the predefined-time optimization of the sliding manifold reaching phase in a pendulum system is performed using the developed methods, and numerical simulations are carried out to show their behavior. Copyright © 2017 John Wiley & Sons, Ltd.

Adaptive finite‐time fault‐tolerant tracking control for a class of MIMO nonlinear systems with output constraints

Abstract: Summary In this work, we present a novel adaptive finite-time fault-tolerant control algorithm for a class of multi-input multi-output nonlinear systems with constraint requirement on the system output tracking error. Both parametric and nonparametric system uncertainties can be effectively dealt with by the proposed control scheme. The gain functions of the nonlinear systems under discussion, especially the control input gain function, can be not fully known and state-dependent. Backstepping design with a tan-type barrier Lyapunov function and a new structure of stabilizing function is presented. We show that under the proposed control scheme, finite-time convergence of the output tracking error into a small set around zero is guaranteed, while the constraint requirement on the system output tracking error will not be violated during operation. An illustrative example on a robot manipulator model is presented in the end to further demonstrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.

Security-guaranteed filtering for discrete-time stochastic delayed systems with randomly occurring sensor saturations and deception attacks

Abstract: Summary In this paper, the security-guaranteed filtering problem is studied for a class of nonlinear stochastic discrete time-delay systems with randomly occurring sensor saturations (ROSSs) and randomly occurring deception attacks (RODAs). The nonlinearities in systems satisfy the sector-bounded conditions, and the time-varying delays are unknown with given lower and upper bounds. A novel measurement output model is proposed to reflect both the ROSSs and the RODAs. A new definition is put forward on the security level with respect to the noise intensity, the energy bound of the false signals, the energy of the initial system state, and the desired security degree. We aim at designing a filter such that, in the presence of ROSSs and RODAs, the filtering error dynamics achieves the prescribed level of security. By using the stochastic analysis techniques, a sufficient condition is first derived under which the filtering error system is guaranteed to have the desired security level, and then, the filter gain is designed by solving a linear matrix inequality with nonlinear constraints. Finally, a numerical example is provided to demonstrate the feasibility of the proposed filtering scheme. Copyright © 2016 John Wiley & Sons, Ltd.

Improving transient performance of adaptive control via a modified reference model and novel adaptation

Abstract: Summary This paper presents a new model reference adaptive control (MRAC) framework for a class of nonlinear systems to address the improvement of transient performance. The main idea is to introduce a nonlinear compensator to reshape the closed-loop system transient, and to suggest a new adaptive law with guaranteed convergence. The compensator captures the unknown system dynamics and modifies the given nominal reference model and the control action. This modified controlled system can approach the response of the ideal reference model. The transient is easily tuned by a new design parameter of this compensator. The nominal adaptive law is augmented by new leakage terms containing the parameter estimation errors. This allows for fast, smooth and exponential convergence of both the tracking error and parameter estimation, which again improves overall reference model following. We also show that the required excitation condition for the estimation convergence is equivalent to the classical persistent excitation (PE) condition. In this respect, this paper provides an intuitive and numerically feasible approach to online validate the PE condition. The salient feature of the suggested methodology is that the rapid suppression of uncertainties in the controlled system can be achieved without using a large, high-gain induced, learning rate in the adaptive laws. Extensive simulations are given to show the effectiveness and the improved response of the proposed schemes. Copyright © 2016 John Wiley & Sons, Ltd.

Adaptive fault‐tolerant spacecraft attitude control using a novel integral terminal sliding mode

Abstract: Summary The attitude tracking of a rigid spacecraft is approached in the presence of uncertain inertias, unknown disturbances, and sudden actuator faults. First, a novel integral terminal sliding mode (ITSM) is designed such that the sliding motion realizes the action of a quaternion-based nonlinear proportional-derivative controller. More precisely, on the ITSM, the attitude dynamics behave equivalently to an uncertainty-free system, and finite-time convergence of the tracking error is achieved almost globally. A basic ITSM controller is then designed to ensure the ITSM from onset when an upper bound on the system uncertainties is known. Further, to remove this requirement, adaptive techniques are employed to compensate for the uncertainties, and the resultant adaptive ITSM controller stabilizes the system states to a small neighborhood around the sliding surface in finite time. The proposed schemes avoid the singularity intrinsic to terminal sliding mode-based controllers and the unwinding phenomenon associated with some quaternion-based controllers. Numerical examples demonstrate the advantageous features of the proposed algorithm. Copyright © 2017 John Wiley & Sons, Ltd.

Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors

Abstract: Summary This paper exploits a nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors subject to thrust constraint and inertial parameter uncertainty to accomplish trajectory tracking missions. Because of under-actuated nature of the quadrotor, a hierarchical control strategy is available; and position and attitude loop controllers are synthesized according to adaptive sliding mode control projects, where adaptive updates with projection algorithm are developed to ensure bounded estimations for uncertain inertial parameters. Further, during the position loop controller development, an auxiliary dynamic system is introduced, and selection criteria for controller parameters are established to maintain the thrust constraint and to ensure the non-singular requirement of command attitude extraction. It has demonstrated that, the asymptotically stable trajectory tracking can be realized by the asymptotically stable cascaded closed-loop system and auxiliary dynamic system. Simulations validate and highlight the proposed control approach. Copyright © 2016 John Wiley & Sons, Ltd.

Integrated fault estimation and fault-tolerant control for uncertain Lipschitz nonlinear systems

Abstract: Summary This paper proposes an integrated fault estimation and fault-tolerant control (FTC) design for Lipschitz non-linear systems subject to uncertainty, disturbance, and actuator/sensor faults. A non-linear unknown input observer without rank requirement is developed to estimate the system state and fault simultaneously, and based on these estimates an adaptive sliding mode FTC system is constructed. The observer and controller gains are obtained together via H∞ optimization with a single-step linear matrix inequality (LMI) formulation so as to achieve overall optimal FTC system design. A single-link manipulator example is given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.

Stability of active disturbance rejection control for uncertain systems: A Lyapunov perspective

Abstract: Summary In this work, we introduce a simple stability analysis to justify, under some suitable assumptions, the active disturbance rejection control method, used in the feedback regulation of a substantially uncertain plant. A criterion is obtained that allows us to define under what conditions closed-loop stability can be assured. When the plant is mostly unknown, the criterion allows us to guarantee exponential convergence for the output-feedback regulation problem, in the presence of a constant external perturbation, and practical stability when the external perturbation and the tracking reference signal are both time-varying. In the latter case, the confinement error can be made as small as desired. To carry out the corresponding stability analysis, we derive the tracking error equation, and the observation error equation. To decouple these error equations, we use the Sylvester equation. Finally, we applied the direct Lyapunov method to analyze the corresponding convergence of the observation error and of the tracking error. Copyright © 2017 John Wiley & Sons, Ltd.

An adaptive event‐triggering scheme for networked interconnected control system with stochastic uncertainty

Abstract: Summary This paper investigates the problem of adaptive event-triggering scheme for networked interconnected systems to relieve the burden of the network bandwidth. The data releasing is triggered by an adaptive event-triggering device. The triggering condition depends on the state information at both the latest releasing instant and the current sampling instant. The threshold of the triggering parameter is achieved online rather than a predetermined constant. Taking the network-induced delays and the coupling delays of the subsystems into account, together with the hybrid adaptive event-triggering scheme and the stochastic uncertainty, we propose an unified model of the networked interconnected system. Sufficient conditions for the mean square stability and stabilization of the interconnected systems are developed by using Lyapunov–Krasovskii functional approach. A co-designed method is put forward to obtain the controller gains and the weight of the triggering condition simultaneously. Finally, an example is provided to demonstrate the design method. Copyright © 2016 John Wiley & Sons, Ltd.

Finite‐time guaranteed cost control for Itô Stochastic Markovian jump systems with incomplete transition rates

Abstract: Summary This paper is concerned with the finite-time guaranteed cost control problem for stochastic Markovian jump systems with incomplete transition rates. By a mode-dependent approach (MDA), several new sufficient conditions for the existence of state and output feedback finite-time guaranteed cost controllers are provided, and the upper bound of cost function is more accurately expressed. Moreover, these results' superiorities are analyzed and shown. A new N-mode optimization algorithm is given to minimize the upper bound of cost function. Finally, a detailed example is utilized to demonstrate the merit of the proposed results. Copyright © 2016 John Wiley & Sons, Ltd.

Robust IDA‐PBC for underactuated mechanical systems subject to matched disturbances

Abstract: The problem of robustification of interconnection and damping assignment passivity-based control for underactuated mechanical system vis-a-vis matched, constant, and unknown disturbances is addressed in the paper. This is achieved adding an outer-loop controller to the interconnection and damping assignment passivity-based control. Three designs are proposed, with the first one being a simple nonlinear PI, while the second and the third ones are nonlinear PIDs. While all controllers ensure stability of the desired equilibrium in spite of the presence of the disturbances, the inclusion of the derivative term allows us to inject further damping enlarging the class of systems for which asymptotic stability is ensured. Numerical simulations of the Acrobot system and experimental results on the disk-on-disk system illustrate the performance of the proposed controller. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.

Fault diagnosis and compensation for two‐dimensional discrete time systems with sensor faults and time‐varying delays

Abstract: Summary A fault diagnosis and compensation problem for two-dimensional discrete time systems with time-varying state delays is studied in this paper. The concerned two-dimensional systems are described by the Fornasisi–Marchesini second model and are subject to unknown disturbances. First, a fault detection and diagnosis module is designed to obtain the information on sensor faults; a new fault detection and diagnosis integrated design, using the observer based on descriptor system approach, is proposed to detect and estimate the sensor faults. The integrated design can maximize the fault detection rate for a given false alarm rate. Sufficient conditions for the existence of the integrated fault detection and diagnosis design are derived in the context of norm evaluation and provided in terms of matrix inequalities. Second, a fault-tolerant control module is proposed upon an existing output feedback controller. When the sensor fault occurs, the faulty measurement can be identified and corrected by the proposed fault detection and diagnosis module. In this case, the feedback controller can guarantee the performance of the closed-loop system even when encountering sensor faults. Finally, the proposed method is applied to a thermal process to illustrate its effectiveness. Copyright © 2017 John Wiley & Sons, Ltd.

Composite anti‐disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances

Abstract: Summary In this paper, the problem of composite anti-disturbance resilient control is studied for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. The multiple disturbances include two types: one is in the input channel generated by an exogenous system with perturbations, and the other is belong to L2[0,∞). The first class of disturbances is estimated by designing a disturbance observer. Combining the disturbance estimation with conventional L2 − L∞ resilient control law, a composite anti-disturbance control scheme is constructed such that the closed-loop system is stochastically stable, and different types of disturbances can be attenuated and rejected. By using Lyapunov function method and linear matrix inequalities technique, some sufficient conditions for the desired controller and observer gains are developed. Finally, an application example is provided to demonstrate the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

A method to construct reduced‐order parameter‐varying models

Abstract: This paper describes a method to construct reduced-order models for high-dimensional nonlinear systems. It is assumed that the nonlinear system has a collection of equilibrium operating points parameterized by a scheduling variable. First, a reduced-order linear system is constructed at each equilibrium point using state, input, and output data. This step combines techniques from proper orthogonal decomposition, dynamic mode decomposition, and direct subspace identification. This yields discrete-time models that are linear from input to output but whose state matrices are functions of the scheduling parameter. Second, a parameter varying linearization is used to connect these linear models across the various operating points. The key technical issue in this second step is to ensure the reduced-order linear parameter varying system approximates the nonlinear system even when the operating point changes in time. Copyright c © 2016 John Wiley & Sons, Ltd.

Smooth output feedback stabilization for a class of nonlinear systems with time-varying powers

Abstract: Summary This paper investigates the global asymptotic stabilization problem for a class of nonlinear systems with time-varying powers. First, adding a power integrator technique is revamped to design a smooth state feedback controller, which is implementable with only upper and lower bounds of the time-varying powers. When the system state is not fully available and the time-varying power is exactly known, a smooth output feedback controller constituted by a state feedback and a nonlinear state observer is constructed to globally stabilize the system. Copyright © 2017 John Wiley & Sons, Ltd.

Finite-time output tracking for a class of switched nonlinear systems

Abstract: Summary This paper investigates the finite-time output tracking for a class of switched nonlinear systems in p-normal form. Compared with the existing results, the restrictions on power orders of the system are relaxed. Using the convex combination method and the adding a power integrator technique, a state-dependent switching and law, and state feedback controllers of individual subsystems are constructed. It is shown that all states of the closed-loop system are bounded, and the tracking error can converge to a small neighborhood of zero in finite time. An example is provided to show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Heterogeneous consensus of higher‐order multi‐agent systems with mismatched uncertainties using sliding mode control

Abstract: Summary A robust consensus controller is proposed for heterogeneous higher-order nonlinear multi-agent systems, when the agent dynamics are involved with mismatched uncertainties. A distributed consensus protocol based on a time-varying nonhomogeneous finite-time disturbance observer and sliding mode control is designed to realize the network consensus of higher-order multi-agent systems. The time-varying finite-time disturbance observer overcomes the problem of peaking value near the initial time caused by the constant gain one and is designed to estimate the uncertainties and to mitigate the effect of mismatched uncertainties during the sliding mode. To eliminate the chattering phenomenon and ensure finite-time convergence to the sliding surface, the control law is designed by using the super twisting algorithm. Finally numerical simulations are given to illustrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Robust consensus control of uncertain multi-agent systems with input delay: a model reduction method

Abstract: Summary This paper addresses the robust consensus control design for input-delayed multi-agent systems subject to parametric uncertainties. To deal with the input delay, the Artstein model reduction method is employed by a state transformation. The input-dependent integral term that remains in the transformed system, owing to the model uncertainties, is judiciously analysed. By carefully exploring certain features of the Laplacian matrix, sufficient conditions for the global consensus under directed communication topology are identified using Lyapunov–Krasovskii functionals in the time domain. The proposed control only relies on relative state information of the subsystems via network connections. The effectiveness and robustness of the proposed control design are demonstrated through a numerical simulation example. Copyright © 2016 John Wiley & Sons, Ltd.

Distributed hierarchical control design of coupled heterogeneous linear systems under switching networks

Abstract: Summary In this paper, the distributed hierarchical control design is investigated for cooperations of heterogeneous linear systems subjected to the switching networks, where each subgraph of switching networks is allowed to be disconnected. Each heterogeneous system contains uncontrollable states and evolves in different dimension with different dynamics. The hierarchical control framework proposed in this paper consists of distributed hierarchical controllers, which contain the upper-layers dealing with the communication topologies and the lower-layers dealing with the heterogeneity of the systems. Under the framework, the cooperation problem of heterogeneous linear systems is decoupled into a cooperation problem of homogeneous virtual systems in the upper-layer and tracking problems of each single systems in the lower-layer. These two layers are designed based on the optimal control method and the output regulation method, respectively. Under the hierarchical control framework, the leader-following consensus of heterogeneous linear systems is achieved and the result is extended to the formation control problem. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

Robust observer-based stabilization of Lipschitz nonlinear uncertain systems via LMIs - discussions and new design procedure

Abstract: This paper presents a new observer-based controller design method for Lipschitz nonlinear systems with uncertain parameters and math formula-bounded disturbance inputs. In the presence of uncertain parameters, the separation principle is not applicable even in the case of linear time invariant systems. A state of the art review for uncertain linear systems is first presented to describe the shortcomings and conservatism of existing results for this problem. Then a new LMI-based design technique is developed to solve the problem for both linear and Lipschitz nonlinear systems. The features of the new technique are the use of a new matrix decomposition, the allowance of additional degrees of freedom in design of the observer and controller feedback gains, the elimination of any need to use equality constraints, the allowance of uncertainty in the input matrix and the encompassing of all previous results under one framework. An extensive portfolio of numerical case studies is presented to illustrate the superiority of the developed design technique to existing results for linear systems from literature and to illustrate application to Lipschitz nonlinear systems.

Finite‐time angular velocity observers for rigid‐body attitude tracking with bounded inputs

Abstract: Summary The attitude tracking of a rigid body without angular velocity measurements is addressed. A continuous angular velocity observer with fractional power functions is proposed to estimate the angular velocity via quaternion attitude information. The fractional power gains can be properly tuned according to a homogeneous method such that the estimation error system is uniformly almost globally finite-time stable, irrespective of control inputs. To achieve output feedback attitude tracking control, a quaternion-based nonlinear proportional-derivative controller using full-state feedback is designed first, yielding uniformly almost globally finite-time stable of the attitude tracking system as well as bounded control torques a priori. It is then shown that the certainty equivalent combination of the observer and nonlinear proportional-derivative controller ensures finite-time convergence of the attitude tracking error for almost all initial conditions. The proposed methods not only avoid high-gain injection, as opposed to the semi-global results, but also overcome the unwinding problem associated with some quaternion-based observers and/or controllers. Numerical simulations are presented to verify the effectiveness of the proposed methods.

H∞ output tracking control for a class of switched LPV systems and its application to an aero‐engine model

Abstract: Summary This paper aims to investigate the problem of H∞ output tracking control for a class of switched linear parameter-varying (LPV) systems. A sufficient condition ensuring the H∞ output tracking performance for a switched LPV system is firstly presented in the format of linear matrix inequalities. Then, a set of parameter and mode-dependent switching signals are designed, and a family of switched LPV controllers are developed via multiple parameter-dependent Lyapunov functions to enhance control design flexibility. Even though the H∞ output tracking control problem for each subsystem might be unsolvable, the problem for switched LPV systems is still solved by the designed controllers and the designed switching law. Finally, the effectiveness of the proposed control design scheme is illustrated by its application to an H∞ speed adjustment problem of an aero-engine. Copyright © 2016 John Wiley & Sons, Ltd.

Leader‐following attitude consensus of multiple uncertain spacecraft systems subject to external disturbance

Abstract: Summary The attitude consensus problem of multiple rigid spacecraft systems is one of the key issues in spacecraft formation flying and has been extensively studied. In this paper, we further consider the leader-following attitude consensus problem of multiple rigid uncertain spacecraft systems subject to a class of multi-tone sinusoidal disturbances with arbitrarily unknown amplitudes, initial phases, frequencies, and constant biases. In contrast to the existing results, in order to achieve asymptotic reference tracking and disturbance rejection by smooth control, we have integrated the distributed observer approach with internal model and adaptive control techniques. Simulation results are shown to validate the effectiveness of the proposed control law. Copyright © 2016 John Wiley & Sons, Ltd.