Showing papers in "International Journal of Control in 2016"

Event-triggered sliding mode control for a class of nonlinear systems

Abstract: Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into a...

Adaptive periodic event-triggered consensus for multi-agent systems subject to input saturation

Abstract: This paper investigates the distributed adaptive event-triggered consensus control for a class of nonlinear agents Each agent is subject to input saturation Two kinds of distributed event-triggered control scheme are introduced, one is continuous-time-based event-triggered scheme and the other is sampled-data-based event-triggered scheme Compared with the traditional event-triggered schemes in the existing literatures, the parameters of the event-triggered schemes in this paper are adaptively adjusted by using some event-error-dependent adaptive laws The problem of simultaneously deriving the controller gain matrix and the event-triggering parameter matrix, and tackling the saturation nonlinearity is cast into standard linear matrix inequalities problem A convincing simulation example is given to demonstrate the theoretical results

Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

Abstract: An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed ada...

Adaptive dual-layer super-twisting control and observation

Abstract: In this paper, a super-twisting-like structure with adaptive gains is proposed. The structure is parameterised by two scalar gains, both of which adapt, and by an additional time-varying term. The magnitudes of the adaptive terms are allowed to both increase and decrease as appropriate so that they are as small as possible, in the sense that they do not unnecessarily over-bound the uncertainty, and yet are large enough to sustain a sliding motion. In the paper, a new time varying gain is incorporated into the traditional super-twisting architecture. The proposed adaption law has a dual-layer structure which is formally analyzed using Lyapunov techniques. The additional term has the effect of simplifying the stability analysis whilst guaranteeing the second-order sliding mode properties of the traditional super-twisting scheme.

Adaptive Continuous Twisting Algorithm

Abstract: In this paper, an adaptive continuous twisting algorithm (ACTA) is presented. For double integrator, ACTA produces a continuous control signal ensuring finite time convergence of the states to zero. Moreover, the control signal generated by ACTA compensates the Lipschitz perturbation in finite time, i.e. its value converges to the opposite value of the perturbation. ACTA also keeps its convergence properties, even in the case that the upper bound of the derivative of the perturbation exists, but it is unknown.

Adaptive suboptimal second-order sliding mode control for microgrids

Abstract: This paper deals with the design of adaptive suboptimal second-order sliding mode (ASSOSM) control laws for grid-connected microgrids. Due to the presence of the inverter, of unpredicted load changes, of switching among different renewable energy sources, and of electrical parameters variations, the microgrid model is usually affected by uncertain terms which are bounded, but with unknown upper bounds. To theoretically frame the control problem, the class of second-order systems in Brunovsky canonical form, characterised by the presence of matched uncertain terms with unknown bounds, is first considered. Four adaptive strategies are designed, analysed and compared to select the most effective ones to be applied to the microgrid case study. In the first two strategies, the control amplitude is continuously adjusted, so as to arrive at dominating the effect of the uncertainty on the controlled system. When a suitable control amplitude is attained, the origin of the state space of the auxiliary syste...

Adaptive boundary control of a flexible manipulator with input saturation

Abstract: In this study, we consider the anti-windup design as one of the approaches for the boundary control problem of a flexible manipulator in the presence of system parametric uncertainties, external disturbances and bounded inputs. The dynamics of the system are represented by partial differential equations (PDEs). Using the singular perturbation approach, the PDE model is divided into two simpler subsystems. With the Lyapunov's direct method, an adaptive boundary control scheme is developed to regulate the angular position and suppress the elastic vibration simultaneously and the adaptive laws are designed to compensate for the system parametric uncertainties and the disturbances. The proposed control scheme allows the application of smooth hyperbolic functions, which satisfy physical conditions and input restrictions, be easily realised. Numerical simulations demonstrate the effectiveness of the proposed scheme.

Adaptive neural control for an uncertain robotic manipulator with joint space constraints

Abstract: In this paper, adaptive neural tracking control is proposed for a robotic manipulator with uncertainties in both manipulator dynamics and joint actuator dynamics. The manipulator joints are subject to inequality constraints, i.e., the joint angles are required to remain in some compact sets. Integral barrier Lyapunov functionals (iBLFs) are employed to address the joint space constraints directly without performing an additional mapping to the error space. Neural networks (NNs) are utilised to compensate for the unknown robot dynamics and external force. Adapting parameters are developed to estimate the unknown bounds on NN approximations. By the Lyapunov synthesis, the proposed control can guarantee the semi-global uniform ultimate boundedness of the closed-loop system, and the practical tracking of joint reference trajectory is achieved without the violation of predefined joint space constraints. Simulation results are given to validate the effectiveness of the proposed control scheme.

Group consensus control for heterogeneous multi-agent systems with fixed and switching topologies

Abstract: In this paper, the group consensus problems of heterogeneous multi-agent systems with fixed and switching topologies are investigated. First, a class of distributed group consensus protocol is proposed for achieving the group consensus of heterogeneous multi-agent systems by using the neighbours’ information. Then, some corresponding sufficient conditions are obtained to guarantee the achievement of group consensus. Rigorous proofs are given by using graph theory, matrix theory and Lyapunov theory. Finally, numerical simulations are also given to verify the theoretical analysis.

Multi-input control-affine systems static feedback equivalent to a triangular form and their flatness

Abstract: In this paper, we give a complete geometric characterisation of systems locally static feedback equivalent to a triangular form compatible with the chained form, for m = 1, respectively with the m-chained form, for m ≥ 2, where the number of controls is m + 1. They are x-flat systems. We provide a system of first-order PDE's to be solved in order to find all x-flat outputs, for m = 1, respectively all minimal x-flat outputs, for m ≥ 2. We illustrate our results by examples, in particular, by an application to a mechanical system: the coin rolling without slipping on a moving table.

Tuning algorithms for fractional order internal model controllers for time delay processes

Abstract: This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC...

Controllability of heterogeneous multi-agent systems under directed and weighted topology

Abstract: This paper considers the controllability problem for both continuous- and discrete-time linear heterogeneous multi-agent systems with directed and weighted communication topology. First, two kinds of neighbour-based control protocols based on the distributed protocol of first-order and second-order multi-agent systems are proposed, under which it is shown that a heterogeneous multi-agent system is controllable if the underlying communication topology is controllable. Then, under special leader selection, the result shows that the controllability of a heterogeneous multi-agent system is solely decided by its communication topology graph. Furthermore, some necessary and/or sufficient conditions are derived for controllability of communication topology from algebraic and graphical perspectives. Finally, simulation examples are presented to demonstrate the effectiveness of the theoretical results.

Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control

Abstract: This paper presents an adaptive gain algorithm for second-order sliding-mode control (2-SMC), specifically a super-twisting (STW)-like controller, with uniform finite/fixed convergence time, that is robust to perturbations with unknown bounds. It is shown that a second-order sliding mode is established as exact finite-time convergence to the origin if the adaptive gain does not have the ability to get reduced and converge to a small vicinity of the origin if the adaptation algorithm does not overestimate the control gain. The estimate of fixed convergence time of the studied adaptive STW-like controller is derived based on the Lyapunov analysis. The efficacy of the proposed adaptive algorithm is illustrated in a tutorial example, where the adaptive STW-like controller with uniform finite/fixed convergence time is compared to the adaptive STW controller with non-uniform finite convergence time.

Network-based event-triggered filtering for Markovian jump systems

Abstract: The problem of event-triggered H∞ filtering for networked Markovian jump system is studied in this paper. A dynamic discrete event-triggered scheme is designed to choose the transmitted data for different Markovian jumping modes. The time-delay modelling method is employed to describe the event-triggered scheme and the network-related behaviour, such as transmission delay, data package dropout and disorder, into a networked Markovian time-delay jump system. Furthermore, a sufficient condition is derived to guarantee that the resulting filtering error system is stochastically stable with a prescribed performance index. A co-design method for the H∞ filter and the event-triggered scheme is then proposed. The effectiveness and potential of the theoretic results obtained are illustrated by a simulation example.

Robust estimation-free prescribed performance back-stepping control of air-breathing hypersonic vehicles without affine models

Abstract: This paper investigates the design of a novel estimation-free prescribed performance non-affine control strategy for the longitudinal dynamics of an air-breathing hypersonic vehicle (AHV) via back-stepping. The proposed control scheme is capable of guaranteeing tracking errors of velocity, altitude, flight-path angle, pitch angle and pitch rate with prescribed performance. By prescribed performance, we mean that the tracking error is limited to a predefined arbitrarily small residual set, with convergence rate no less than a certain constant, exhibiting maximum overshoot less than a given value. Unlike traditional back-stepping designs, there is no need of an affine model in this paper. Moreover, both the tedious analytic and numerical computations of time derivatives of virtual control laws are completely avoided. In contrast to estimation-based strategies, the presented estimation-free controller possesses much lower computational costs, while successfully eliminating the potential problem of pa...

Output feedback robust MPC for LPV system with polytopic model parametric uncertainty and bounded disturbance

Abstract: The output feedback robust model predictive control (MPC), for the linear parameter varying (LPV) system with norm-bounded disturbance, is addressed, where the model parametric matrices are only known to be bounded within a polytope. The previous techniques of norm-bounding technique, quadratic boundedness (QB), dynamic output feedback, and ellipsoid (true-state bound; TSB) refreshment formula for guaranteeing recursive feasibility, are fused into the newly proposed approaches. In the notion of QB, the full Lyapunov matrix is applied for the first time in this context. The single-step dynamic output feedback robust MPC, where the infinite-horizon control moves are parameterised as a dynamic output feedback law, is the main topic of this paper, while the multi-step method is also suggested. In order to strictly guarantee the physical constraints, the outer bound of the true state replaces the true state itself, so tightness of this bound has a major effect on the control performance. In order to ti...

Computing actuator bandwidth limits for model reference adaptive control

Abstract: Although model reference adaptive control theory has been used in numerous applications to achieve system performance without excessive reliance on dynamical system models, the presence of actuator dynamics can seriously limit the stability and the achievable performance of adaptive controllers. In this paper, a linear matrix inequalities-based hedging approach is developed and evaluated for model reference adaptive control of uncertain dynamical systems in the presence of actuator dynamics. The hedging method modifies the ideal reference model dynamics in order to allow correct adaptation that is not affected by the presence of actuator dynamics. Specifically, we first generalise the hedging approach to cover a variety of cases in which actuator output and the control effectiveness matrix of the uncertain dynamical system are known and unknown. We then show the stability of the closed-loop dynamical system using Lyapunov-based stability analysis tools and propose a linear matrix inequality-based ...

A note on interval observer design for unknown input estimation

Abstract: This paper addresses the problem of interval observer design for unknown input estimation in linear time-invariant systems. Although the problem of unknown input estimation has been widely studied in the literature, the design of joint state and unknown input observers has not been considered within a set-membership context. While conventional interval observers could be used to propagate with some additional conservatism, unknown inputs by considering them as disturbances, the proposed approach allows their estimation. Under the assumption that the measurement noise and the disturbances are bounded, lower and upper bounds for the unmeasured state and unknown inputs are computed. Numerical simulations are presented to show the efficiency of the proposed approach.

Non-fragile reduced-order dynamic output feedback H∞ control for switched systems with average dwell-time switching

Abstract: This paper is concerned with the problem of non-fragile reduced-order dynamic output feedback H∞ control for both continuous- and discrete-time switched systems with average dwell-time switching. First, Lyapunov conditions for the analysis of asymptotic stability and weighted H∞ performance are presented. Then, sufficient conditions for the solvability of the problem of controller design are developed in terms of linear matrix inequalities. The design methods are suitable for general switched systems, without the need to impose extra constraints on the system matrices. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methods.

Adaptive sliding mode control and observation

Abstract: This editorial article gives a short introduction to Special Issue of International Journal of Control on Adaptive Sliding Mode Control and Observation.

Consensus tracking for second-order nonlinear multi-agent systems with switching topologies and a time-varying reference state

Abstract: In this study, the authors consider the consensus tracking problem for second-order nonlinear multi-agent systems with switching topologies and a time-varying reference state. The dynamics of each agent consists of nonlinear inherent dynamics. In order to reach consensus tracking, a class of nonsmooth control protocols is proposed which only depends on the agent's own information and its neighbours’ information. With the aid of algebraic graph theory, matrix theory, and Lyapunov theory, some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived. Finally, the numerical simulations are given to illustrate the effectiveness of the developed theoretical results.

Robust finite-time tracking control of nonholonomic mobile robots without velocity measurements

Abstract: The problem of robust finite-time trajectory tracking of nonholonomic mobile robots with unmeasurable velocities is studied. The contributions of the paper are that: first, in the case that the angular velocity of the mobile robot is unmeasurable, a composite controller including the observer-based partial state feedback control and the disturbance feed-forward compensation is designed, which guarantees that the tracking errors converge to zero in finite time. Second, if the linear velocity as well as the angular velocity of mobile robot is unmeasurable, with a stronger constraint, the finite-time trajectory tracking control of nonholonomic mobile robot is also addressed. Finally, the effectiveness of the proposed control laws is demonstrated by simulation.

Adaptive second-order sliding mode control with uncertainty compensation

Abstract: This paper endows the second-order sliding mode control (2-SMC) approach with additional capabilities of learning and control adaptation. We present a 2-SMC scheme that estimates and compensates for the uncertainties affecting the system dynamics. It also adjusts the discontinuous control effort online, so that it can be reduced to arbitrarily small values. The proposed scheme is particularly useful when the available information regarding the uncertainties is conservative, and the classical `fixed-gain’ SMC would inevitably lead to largely oversized discontinuous control effort. Benefits from the viewpoint of chattering reduction are obtained, as confirmed by computer simulations.

Event-based broadcasting containment control for multi-agent systems under directed topology

Abstract: The event-based broadcasting containment control problem for both first-order and second-order multi-agent systems under directed topology is investigated. Based on certain event, each agent decides when to transmit its current states to its neighbours and the agents’ distributed control algorithms are based on these sampled state measurements, which can significantly decrease the number of the controllers’ updates. All the agents are divided into two groups, namely, the leaders and the followers. The formation control is introduced. The leaders exchange their information to converge to a formation. The followers utilise the information from both their leader neighbours and their follower neighbours and are driven to the convex hull of the leaders using the proposed control algorithms. Numerical simulations are provided to illustrate the effectiveness of the obtained theoretical results.

Output regulation problem for a class of regular hyperbolic systems

Abstract: This paper investigates the output regulation problem for a class of regular first-order hyperbolic partial differential equation (PDE) systems. A state feedback and an error feedback regulator are considered to force the output of the hyperbolic PDE plant to track a periodic reference trajectory generated by a neutrally stable exosystem. A new explanation is given to extend the results in the literature to solve the regulation problem associated with the first-order hyperbolic PDE systems. Moreover, in order to provide the closed-loop stability condition for the solvability of the regulator problems, the design of stabilising feedback gain and its dual problem design of stabilising output injection gain are considered in this paper. This paper develops an easy method to obtain an adjustable stabilising feedback gain and stabilising output injection gain with the aid of the operator Riccati equation.

A distributed model predictive control (MPC) fault reconfiguration strategy for formation flying satellites

Abstract: In this paper, an active distributed (also referred to as semi-decentralised) fault recovery control scheme is proposed that employs inaccurate and unreliable fault information into a model-predictive-control-based design. The objective is to compensate for the identified actuator faults that are subject to uncertainties and detection time delays, in the attitude control subsystems of formation flying satellites. The proposed distributed fault recovery scheme is developed through a two-level hierarchical framework. In the first level, or the agent level, the fault is recovered locally to maintain as much as possible the design specifications, feasibility, and tracking performance of all the agents. In the second level, or the formation level, the recovery is carried out by enhancing the entire team performance. The fault recovery performance of our proposed distributed (semi-decentralised) scheme is compared with two other alternative schemes, namely the centralised and the decentralised fault rec...

Output feedback stabilisation for a cascaded wave PDE-ODE system subject to boundary control matched disturbance

Abstract: In this paper, we consider output feedback stabilisation for a wave PDE-ODE system with Dirichlet boundary interconnection and external disturbance flowing the control end. We first design a variable structure unknown input type state observer which is shown to be exponentially convergent. Then, we estimate the disturbance in terms of the estimated state, an idea from active disturbance rejection control. These enable us to design an observer-based output feedback stabilising control to this uncertain PDE-ODE system.

Distributed adaptive consensus control of Lipschitz nonlinear multi-agent systems using output feedback

Abstract: This paper addresses output-feedback-based distributed adaptive consensus control of multi-agent systems having Lipschitz nonlinear dynamics. Distributed dynamic protocols are designed based on the relative outputs of neighbouring agents and the adaptive coupling weights, under which consensus is reached between the nonlinear systems for all undirected connected communication topologies. Extension to the case of Lipschitz nonlinear multi-agent systems subjected to external disturbances is further studied, and a robust adaptive fully distributed consensus protocol is suggested. By application of a decoupling technique, necessary and sufficient conditions for the existence of these consensus protocols are provided in terms of linear matrix inequalities. Finally, numerical simulation results are demonstrated to validate the effectiveness of the theoretical results.

Global finite-time stabilisation for a class of stochastic high-order time-varying nonlinear systems

Abstract: In this paper, the problem of global finite-time stabilisation by state feedback is investigated for a class of stochastic high-order nonlinear systems with time-varying nonlinearities. Based on the generalised stochastic Lyapunov theorem on finite-time stability, and by skillfully using the method of adding a power integrator, a continuous state feedback controller is successfully constructed to guarantee that the closed-loop system is globally finite-time stable in probability. Finally, several simulation examples are provided to illustrate the effectiveness of the proposed method.

Decentralised consensus for multiple Lagrangian systems based on event-triggered strategy

Abstract: This paper considers the decentralised event-triggered consensus problem for multi-agent systems with Lagrangian dynamics under undirected graphs. First, a distributed, leaderless, and event-triggered consensus control algorithm is presented based on the definition of generalised positions and velocities for all agents. There is only one triggering function for both the generalised positions and velocities and no Zeno behaviour exhibited under the proposed consensus strategy. Second, an adaptive event-triggered consensus control algorithm is proposed for such multi-agent systems with unknown constant parameters. Third, based on sliding-mode method, an event-triggered consensus control algorithm is considered for the case with external disturbance. Finally, simulation results are given to illustrate the theoretical results.