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This paper studies the approximate optimal event-triggered tracking control problem for a class of second-order nonlinear systems with prescribed performances. By employing a prescribed performances function, restrictions on tracking errors are removed for prescribed performances including convergence rate, maximum overshoot, and steady-state error. On this basis, a complex optimal tracking control problem can be transformed into an optimal stabilising control problem by constructing an augmented system. Subsequently, an event-triggered mechanism is introduced to reduce communication resources. Then, an adaptive critic learning algorithm is used to solve the Hamilton-Jacobi-Bellman equation, where the weights in the critic networks are tuned through the gradient descent approach and experience replay technology. Through the developed learning method, the persistence of excitation condition is released, and the data efficiency is improved. The Lyapunov stability theory is introduced to verify the stability of the close-loop system and the tracking errors are uniformly ultimately bounded. Finally, simulation results are presented to show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

We consider a class of forced continuous-time Lur'e systems obtained by applying nonlinear feedback to a higher-order linear differential equation which defines an input-output system in the sense of behavioural systems theory. This linear system directly relates the input and output signals and does not involve any internal, latent or state variables. A stability theory subsuming results of circle criterion type is developed, including criteria for input-to-output stability and strong integral input-to-output stability, concepts which are very much reminiscent of input-to-state stability and strong integral input-to-state stability, respectively. The methods used in the paper combine ideas from the behavioural approach to systems and control, absolute stability theory and input-to-state stability theory. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time adaptive practical tracking control for a class of high-order nonlinear systems with full-state constraints and input saturation. The state constraints are handled by applying nonlinear transformed functions (NTFs) and the input saturation is estimated by an auxiliary hyperbolic tangent function. On the basis of adding a power integrator technique and adaptive control method, an adaptive state feedback controller is designed for the closed-loop system. With the aid of finite-time stability theory, the tracking error converges to a bounded neighbourhood of the origin in a finite time, and all the signals in the closed-loop system are bounded. At last, a simulation example and a practical example are presented to show the effectiveness of the proposed control procedure. [ABSTRACT FROM AUTHOR]

The Gilpin-Ayala (GA) ecosystem is one of the most important biological mathematical models. The exploration of various kinetics behaviours of GA-ecological model has attracted the attention of many mathematicians. This paper focuses on a nonlinear periodic GA-predation ecosystem with infinite distributed lags on time scales. In the sense of time scale, our model unifies the difference model and differential model of GA-predation ecosystem. We first discuss a class of auxiliary functions with only two real roots. By using these auxiliary functions, coincidence degree and some inequality techniques, we next obtain some existence conditions of periodic solution. Furthermore, we explore the global asymptotic stability of periodic solution on account of Lyapunov stability theory. An example and its simulation are provided to inspect the correctness and availability of our main results at last. [ABSTRACT FROM AUTHOR]

This article is concerned with the practical stability performance of nonlinear impulsive stochastic functional differential systems driven by G-Brownian motion (G-ISFDSs). Comparing with traditional Lyapunov stability theory, practical stability can portray qualitative behaviour and quantitative properties of suggested systems. By employing G-Itô formula, Lyapunov–Razumikhin approach and stochastic analysis theory, some novel conditions for pth moment practical exponential stability and quasi-sure global practical uniform exponential stability of G-ISFDSs are established. The obtained results show that impulses may influence dynamic behaviour of the addressed system. Two numerical examples are given to verify the validity of our developed results. [ABSTRACT FROM AUTHOR]

This paper suggests a new dynamic sliding mode controller incorporating a disturbance observer for controlling integrating processes with time delay. Here, a new reaching law has been introduced to expedite the system response without evoking chattering. The convergence of this law is also studied. Additionally, the whole system stability is proved using the Lyapunov stability theory. This paper also proposes a new disturbance observer to improve the disturbance rejection and to help suppress chattering further. The suggested observer has only one parameter to be designed. Therefore, this observer can easily be implemented. Several simulation examples and a real-time application are considered to prove the superiority of the suggested controller over the reported controllers in the literature. [ABSTRACT FROM AUTHOR]

A complex dynamical network (CDN) can be considered as the composition system with the nodes subsystem (NS) and the links subsystem (LS), and both subsystems are coupled with each other. In this paper, two vector differential equations (VDE) are used to describe the dynamical behaviours of NS and LS, respectively, in which the dynamical behaviour of NS is considered as the VDE with the second derivative term (SDT). This paper mainly focuses on the dynamics of LS, which is represented as VDE with the intuitive topologic feature of outgoing links, and investigates the design of the tracking controller for NS and the auxiliary tracking objectives (ATO) for LS. Firstly, the dynamical models of NS and LS in CDN are proposed, and the corresponding assumptions are given. Secondly, based on Lyapunov stability theory, the controller of NS and the ATO of LS are designed so that the state of NS can asymptotically track the given reference signal. Finally, the effectiveness of the proposed control strategy in this paper is verified by the numerical simulation example with N two-links robots. Abbreviations: ATO: auxiliary tracking objectives; CDN: complex dynamical network; LS: links subsystem; MDE: matrix differential equation; NS: nodes subsystem; SDT:second derivative term; VDE: vector differential equation; [ABSTRACT FROM AUTHOR]

In this study, a method for fault detection of a permanent magnet synchronous generator (PMSG) wind turbine is proposed. The dynamic model of the wind energy conversion system is simulated and the system's fault is diagnosed using a proposed terminal sliding mode observer (TSMO). The nonlinear state-space equations of the closed-loop wind turbine are derived, which include a robust adaptive controller that is implemented for maximum power capture and a PI controller that is designed for pitch angle control. Then, utilising a new approach, a TSMO is designed for estimating the states and faults in a finite time. The stability and convergence of the states and fault estimation error are investigated via the Lyapunov stability theory. A $ 3kw $ 3 kw PMSG wind turbine is simulated and using TSMO the states are estimated and a blade imbalance fault (BIF) fault is detected. The state and fault estimation errors converge to zero in a finite time. [ABSTRACT FROM AUTHOR]

This article addresses the backstepping control problem of the nonlinear strict-feedback system with an immeasurable state. To eliminate the effect coming from the immeasurable state variable, a new adaptive state observer method is developed for backstepping design by employing a neural network (NN) approximation strategy. As one of the highlighting contributions, the observer method can be performed with the relaxed condition because it does not require the design parameters to satisfy the Hurwitz equation, therefore it can be more easily applied and extended to serve for nonlinear system control than the existing observer methods. Finally, by integrating the observer dynamic into the backstepping design, the adaptive tracking control is achieved. Lastly, the feasibility of the method is proved by both stability theory and computer simulation. [ABSTRACT FROM AUTHOR]

Recent advances in practical fields like robotics and the miniaturisation of many sensors and actuators have turned autonomous vehicles into a reality. These systems come in many shapes and forms depending on the medium and their design but can be classified in one of two categories according to their mechanical configuration and number of actuators: fully-actuated and under-actuated vehicles; the second group still poses many challenges for the automatic control and robotics communities. This work introduces an easy methodology, based on quaternions, for designing controllers for a class of under-actuated systems, such as multicopter vehicles. The methodology starts from a fully-actuated representation of the system and adapts it to be implemented in under-actuated systems. In addition, it allows the easy development of controllers without taking care the coupled dynamics of the system. The proposed approach is based on Lyapunov's stability theory and is proven for certain criteria of the system's dynamics. The quadcopter configuration is used to validate the proposed methodology in simulations and in experimental tests. Abbreviations: AGV: autonomous ground vehicle; AUV: autonomous underwatervehicle; DoF: degree(s) of freedom; ESC: energy shaping controller; SFC: statefeedback controller; SSC: separated saturations controller; UAV: unmanned aerialvehicle [ABSTRACT FROM AUTHOR]

Event-triggered finite-time formation control is considered for second-order leader-following multi-agent systems with nonlinear term time delay in this study. Collision avoidance radius is designed for a class of second-order nonlinear multiagent systems to avoid collisions between agents. Collision avoidance control is realised by detecting the flight radius. Control cost is economised, and communication volume is reduced by controlling key nodes and designing an event-triggered control strategy. The system can realise formation control in finite time by designing an FTC function. Some sufficient conditions for the formation of the second-order multi-agent system in finite time are obtained by using Lyapunov stability theory and analysis. The integral sliding mode control algorithm and finite-time stability theory are used to enhance the robustness of the system, and the upper bound of finite time is given. At the same time, the ability of the designed event-triggered function to avoid Zeno behaviour is proven. Finally, the feasibility of the results is verified through a numerical simulation. [ABSTRACT FROM AUTHOR]

This paper focuses on the exponential stabilisation problem of inertial memristive neural networks (IMNNs) with unbounded discrete time-varying delays. The considered IMNNs are modelled by second-order derivatives equations by introducing the inertial terms. By using nonsmooth analysis, Lyapunov stability theory, inequality techniques and integral-differential of Lyapunov functional method, a feedback controller is designed to guarantee pth moment exponential stabilisation of the addressed IMNNs under the framework of Filippov solutions. It is worth noticing that the considered time delays of IMNNs can be unbounded. Finally, a numerical example is presented to illustrate the effectiveness of the main theoretical result. [ABSTRACT FROM AUTHOR]

Based on Lyapunov finite-time stability theory and backstepping strategy, we put forward a novel fixed-time bounded H infinity tracking control scheme for a single-joint manipulator system with input saturation. The main control objective is to maintain that the system output variable tracks the desired signal at fixed time. The advantages of this paper are the settling time of the tracking error converging to the origin is independent of the initial conditions, and its convergence speed is more faster. Meanwhile, bounded H infinity control is adopted to suppress the influence of external disturbances on the controlled system. At the same time, the problem of input saturation control is considered, which effectively reduces the input energy consumption. Theoretical analysis shows that the tracking error of the closed-loop system converges to a small neighbourhood of the origin within a fixed time. In the end, a simulation example is presented to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

The anti-disturbance control problem is investigated for systems with multiple disturbances. For the disturbance with partially known information, an observer was designed to give the online estimation. Based on which, a fixed-time anti-disturbance control scheme was proposed by combing regional pole placement, the H ∞ control method and fixed-time stability theory. The proposed controller can make the closed-loop system globally stable in fixed time, which has the advantages of high control accuracy, fast convergence speed, and the convergence time is independent of the initial conditions. Finally, two simulation examples including a numerical example and a doubly fed induction generators system are provided to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the non-fragile output-feedback H ∞ control problem for event-triggered networked control system with probabilistic time-varying delay and controller gain uncertainties. With known conditional probability distribution, the time-varying delay is modelled as a Bernoulli distributed white sequences. An improved two-side closed-loop functional is constructed by using the sawtooth structure characteristic of artificial time delay. By applying the Lyapunov–Krasovskii stability theory, the lower conservative stability criterions for time-delay system are derived. Aiming at the external disturbance and the parameter uncertainty of controller gain, a non-fragile output-feedback H ∞ control strategy based on event-triggered mechanism is proposed. Moreover, a co-design scheme of controller gain and event-triggered matrix is obtained based on linear matrix inequality technique. Finally, three simulation examples are utilised to verify the effectiveness of the presented method. [ABSTRACT FROM AUTHOR]

Ayala-Gilpin ecosystem is one of the most famous differential equation models based on experimental and theoretical analysis. Most of the previous works on the almost periodic solution and its stability are mainly about the existence of an almost-periodic solution and its global stability. In fact, the real ecosystem presents multiple stable states due to the influence of various external factors. However, there are few researches on multiple almost-periodic solutions and local stability of Ayala-Gilpin ecosystem. Therefore, we focus on the existence and local exponential stability of multiple almost-periodic solutions for a classical nonlinear competitive Ayala-Gilpin ecosystem provided with varying-lags and control terms in this paper. Firstly, a class of functions having only two zeros in (− ∞ , + ∞) is investigated. Next, based on the existence of zeros of these functions, we obtain some sufficient conditions to ensure the existence of at least four almost-periodic positive solutions by utilising theorem of coincidence degree and some inequality techniques. Furthermore, we also conclude that this ecosystem exists at least two almost-periodic positive solutions under relatively weak conditions. Finally, we build some Lyapunov functionals to discuss the local exponential stability of each almost-periodic positive solution in its own region. As an application, a numerical simulation inspect the effectiveness of our major results. [ABSTRACT FROM AUTHOR]

This paper investigates the trajectory tracking control problem of a dynamic positioning vessel (DPV) subject to tracking performance, time-varying sea loads and inertia uncertainties. Firstly, a novel cascade model of the DPV is built to describe the dynamics. Then, in order to guarantee the performance constraints of the trajectory tracking, a new-type fixed-time performance function is proposed, which can not only guarantee the transient and steady-state performance during task execution, but also achieve convergence at a fixed time. In addition, an adaptive neural network is introduced to handle the problem of parameter uncertainty and unknown sea loads in the system. Furthermore, it is proved by the Lyapunov stability theory that all signals in the closed-loop system are bounded. Finally, numerical simulation results verified the effectiveness of the proposed method and ensure that the tracking error is stable in the interval of 2 m or less within a given time. [ABSTRACT FROM AUTHOR]

This paper presents a fixed-time neuro-adaptive control design for a class of uncertain under-actuated nonlinear systems (UNS) using a non-singular fast terminal sliding mode control (TSMC) with a radial basis function (RBF)-based estimator to achieve the convergence and robustness against the uncertainties. The mathematical model of the considered class is reduced into an equivalent regular form. A fast TSMC is designed for the transformed form to improve the control performance and annihilate the associated singularity problem of the conventional TSMC. Lyapunov stability theory ensures the steering of the sliding manifold and system states in fixed time. RBF neural networks are adaptively estimate the nonlinear drift functions. The theoretical design, analysis, and simulations of cart-pendulum and quadcopter demonstrate the feasibility and benefits of the regular form transformation and the designed control design. Comparing the proposed synthesis with the standard literature presents the attractive nature of proposed method for such a class. [ABSTRACT FROM AUTHOR]

Since its introduction in the late 1980s, passivity-based control (PBC) has proven to be successful in controlling many robotic systems. The connection between stability and passivity theory is the most attractive feature of controllers designed using this methodology. However, the need to solve nonlinear partial differential equations (PDE) in closed-form has been a major challenge in applying PBC to general robotic systems. Here, we introduce a systematic approach to design controllers for a class of underactuated mechanical systems based on interconnection and damping assignment. Exploiting the universal approximation capability of neural networks, we formulate a data-driven optimisation problem that discovers solutions to the required PDEs automatically. Our approach does not destroy the passivity structure, preserving the inherent stability properties. We demonstrate the efficacy of our framework on two benchmark problems: the inertia wheel pendulum and the ball and beam system. [ABSTRACT FROM AUTHOR]

This paper proposes a novel prescribed-time cooperative guidance law (PTCGL) for multiple missiles cooperatively attacking a manoeuvring target. Guidance models in two directions are used and the acceleration saturations are also considered in both two directions. In line-of-sight (LOS) direction, by applying prescribed-time multi-agent consensus theory, the problem of the times-to-go ( T g o s ) of multiple missiles converging to a same value is transformed into a stabilisation problem. Then the cooperative guidance law in LOS direction is designed based on the prescribed time integral sliding mode surface (PTISMS) and a new variable coefficient exponential reaching law, and a first-order auxiliary system is introduced to deal with the input saturation problem; based on a prescribed time linear sliding surface (PTLSMS), the cooperative guidance law in normal LOS direction is designed to ensure the LOS angle and LOS angle rate convergence within a prescribed time, and a second-order auxiliary system is designed to deal with the input saturation problem. Furthermore, the prescribed time convergence of the PTCGL is proved with the Lyapunov stability theory. Finally, numerical simulations demonstrate the effectiveness and advantages of the proposed PTCGL. [ABSTRACT FROM AUTHOR]

This paper investigates adaptive finite-time stabilisation for a class of output-constrained low-order nonlinear systems with unknown time-varying powers, parametric and dynamic uncertainties. Due to low-order nonlinear systems being merely continuous but not smooth, and the presence of time-varying powers and multiple unknowns, all the existing control methods of output-constrained nonlinear systems are inapplicable. By characterising unmeasured dynamic uncertainty with finite-time input-to-state stability (FTISS), applying finite-time stability theory and introducing the tan-type barrier Lyapunov function, low-power and high-power terms into control design, a unified adaptive state-feedback controller, which can deal with both constrained and unconstrained systems, is constructed. It is proved that all the closed-loop signals are uniformly bounded, the output constraint is not violated, and system states converge to zero in a finite time. Finally, a simulation example is given to illustrate the effectiveness of this control scheme. [ABSTRACT FROM AUTHOR]

This paper presents a discrete-time Robust Adaptive Super-Twisting Sliding Mode controller and its stability analysis by means of Lyapunov stability theory. The control law is composed by two different control structures: a Robust Model Reference Adaptive Controller (RMRAC) and an Adaptive Super-Twisting Sliding Mode (STSM) Controller. The main advantage of the control structure is its robust performance and high adaptability in face of unmodelled dynamics, presenting a fast reference tracking without chattering, since it uses a second-order Sliding Mode action into adaptive control structure. The stability and robustness analysis of the control structure are presented in discrete time, considering the overall plant, that is, in presence of matched and unmatched dynamics. In addition, the control structure performance is corroborated with simulation results, considering a non-minimum phase unstable plant. Moreover, the presented results are compared with an adaptive first-order SM control-based RMRAC, which can be clearly seen that proposed controller has better performance, mainly by means of chattering mitigation. [ABSTRACT FROM AUTHOR]

In this paper, we analyse the convergence properties of the Dynamic Programming Value Iteration algorithm by exploiting the stability theory of discrete-time switched affine systems. More specifically, by formulating the Value Iteration algorithm as a switched affine system, a Lyapunov-based optimal policy selection strategy is designed to guarantee the practical stabilisation of the resulting system towards an invariant set of attraction containing a given target value function. The switching control algorithm, referred to as Lyapunov-based Value Iteration algorithm, can be regarded as a convergence analysis tool and can be adopted to verify if and how such target value function can be approached by choosing from a subset of suitable stationary policies, at each time slot. The usage of the proposed algorithm in practice is also discussed. Finally, two different applications are provided to further illustrate and examine the key-aspects of the approach presented. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive control strategy for solving multi-player noncooperative differential games with dynamics modelled as general nonlinear input-state-output port-Hamiltonian systems. The proposed controller is obtained by extending an existing single-player feedback Nash strategy to N players and by using the Hamiltonian of the port-Hamiltonian system as an admissible control-Lyapunov function for each player. Necessary and sufficient conditions for the stability of the resulting controlled system are provided by employing Lyapunov stability theory. Furthermore, the N player feedback strategy is extended by adaptively weighting the individual value functions to ensure convergence to the Nash solution. Finally, numerical simulations demonstrate the effectiveness of the proposed explicit control laws. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal synchronisation problem for unknown nonlinear heterogeneous multi-agent systems (MASs) with an active leader and disturbances. Due to the external input signal of the active leader, the resulted uncooperative behaviours and unpredictability increase difficulty to derive the analytical solution of the coupled Bellman equation. To this end, we develop a distributed model reference adaptive critic learning algorithm with a hierarchical and distributed synchronisation control framework, which transforms the synchronisation problem of unknown nonlinear MASs into that of defined reference ones. Moreover, the algorithm extends our previous work to the distributed MASs, so that it is guaranteed that all the agents reach an agreement with the minimised transient errors and robustness against the disturbances and the neural network (NN) approximation errors. It is proved that the local neighbour tracking errors and the NN weight estimation errors are uniformly ultimately bounded via Lyapunov stability theory. A simulation example for multi-manipulator systems demonstrates the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates the continuous composite control scheme for the tracking of nonlinear system with mismatched disturbances, input saturation and full-state constraints. Based on the fixed-time stability theory, a novel fixed-time disturbance observer is proposed, which switches from a uniform second-order sliding mode observer with high-degree term to the classical continuous super-twisting observer. Then, a command filtered backstepping control scheme is designed to enforce the tracking error into a small neighbourhood of the origin in fixed time while the full-state constraint and input saturation constraint are satisfied. To further reduce the communication burden, an event-triggered communication strategy between the controller and the actuator input is also developed. Furthermore, all the signals in the closed-loop system are proven to be bounded. Finally, the effectiveness of the proposed control strategy is illustrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the distributed optimal consensus problem is investigated for a class of continuous-time nonlinear multi-agent systems with input saturation. Non-quadratic cost functions are introduced to handle input constraints and a novel distributed optimal consensus protocol is derived based on event-triggered adaptive dynamic programming method. An online implement scheme is designed under actor-critic network framework in order to obtain the solutions of Hamilton-Jacobi-Bellman equations online. The computation and communication loads are effectively reduced since the weight estimation vectors and controllers are updated only at event-triggered instants. Detailed analysis is presented based on Lyapunov stability theory which guarantees that the weight estimation errors and local consensus errors are uniformly ultimately bounded. Furthermore, it proves that Zeno behaviour can be effectively avoided. Finally, the simulation examples are presented to validate the proposed strategy. [ABSTRACT FROM AUTHOR]

In this paper, the fixed-time stochastic consensus problem of multi-agent systems with fixed and switching topologies is investigated. To realise the fixed-time stochastic consensus, a class of continuous non-Lipschitz protocols are designed and the effectiveness is rigorously proved. Based on the stability theory of stochastic differential equations, sufficient conditions for consensus are established. Moreover, the upper bound of the settling time is given, the influence of the algebraic connectivity of the network topologies on the convergence time is also investigated. Finally, several simulations are given to illustrate the effectiveness of the theoretical results. The simulation results show that the convergence time depends mainly on the parameters of the finite-time control term, and suitable noise can enable individuals to reach the consensus more rapidly. [ABSTRACT FROM AUTHOR]

The adaptive neural finite-time stabilisation problem is studied for a class of p-normal form nonlinear systems in this paper. An adaptive neural finite-time controller is designed by combining the adding a power integrator technique with Lyapunov finite-time stability theory. And the stability of the closed-loop system is analysed. The designed controller can guarantee that all the states in the closed-loop system are finite-time asymptotic stable. In the design, a new assumption for unknown nonlinear terms is proposed, which is looser than the existed works. A combination vector method is adopted to avoid the effect of the approximation errors of neural networks. The maximal value of norms of the combination vectors is taken as an adaptive parameter, so that the complexity of the design method is reduced. And the settling-time can be adjusted by changing a design parameter. Finally, three simulation examples demonstrate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper studies the distributed controller design problem for linear discrete-time large-scale systems under gossip communication protocol. In this communication protocol, each sub-controller transmits the subsystem's state information to only one randomly chosen neighbour at transmission instants. Distributed controllers are designed such that the closed-loop system is exponentially mean-square stable and that the prescribed L 2 -gain performance is satisfied in the mean-square sense. The design condition is obtained based on Lyapunov stability theory and given in terms of linear matrix inequalities. Finally, two numerical examples are presented to illustrate the advantages of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the distributed fixed-time consensus-based formation tracking problems for multiple nonholonomic wheeled mobile robots under a directed interaction topology. The distributed fixed-time consensus-based controllers under the directed interaction topology are proposed for the multiple wheeled mobile robots with nonholonomic constraints, which can guarantee the group of robots converge to a predefined formation pattern with its centroid moving along the predefined reference trajectory in a fixed time. The fixed-time formation tracking can be achieved within a fixed settling time, which is independent of the initial states of the whole system. Moreover, the conditions of formation stability control are analysed by utilising graph and Lyapunov stability theories. Finally, the feasibility of the proposed distributed controllers is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, the observer-based output consensus of leader-following fractional-order heterogeneous nonlinear multi-agent systems with potentially different state dimensions and different dynamics are investigated. Considering the agents' states may be not available in practice, the distributed state observer is designed for each agent. Then corresponding distributed control protocols based a proposed virtual exosystem are proposed to convert the output consensus problem into the stabilisation problem. By employing matrix theory, algebraic graph theory and the stability theory of fractional system, the state consensus of the virtual exosystem and the output consensus of heterogenous fractional nonlinear MAS is achieved. Moreover, the sufficient conditions are also obtained. Simulation examples are presented to verify the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

This paper investigates a trajectory planning and tracking control scheme to implement the autonomous obstacle avoidance for wheeled inverted pendulum (WIP) vehicles, which enable the mobile platform to avoid obstacles rapidly and stabilise the vehicle body simultaneously. In the first place, an obstacle avoidance trajectory planning method suitable for the WIP vehicle is proposed, which, in particular, is capable of planning an obstacle avoidance trajectory with the merits of continuous curvature and approximately zero longitudinal acceleration in vehicle body-fixed frame system. Then, aiming the feature of the each subsystem, a nonsingular terminal sliding mode control and a nested saturation approach are employed to construct the trajectory tracking algorithm for fully actuated steering subsystem and underactuated longitudinal subsystem of the WIP vehicle, respectively. Besides, the closed-loop system's stability and asymptotical convergence of tracking error are proven in the sense of Lyapunov stability theory. In the end, numerical simulations are performed to demonstrate the feasibility and effectiveness of the proposed scheme for obstacle avoidance of WIP vehicles. [ABSTRACT FROM AUTHOR]

In order to study the traffic jams and congestion, this paper investigated the stability of a car-following model on the basis of synchronisation theory of complex network. By using the Lyapunov stability theory and designing the appropriate controller, the car-following model is quickly stabilised and the stability condition of the model is obtained. In addition, the stability of car-following model is studied when the vehicle is subjected to external stochastic disturbance. Finally, the numerical simulation is carried out by using the MATLAB simulation technology, and the results show that the car-following model is rapidly stabilising, and congestion phenomenon is effectively alleviated under the controller designed. [ABSTRACT FROM AUTHOR]

This paper studies the problem of finite-time H∞ control for strict feedback nonlinear systems with external disturbance. The finite-time stability theory, H∞ control method, backstepping technique, together with adding a power integrator tool are combined to design a finite-time H∞ state feedback controller. The obtained controller can make the closed-loop system finite-time convergent, and the influence of the external disturbance is attenuated to a given degree. Two numerical examples are presented to show the effectiveness and feasibility of the proposed method. Meanwhile, the proposed method is also applied to robot manipulators. [ABSTRACT FROM AUTHOR]

In this paper, we consider a two-player stochastic differential game problem over an infinite time horizon where the players invoke controller and stopper strategies on a nonlinear stochastic differential game problem driven by Brownian motion. The optimal strategies for the two players are given explicitly by exploiting connections between stochastic Lyapunov stability theory and stochastic Hamilton–Jacobi–Isaacs theory. In particular, we show that asymptotic stability in probability of the differential game problem is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution to the steady-state form of the stochastic Hamilton–Jacobi–Isaacs equation, and hence, guaranteeing both stochastic stability and optimality of the closed-loop control and stopper policies. In addition, we develop optimal feedback controller and stopper policies for affine nonlinear systems using an inverse optimality framework tailored to the stochastic differential game problem. These results are then used to provide extensions of the linear feedback controller and stopper policies obtained in the literature to nonlinear feedback controllers and stoppers that minimise and maximise general polynomial and multilinear performance criteria. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following consensus problem of multi-agent systems is studied. It is assumed that there exist gain and bias transmission nonlinearities in the links in the communication network. Two distributed adaptive control schemes, where the transmission nonlinearities are compensated, are designed to guarantee that the consensus problem is solved and synchronisation errors are cooperatively uniformly and ultimately bounded. By using Lyapunov stability theory, the stability of closed-loop system is proven. The effectiveness of the proposed control methods is demonstrated by simulation results. [ABSTRACT FROM AUTHOR]

A stable control strategy is proposed via energy attenuation to realise the position control for a second-order nonholonomic planar four-link active-passive-active-active (APAA) underactuated mechanical system. Since a first-order nonholonomic planar passive-active-active (PAA) system can be stabilised at the target position, we control the first link based on the principle of energy attenuation to target value and the planar APAA systemis reduced to be a first-order nonholonomic PAA system, where the target value is selected to ensure the target position comes within the reachable area of the PAA system. Meanwhile, we divide the control of the reduced-order PAA systeminto two stages based on the holonomic characteristic of planar acrobot, and the target angles of which are obtained according to the target position by using the simulated annealing algorithm. Each stage controllers of the reduced-order system are designed according to its control target. Finally, the validity of the control strategy is demonstrated via the simulations. [ABSTRACT FROM AUTHOR]

It is known that input-output approaches based on scaled small-gain theorems with constant Dscalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with uncertain linear operators. This dramatically contrasts with the case of general linear systems with delays where input-output approaches provide, in general, sufficient conditions only. Using these results, we provide simple alternative proofs for many of the existing results on the stability of linear positive systems with discrete/distributed/neutral timeinvariant/- varying delays and linear difference equations. In particular, we give a simple proof for the characterisation of diagonal Riccati stability for systems with discrete-delays and generalise this equation to other types of delay systems. The fact that all those results can be reproved in a very simple way demonstrates the importance and the efficiency of the input-output framework for the analysis of linear positive systems. The approach is also used to derive performance results evaluated in terms of the L1-, L2- and L∞-gains. It is also flexible enough to be used for design purposes. [ABSTRACT FROM AUTHOR]

This paper addresses the control problem of an important class of hybrid dynamical systems where the desired state does not belong to the set of subsystemequilibria. Beyond the practical stabilisation where the system trajectory has to be driven to a neighbourhood of a desired state, a control law is designed to solve the limit cycle stabilisation problem for planar hybrid systems. Using the hybrid Poincaré map, two hybrid controllers are developed, which guarantee a local asymptotic/finite-time stability of the desired limit cycle. Illustrative examples are provided to highlight the effectiveness of the derived results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of distributed containment fault-tolerant control for a class of nonlinear multi-agent systems in strict-feedback form is studied. The considered nonlinear multi-agent systems are subject to unknown nonlinear functions and actuator faults with loss of effectiveness and lock-in-place. By resorting to the universal approximation capability of fuzzy logical systems, the command filtered backstepping technique and nonlinear fault-tolerant control theory, distributed controllers are designed recursively. From the Lyapunov stability theory, it is proved that all signals of the resulting closed-loop systems are cooperatively semi-globally uniformly ultimately bounded and the containment errors converge to a small neighbourhood of origin by properly tuning the design parameters. Finally, a numerical example is provided to show the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper considers distributed systems arising when multiple agents cooperatively solve a quadratic optimisation problem. To maintain privacy of their states over time, agents implement a noise-adding mechanism according to the classic differential privacy framework. We characterise how the noise due to the privacy mechanism degrades the performance of the multi-agent system. Interestingly, we showthat depending on the desired level of privacy (and thus noise), the systemperformance is optimised by reducing the level of cooperation among the agents. The notion of cooperation level, which is formally introduced and defined in the paper, models the trust of an agent towards the information received from neighbouring agents. For the prototypical examples of consensus and centroidal Voronoi tessellations, we are able to characterise the optimum cooperation level that maximises the system performance while ensuring a desired privacy level. Our results suggest that for the class of problems we study, and in fact for a broad class of multi-agent systems, it is always beneficial for the agents to reduce their cooperation level when the privacy level increases. [ABSTRACT FROM AUTHOR]

This paper concerns the global regulation for a class of stochastic high-order nonlinear systems which admit more general system form than the existing works. For details, except for the serious system nonlinearities which show that the considered systems are the generalisations of the strict-feedback systems, the most distinct feature of the systems is exhibited by the multiple unknown control directions, that is, all control coefficients of the virtual and actual control have unknown signs. By skillfully employing the Nussbaum function, and applying themethod of adding a power integrator, an effective regulation control scheme is successfully provided for the considered systems. In particular, the presented controller can guarantee that all the closed-loop systemstates are bounded, and especially the original system states converge to the origin, both in the sense of probability one. [ABSTRACT FROM AUTHOR]

This paper addresses the global finite-time attitude stabilisation problem on the special orthogonal group (SO(3)) for a rigid spacecraft via homogeneous feedback approach. Considering the topological and geometric properties of SO(3), the logarithm map is utilised to transform the stabilisation problem on SO(3) into the one on its associated Lie algebra (). A model-independent discontinuous state feedback plus dynamics compensation scheme is constructed to achieve the global finite-time attitude stabilisation in a coordinate-invariant way. In addition, to address the absence of angular velocity measurements, a sliding mode observer is proposed to reconstruct the unknown angular velocity information within finite time. Then, an observer-based finite-time output feedback control strategy is obtained. Numerical simulations are finally performed to demonstrate the effectiveness of the proposed finite-time controllers. [ABSTRACT FROM AUTHOR]

This paper is concerned with finite-time and fixed-time consensus of multi-agent systems in a leader-following framework. Different from conventional leader-following tracking approaches where inherent dynamics satisfying the Lipschitz continuous condition is required, a more generalised case is investigated: discontinuous inherent dynamics. By nonsmooth techniques, a nonlinear protocol is first proposed to achieve the finite-time leader-following consensus. Then, based on fixed-time stability strategies, the fixed-time leader-following consensus problem is solved. An upper bound of settling time is obtained by using a new protocol, and such a bound is independent of initial states, thereby providing additional options for designers in practical scenarios where initial conditions are unavailable. Finally, numerical simulations are provided to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this work, we study in a Hilbert state space, the partial stabilisation of non-homogeneous bilinear systems using a bounded control. Necessary and sufficient conditions for weak and strong stabilisation are formulated in term of approximate observability like assumptions. Applications to parabolic and hyperbolic equations are presented. [ABSTRACT FROM AUTHOR]

This work investigates a new formation control problem of multiple underactuated surface vessels. The controller design is based on input-output linearisation technique, graph theory, consensus idea and some nonlinear tools. The proposed smooth time-varying distributed control law guarantees that the multiple underactuated surface vessels globally exponentially converge to some desired geometric shape, which is especially centred at the initial average position of vessels. Furthermore, the stability analysis of zero dynamics proves that the orientations of vessels tend to some constants that are dependent on the initial values of vessels, and the velocities and control inputs of the vessels decay to zero. All the results are obtained under the communication scenarios of static directed balanced graph with a spanning tree. Effectiveness of the proposed distributed control scheme is demonstrated using a simulation example. [ABSTRACT FROM AUTHOR]

This paper considers the problem of flocking with connectivity preservation for a class of disturbed nonlinear multi-agent systems. In order to deal with the nonlinearities in the dynamic of all agents, some auxiliary variables are introduced into the state observer for stability analysis. By proposing a bounded potential function and using adaptive theory, a novel output feedback consensus algorithm is developed to guarantee that the states of all agents achieve flocking with connectivity preservation. [ABSTRACT FROM AUTHOR]

Many disturbance rejection methods have been proposed for processes with dead-time, while these existing methods may not work well under multiple periodic disturbances. In this paper, a multiple periodic disturbance rejection is proposed under the Smith predictor configuration for processes with long dead-time. One feedback loop is added to compensate periodic disturbance while retaining the advantage of the Smith predictor. With information of the disturbance spectrum, the added feedback loop can remove multiple periodic disturbances effectively. The robust stability can be easily maintained through the rigorous analysis. Finally, simulation examples demonstrate the effectiveness and robustness of the proposed method for processes with long dead-time. [ABSTRACT FROM AUTHOR]

To address security issues in oilwell drillstring system, the drilling operation handling which is in generally not autonomous but ensured by an operator may be drill bit destructive or fatal for the machine. To control of stick-slip phenomenon, the drillstring control at the right speed taking only the drillstring vibration is not sufficient as the mud dynamics and the pressure change around the drill pipes cannot be neglected. A coupled torsional vibration and pressure model is presented, and the well-posedness problem is addressed. As a Partial Differential Equation-Ordinary Differential Equation (PDE-ODE) coupled system, and in order to maintain a non destructive downhole pressure, we investigate the control stability with and without the damping term in the wave PDE. In terms of, the torsional variable, the downhole pressure, and the annulus pressure, the coupled system equilibrium is shown to be exponentially stable. [ABSTRACT FROM AUTHOR]