This study investigates distributed regular polygon formation control and obstacle avoidance problem for multi-robot systems with the leader–follower structure. The communication topology of the networked multi-robot system is modelled by a directed graph. Firstly, a distributed state observer is designed such that only part of the follower robots need to know the desired distance between the leader and followers. Based on the state observer, distributed obstacle avoidance can be realised. Then, an improved state transformation is designed such that the formation control of multiple non-holonomic wheeled mobile robots with observed states can be converted into a consensus-like problem. Based on the state transformation, novel controllers are proposed to achieve the formation control objectives. Finally, the effectiveness of the proposed control laws is verified by simulations.

This study considers the uncertainty and disturbance estimator-based control problem for interval type-2 fuzzy stochastic systems with disturbances. The proposed control approach accurately estimates system unknown delays, uncertainties, non-linearities and external disturbances by introducing an appropriate filter. Precisely, the filter's bandwidth is one of the most important parameters in designing and tuning the controller to deal with unknown delays, uncertainties, non-linearities and disturbances. By using the Lyapunov–Krasovskii stability theorem and the linear matrix inequality approach, the required stability conditions and the control gain matrices for the system under consideration are obtained. Further, the effectiveness of the proposed control law is verified using two numerical examples.

This study proposes a novel, relaxed, Lyapunov-based and membership-function dependent stabilisation analysis of discrete-time polynomial-fuzzy-model-based (PFMB) control systems with time delay under positivity constraint. The discrete-time non-linear system with time delay is represented by a polynomial fuzzy model, and corresponding PFMB controller is designed using imperfect premise matching technique which does not require its fuzzy rule and shape of membership functions be matched with those of the model. The authors take advantage of this property to relax the conservativeness of the obtained stability results by introducing the information of membership functions, i.e. the relationship constraint information of membership functions between the model and the controller and boundary information of membership functions, into the stability and positivity conditions. A numerical example is given to demonstrate the effectiveness of the proposed approach.

This study proposes a novel control scheme to investigate the time-varying formation tracking control problem for multi-agent systems with model uncertainties and the absence of leader's velocity measurements. For each agent, a novel fixed-time cascaded leader state observer (CLSO) without velocity measurements is first designed to reconstruct the states of the leader. Radial basis function neural networks (RBFNNs) are adopted to deal with the model uncertainties online. Taking the square of the norm of the NN weight vector as a newly developed adaptive parameter, a novel RBFNN-based adaptive control scheme with minimal learning-parameter approach and fixed-time CLSO is then constructed to tackle the time-varying formation tracking problem. The uniform ultimate boundedness property of the formation tracking error is guaranteed through Lyapunov stability analysis. Finally, two simulation scenario results demonstrate the effectiveness of the proposed formation tracking control scheme.

In order to save the usage of system resources and adapt the variation of plant state, this study first proposes a novel stochastic-sampling-based adaptive event-triggered scheme (AETS). Second, in the framework of time-delay systems, the closed-loop control system is modelled as a class of delayed stochastic systems where time-delay is distributed in some intervals with probability. Then, by employing stochastic analysis tool and Lyapunov stability theory, a stability criterion for this class of delayed stochastic systems is established to ensure that the system possesses stochastically asymptotic stability with an disturbance attenuation performance. Also, a co-design of parameter matrices of the state-feedback controller and the stochastic-sampling-based AETS is implemented. Third, based on the obtained co-design condition, a convex optimisation algorithm for the tradeoffs between disturbance attenuation performance and resource utilisation of the closed-loop control system is further developed. Finally, the effectiveness and feasibility of the proposed control strategy are illustrated by two numerical examples of adaptive event-triggered control for networked control systems under stochastic sampling.

This work investigates a finite time horizon resource allocation problem under a strongly connected multi-agent network. In this network, each agent at each time is associated with a resource variable and a quadratic cost function. The objective is to minimise the total cost of all agents over the finite time horizon in a distributed manner, while enforcing a total amount of resources per time unit and per agent. The major challenge of this problem lies in the coupled equality constraints across the agents and time periods, which should be satisfied simultaneously in the end. In addition, the local information structure imposed by the digraph within the time horizon should be taken into account when solving the problem. This study develops a consensus-based multipliers decomposition method to solve the problem. The authors show that the convergence and optimality can be ensured provided that the digraph within the time horizon is strongly connected. Numerical simulations are presented to verify the effectiveness of the proposed algorithm.

This study investigates the cyber-security control problem of a networked switched system. Firstly, a joint probabilistic model is utilised to characterise the communication failure caused by the jamming attack and random packet loss. Then the attention is focused on designing an observer based controller that can generate the control input using the last successfully received system output. After that, with the average dwell time scheme, sufficient conditions are derived to ensure the almost sure asymptotical stability of the overall-system with stable and unstable subsystems. In addition, an approach is developed to obtain the feasible solution of state feedback and observer gains. Finally, a simulation example implies the effectiveness of the authors' methods.

The randomness and input saturation increase computational complexity and impede the tracking performance of stochastic non-linear systems, therefore, it is necessary to build a simple but effective controller. Based on this, a multi-dimensional Taylor network (MTN) is first applied to a class of stochastic non-linear systems with input saturation constraint in this study. Aiming to solve the tracking control problem, a novel MTN-based controller is proposed via backstepping, and the proposed control scheme has some advantages such as simple structure, good real-time performance and easy realisation. With the help of the hyperbolic tangent function approximating the symmetric saturation non-linearity, an adaptive MTN tracking control scheme is constructively designed via backstepping technique. The simulation results are given to illustrate the validity and accuracy of the model of the proposed approach.

In this study a new algorithm is proposed for distributed blind sensor macro-calibration in networked control systems robust to noise. The proposed distributed algorithm for estimation of gain and offset correction parameters is of stochastic approximation type, with local non-linear transformations of residuals. Convergence of the algorithm in mean-square and with probability one to consensus is proved for a large class of non-linear transformations, network properties and communication and measurement noise characteristics. The choice of the introduced non-linear transformations in accordance with the theory of robust statistics leads to the proposal of new calibration algorithms robustified w.r.t. noise. It is demonstrated by Monte Carlo simulation that the proposed algorithms are very efficient in the presence of large outliers from the point of view of both achievement of high convergence rate and adequate values of convergence points, outperforming the existing linear algorithms.

The consensus problem for leader-following multi-agent systems with general dynamics via event-triggered and self-triggered mechanisms is studied. In the practical leader-following systems, not all followers can access the information of the leader directly, so the agents are divided into two categories according to whether they receive the information of the leader directly or not. For the former, the authors only utilise the leader's state and its own state information to design the distributed consensus protocol, even if there are other neighbours. To achieve the consensus problem that each follower can ultimately track the state of the leader over time, two kinds of event-triggered control schemes are designed for two types of agents, respectively. It is shown that the systems can achieve the consensus problem by utilising the event-triggered mechanisms through a theorem. In this case, Zeno behaviour can be excluded. Furthermore, the self-triggered control algorithm is also proposed to avoid continuous communication with neighbours and there is no Zeno behaviour in the systems. Finally, two examples are used to verify the validity of the main results.

This study considers a filtering problem for discrete-time switched systems with multiple packet dropouts. The switching signal may be lost that is similar to the measurement signal during transmission. Also, the multiple packet-dropouts phenomenon is described by Bernoulli binary sequences. With the aid of a novel switched Lyapunov function containing a random change of switching rate, sufficient conditions in the form of linear matrix inequalities for the desired filter are derived, which ensure the filtering error system is exponentially stable in the sense of mean square with prescribed performance. Finally, a practical example is given to verify the effectiveness of the proposed approaches.

A multi-weighted coupled neural networks (MWCNNs) model with event-triggered communication is studied here. On the one hand, the passivity of the presented network model is studied by utilising Lyapunov stability theory and some inequality techniques, and a synchronisation criterion based on the obtained output-strict passivity condition of MWCNNs with event-triggered communication is derived. On the other hand, some robust passivity and robust synchronisation criteria based on output-strict passivity of the proposed network with uncertain parameters are presented. At last, two numerical examples are provided to testify the effectiveness of the output-strict passivity and robust synchronisation results.

This study investigates the asymptotic properties of mixed-order fractional systems. By using the variation of constants formula, properties of real Mittag-Leffler functions, and Banach fixed-point theorem, the authors first propose an explicit criterion guaranteeing global attractivity for a class of mixed-order linear fractional systems. The criterion is easy to check requiring the system's matrix to be strictly diagonally dominant (C1) and elements on its main diagonal to be negative (C2). The authors then show the asymptotic stability of the trivial solution to a non-linear mixed-order fractional system linearised along with its equilibrium point such that its linear part satisfies the conditions (C1) and (C2). Two numerical examples with simulations are given to illustrate the effectiveness of the results over existing ones in the literature.

In this study, a robust static output feedback (SOF) incentive Stackelberg game for a Markov jump linear stochastic system governed by Itô differential equations with multiple leaders and multiple followers is investigated. The existence conditions for the SOF incentive Stackelberg strategies are derived in terms of the solvability of a set of higher-order cross-coupled stochastic algebraic Lyapunov type equations (CCSALTEs). A classical Lagrange multiplier technique is employed to solve the CCSALTEs; therefore, the solution of the bilinear matrix inequality, which is a common NP-hard problem when designing SOF strategies, is not required. A heuristic algorithm is developed based on the CCSALTEs. In particular, it is shown that a robust convergence is guaranteed by combining the Krasnoselskii–Mann iterative algorithm with a new convergence condition. The performance of the proposed algorithm is discussed and a simple practical example is provided to demonstrate the effectiveness of the proposed algorithm and the SOF incentive Stackelberg strategies.