In this study, a multi-agent coordination problem with steady-state regulation constraints is investigated for a class of non-linear systems. Unlike the existing leader-following coordination formulations, a reference signal is not given by a dynamic autonomous leader but determined as the optimal solution of a distributed optimisation problem. Furthermore, the authors consider a global constraint having noisy data observations for the optimisation problem, which implies that the reference signal is not trivially available with the existing optimisation algorithms. To handle these challenges, the authors present a passivity-based analysis and design approach by using only local objective function, local data observation and exchanged information from their neighbours. The proposed distributed algorithms are shown to achieve the optimal steady-state regulation by rejecting the unknown observation disturbances for passive non-linear agents, which are persuasive in various practical problems. Applications and simulation examples are then given to verify the effectiveness of the proposed design.

For an air-breathing hypersonic vehicle with a variable geometry inlet (AHV-VGI), a movable translating cowl is used to track the shock on lip conditions to capture enough air mass flow, which can extend the velocity range and be favourable to the acceleration and manoeuvring flight. The authors firstly establish longitudinal dynamics for AHV-VGI, and consider the lumped disturbances which include the unknown external disturbance, the parameter uncertainties and the uncertainty parts introduced by translating cowl. Then, the dynamic surface control strategy based on a fuzzy disturbance observer (FDO) is proposed for AHV-VGI control. The control process for AHV-VGI is divided into two subsystems. For each subsystem, a sliding mode controller is designed, and FDOs are adopted to compensate the lumped disturbances, which can render the disturbance estimate errors convergent. Numerical simulations are presented to illustrate the effectiveness of the proposed method and the advantages of translating cowl.

The output consensus of multi-agent systems is investigated, where constant communication delay is present and the dynamics of the agents are heterogeneous. Based on the networked predictive control scheme, the distributed consensus protocol with dynamic output feedback controller is designed, and the sufficient conditions of the output consensus are obtained. Numerical examples illustrate the effectiveness of the proposed method.

The controller design for a polynomial system with uncertainties and some/all un-measurable states is a hard issue for researchers. Furthermore, if there is no information for the upper bounds of uncertainties, the design work will be more challenging. In order to overcome these difficulties, this study proposes a novel approach based on the unknown input method and disturbance observer to synthesise an observer-based controller for the mentioned system such that the states are estimated and stability of the system is achieved asymptotically. First, based on the unknown input method, let the uncertainties of the polynomial system be regarded as the disturbance, and then a new observer is proposed to estimate the disturbance and states simultaneously. Next, the observer-based controller is synthesised with suitable parameters which are computed from the conditions in the main theorems. Those parameters are obtained by using Matlab tool to solve a set of polynomial linear matrix inequalities which are derived in the main theorems too. With the aid of Lyapunov theory and sum-of-square technique, the above two main theorems are derived. It is noted that this study allows the uncertainty bounds are unknown and some/all states are un-measurable. Finally, two examples are presented to show the effectiveness of the proposed method.

A Kalman filtering-based robust iterative learning control algorithm is proposed in this study for linear stochastic systems with uncertain dynamics and unknown noise statistics. Firstly, a learning gain matrix is designed for the nominal case by minimising the trace of the mean-square matrix of the input tracking error. Theoretical results show that the proposed algorithm guarantees not only the asymptotic but also monotonic convergence of the input tracking error in the mean-square error sense, especially when random noises are Gaussian distributed the proposed algorithm is further proved to be asymptotically efficient. In addition, a new mean-square error constrained approach is presented in designing the robust learning gain matrix, taking into account model uncertainties. A sufficient condition is provided such that the mean-square matrix of the input tracking error is constrained within a predesigned upper bound which can monotonically converge to zero. Finally, numerical examples considering both structured and unstructured model uncertainties are included to illustrate the effectiveness of the proposed algorithms.

This paper deals with the design and analysis of robust model reference control systems for a class of linear parameter-varying (LPV) systems with disturbances. Two types of robust model reference control systems are proposed to achieve a prescribed tracking performance. The first type is the LPV state-feedback model reference control system and the second type is the LPV output-feedback model reference control system. Based on the notion of quadratic stability, necessary and sufficient conditions for the existence of LPV reference models are given. Also, a parameterisation of LPV reference models is derived in this study. A practical example of a single-link flexible-joint robot is given to illustrate the design steps and to show the effectiveness of the proposed LPV model reference controllers.

This study investigates the robust fixed-time consensus tracking problem of second-order multi-agent systems under fixed topology. A novel type of non-linear protocol and the corresponding sufficient conditions for achieving robust fixed-time consensus tracking are proposed with the aid of sliding mode technique and Lyapunov theory. Compared to finite-time consensus tracking, the convergence time of the tracking errors is globally bounded for any initial conditions of the agents, which is also the global information for each agent. Furthermore, the results obtained for second-order multi-agent systems are also extended to deal with the fixed-time formation tracking problem for unicycle-type robots. Extensive numerical experiments are performed to illustrate the effectiveness of the present theoretical results.

In this study, the authors investigate the fault-tolerant control problem of a cascaded asynchronous sequential machine (ASM) in which two ASMs subject to adversarial inputs constitute a cascade composition. The main objective is to develop a corrective controller that can diagnose and tolerate any unauthorised state transition occurring in the cascaded machine. In particular, the authors address fault-tolerant control for two control configurations, one with a state feedback and the other with an output feedback. The existence condition for a controller is found to be different with respect to each feedback availability. The authors apply the proposed control scheme to robust operations of memory scrubbing modules in space-borne computers implemented on field-programmable gate array systems. Experimental results show the practicability of the proposed methodology.

This study investigates the optimal filter for Markov jump linear (MJL) system with multiple delayed modes and observations, in which the data losses are introduced naturally and the Markov chains are assumed to be known up to the present time. To deal with the mode and observation delays, a reorganised observation sequence is defined. Moreover, the optimal filter problem is transformed into one of the delay-free system which is just with jumping parameters and multiplicative noises. An optimal MJL filter is presented based on the mean squared method, where the filter gains are determined by solving a set of generalised coupled Riccati difference equations based on a set of coupled Lyapunov equations. Alternatively, an optimal stationary MJL filter is developed, where the filter gains are derived by solving a set of generalised coupled algebraic Riccati equations based on coupled algebraic Lyapunov equations. It can be shown that the difference Riccati equations developed in the former filter converge to the stationary ones under appropriate conditions.

To deal with the distributed estimation problem for mobile sensor networks with non-linear systems and a large amount of data transfer, the distributed event-triggered cubature information filtering based on weighted average consensus is proposed. The filter benefits from the non-linear filtering algorithm with consensus technique and event-triggered mechanism which reduces the amount of data transfer. The triggering decision is based on the data transmission mechanism, which is that each sensor makes a request to exchange information with its neighbours only if the difference between the most recent transmitted estimate and the current estimate exceeds a tolerable threshold. The estimation error of the proposed filter is proved to be bounded in mean square. Finally, numerical examples are provided to demonstrate the effectiveness of the theoretical results.

Fractional-order fuzzy generalised predictive control (FFGPC) for a class of non-linear systems is studied. Based on the Grünwald–Letnikov fractional calculus, Laplace transform, and discretisation, a class of fractional-order non-linear systems are transformed to fit the standard controlled autoregressive integrating moving average (CARMA) model. With the help of the Takagi–Sugeno fuzzy linearisation theory, a linear CARMA model for the non-linear systems is represented. Then, a new FFGPC method is proposed for the fractional-order non-linear systems based on the obtained CARMA predictive model and generalised predictive control theory. Numerical simulations are implemented to verify the effectiveness and superiority of the new method. This work also provides a reference for the control of relevant fractional-order systems.

Here, the global and coordinate-free approach has been applied to study the leaderless attitude synchronisation problem of multiple rigid bodies with kinematic evolving on Lie group SO(3). A decentralised consensus law based on the gradient of a smooth cost function which depends on the relative attitude of neighbouring agents is proposed. The advantage of using this cost function lies in the fact that there is a relation between the Hessian matrix of this function in a consensus configuration and the Laplacian matrix of a graph. In addition, a new approach for analysing the attitude synchronisation problem was developed and proved that convergence to synchronisation can be achieved for any connected and undirected graph if the initial attitudes of neighbouring agents are sufficiently close. Using the critical points of the cost function, the effects of graph topology on synchronisation problem were investigated. The initial attitudes sets ensuring the convergence to synchronisation are obtained for the undirected tree, complete, and ring graphs. The initial set is more restrictive for ring graph owing to the existence of other critical points induced by graph topology. Eventually, using the appropriate Lyapunov function, sufficient condition that guarantees convergence to synchronisation for general connected graph was obtained, and numerical simulation carried out to illustrate the theoretical results.

In this study, the authors develop a novel approach to a class of pursuit-evasion problems modelled in the form of discrete time feedback control systems, where the opposing parties have asymmetric capability. The authors assume the control policy of the evader, described as a random variable, is unknown to the pursuer. This pursuit-evasion problem is formulated as a quadratic optimisation problem from the perspective of the pursuer. Due to the curse of dimensionality, this pursuit-evasion problem cannot be practically solved by dynamic programming. In this study, the authors reformulate it as a multi-armed bandit problem. A heuristic policy based on the Gittins index is proposed to solve this problem, which can be computed based on a forward induction. Simulation results show the proposed policy outperforms a random decision policy.

This study studies the matrix equation , which has many important applications in control theory, by using spectral decompositions of A and B. By establishing solvability conditions and solutions to the standard vector equation , and the spectral decompositions of the associated nivellateur of the matrix equation, necessary and sufficient conditions for the solvability of the matrix equation are provided in terms of the coefficients of the spectral decompositions of A and B. Moreover, explicit solutions are provided, which are also based on the coefficients of the spectral decompositions of A and B. The obtained results include the existing ones as special cases, and, moreover, correct some errors in the existing methods. The effectiveness of the proposed approach is demonstrated by some illustrative examples.

A novel iterative learning control (ILC) scheme is proposed to improve the convergence rate of ILC by ensuring the convergence in both the time and iteration domains simultaneously. First, an iteration-varying reference is generated by a high-order IM (HOIM) along the iteration axis, and is approximated by an HOIM along the time axis. Then, the HOIM-based repetitive control (RC) and ILC design methods are introduced, which can update the input along the time and iteration axes, respectively. Motivated by the separately tracking abilities of the HOIM-based RC and ILC in the time and iteration domains, a new ILC scheme is proposed by incorporating both the time-domain and iteration-domain HOIMs of the reference. The new ILC scheme is the combination of the HOIM-based RC and ILC, which can update the input along both the time and iteration axes. The new ILC scheme consists of two loops: (i) the HOIM-based ILC loop can learn the control input from previous iterations and (ii) the HOIM-based RC loop can learn the control input from previous times at the current iteration. Moreover, the new ILC scheme is established on a dual-HOIM (DHOIM) that is the assembly of the two HOIMs of the reference. In consequence, the new ILC scheme is named as DHOIM-based repetitive ILC (RILC). On rthe basis of the two-dimensional theory, a DHOIM-based RILC design criterion is presented. Meanwhile, it is shown that the convergence rate of the proposed DHOIM-based RILC scheme outperforms that of traditional ILC schemes. Finally, a microscale robotic deposition system is given to illustrate the efficiency of the proposed RILC scheme.

This note considers the problem of finite-time stability (FTS) for impulsive switched linear time-varying (LTV) systems. First, two improved necessary and sufficient conditions are proposed to verify the FTS of LTV by employing an indefinite Lyapunov function. Then, the results obtained are extended to study the FTS of impulsive switched LTV systems, two new necessary and sufficient conditions are given by using common indefinite Lyapunov function and piecewise indefinite Lyapunov functions. Compared with the existing results, the conditions obtained allow the time derivative of Lyapunov functions of subsystems to be indefinite and have a tighter upper bound, moreover, all subsystems are also allowed to be not FTS. Furthermore, the construction method of switching signal is given, moreover, using function-dependent dwell time methods, three sufficient conditions of FTS are also proposed for the systems. Two numerical examples are given to illustrate the theoretical results.

Distributed finite-time tracking problem of a multi-agent system with second-order non-linear dynamics is studied in this article. Based on measurements of edges, a finite-time tracking protocol is proposed without relying the complete position and velocity measurements. It means that the proposed protocol only requires a binary information between the neighbouring agent. By designing a carefully constructed Lyapunov function, the distributed finite-time tracking problem is solved if the sub-topology among the followers is connected and undirected and the topology of whole systems has a spanning tree with a leader been a root node. Furthermore, it has successfully estimated the finite settling time in theory with the proposed control protocol. The authors provide a numerical example to illustrate the effectiveness of the analytical results.

The aim of this study is to develop an improved relaxation technique (especially in terms of conservatism and computational complexity) for the control design of a class of non-homogeneous Markovian jump fuzzy systems with general transition descriptions. With this point of view, novel component-summation-based constraints are introduced to stringently establish the overall constraints on completely unknown transition rates, which play a key role in making relaxation techniques less conservative. Further, to reduce the computational complexity of relaxation processes with multiple slack variables, this study provides a method of replacing all self-mode-transitions with other transitions.

This study presents a linear matrix inequality (LMI) approach to the sampled-data control of Takagi–Sugeno fuzzy systems, based on the intelligent digital redesign (IDR) technique. The objective of the IDR is to design a digital control system whose trajectory closely matches that of a given well-constructed analogue control system by minimising the state-matching error. In this study, state-matching performance is enhanced by using a continuous-time state-matching criterion, which guarantees that the state-matching error is minimised through the entire time interval. Unlike previous studies, mismatched information of membership functions for both analogue and digital control systems is directly manipulated. Moreover, the authors introduce an improved fuzzy Lyapunov functional that consists of both membership functions for analogue and digital control systems, which relaxes the conservativeness of LMI conditions. Finally, two examples demonstrating the effectiveness of the authors' method are provided.

This study is concerned with the adaptive stabilisation problem for a class of large-scale output-constrained non-linear time-delay systems in strict-feedback form. The investigative system satisfies a more general growth condition and the precise knowledge of the time delay is not required to be known a priori. Firstly, an observer is designed by the dynamic gain control design technique. Then, based on a novel Lyapunov–Krasovskii functional, the output constraints are satisfied and the stability of the closed-loop control system is achieved. Finally, a numerical example is given to demonstrate the effectiveness of the proposed design procedure.