This study focuses on the observer-based non-linear H _∞ (OBNH) attitude control for a flexible satellite with external disturbances and local state-region constraints. By considering the structural features of the attitude system and applying Lyapunov stability theory, the solvable conditions of the OBNH attitude control problem are provided. An advantage of this study is that the state-feedback controller and the reduced-order state observer can be designed independently, thus significantly reducing the complexity of the attitude control algorithm. Furthermore, based on the polynomial sum of squares (SOSs) and the generalised S-procedure techniques, the above problem can be transformed into a convex optimisation problem with SOS constraints. This conversion can effectively overcome the computational difficulties widely present in the control problem of non-linear systems. Finally, a numerical example is given to illustrate the effectiveness and feasibility of the proposed approach.

This study presents a new Kalman filter (KF) implementation useful in applications where the accuracy of numerical solution of the associated Riccati equation might be crucially reduced by influence of roundoff errors. Since the appearance of the KF in 1960s, it has been recognised that the factored form of the KF is preferable for practical implementation. The most popular and beneficial techniques are found in the class of square-root algorithms based on the Cholesky decomposition of error covariance matrix. Another important matrix factorisation method is the singular value decomposition (SVD) and, hence, further encouraging implementations might be found under this approach. The analysis presented here exposes that the previously proposed SVD-based KF variant is still sensitive to roundoff errors and poorly treats ill-conditioned situations, although the SVD-based strategy is inherently more stable than the conventional KF approach. In this study, the authors design a new SVD-based KF implementation for enhancing the robustness against roundoff errors, provide its detailed derivation, and discuss the numerical stability issues. A set of numerical experiments are performed for comparative study. The obtained results illustrate that the new SVD-based method is algebraically equivalent to the conventional KF and to the previously proposed SVD-based method, but it outperforms the mentioned techniques for estimation accuracy in ill-conditioned situations.

This study investigates the fuzzy control problem for a class of non-linear Markov jump systems with sampled-data inputs and actuator constraints over a finite-time interval. Takagi–Sugeno (T–S) fuzzy models are employed to approximate the non-linearity. The partly known transition probability matrix consisting of known, uncertain, and unknown elements is considered. The asynchronous errors of the membership functions induced by aperiodic sampling are taken care of to avoid conservative results. The objective is to procure a sampled-data fuzzy controller such that the resulting closed-loop system is finite-time bounded and a prescribed performance index is guaranteed simultaneously. By establishing a new piecewise Lyapunov–Krasovskii functional and utilising convex optimisation technique, a novel set of sufficient conditions for the existence of anticipated sampled-data controller are developed. Finally, two illustrative examples are presented to prove the effectiveness of the proposed approaches.

This study focuses on the exponential stabilisation problem for a general class of memristive neural networks subjected to both stochastic disturbance and time-varying delays under periodically intermittent adaptive control. The stochastic disturbances are described as Brownian motions in the considered networks. An adaptive updated rule and a periodically intermittent adaptive control strategy are designed for the exponential stabilisation of memristive neural networks subjected to both stochastic disturbance and time-varying delays. Then, by adopting the adaptive control technique, differential inclusion theory and set-valued maps, and by building a new Lyapunov–Krasovskii functional, many novel sufficient conditions are proposed to guarantee exponential stabilisation for stochastic memristive neural networks. Different from existing results on stabilisation of stochastic memristive neural networks, the obtained criteria in this study are directly derived according to the parameters of networks. Finally, an example is carried out to demonstrate the validity of the theoretic results.

This study addresses a robust iterative learning control (ILC) scheme for non-linear discrete-time systems in which both the trail lengths and the initial state shifts could be randomly variant in iteration domain. The proposed higher-order ILC law guarantees that as the iteration number goes to infinity, the ILC tracking errors at the desired output trail period are bounded in mathematical expectation, and the bound of tracking errors is proportional to the random initial state shifts. Specifically, the ILC tracking errors in mathematical expectation can be driven to zero as the expectation of initial state shifts is zero. Two numerical examples are carried out to demonstrate the effectiveness of the proposed higher-order ILC law.

The problem of fault tolerant shape control for particle size distribution (PSD) process subject to simultaneous time-varying actuator and sensor faults is studied. In this work, sensor and actuator faults are taken into consideration in a unified framework, and estimated by using adaptive observer technique. For the PSD process, the output distribution, rather than the system output signal itself, is adopted for shape control. Square root rational B-spline approximation is used to fit the distribution shape. An innovative on-line fault estimation scheme is proposed for simultaneous actuator and sensor faults estimation. Then an augmented controller based on the virtual actuator and virtual sensor techniques is designed to compensate for the faults and realise PSD shape tracking. A simulation example of emulsion polymerisation is used to validate the proposed scheme and satisfactory performance is obtained.

This study investigates the finite-time consensus problem for a class of first-order non-linear multi-agent networks under directed network topology. A novel non-linear consensus protocol is proposed based on event-triggered strategy. By using the combinational measurement approach, two kinds of event triggers are designed, one depends on continuous communications between the agents, the other avoids the continuous communications. For such two classes of event-triggers, sufficient conditions guaranteeing the finite-time consensus are derived, respectively, provided that the coupling network topology contains at least a rooted directed spanning tree. Meanwhile, some numerical simulations are given to illustrate the effectiveness of the theoretical results.

This study solves the consensus problem of networked Lue' system over a directed graph. First, a novel unified framework for multi-agent systems and complex networks is proposed, where the inner-linking function is given in advance, while the control protocols have to be designed through a communication topology. Then, for both leaderless and leader–follower situations, adaptive consensus protocols are designed in a fully distributed fashion, without using any global information of the communication graphs. Sufficient conditions are provided to design distributed protocols to ensure consensus. Furthermore, compared with other works, the simulation result of a coupled Chua's circuit shows that these conditions can be further released, since the consensus can be achieved with the union graph of the inherent connections and communication graph containing a directed spanning tree. In particular, special case of first-order system is discussed, where specific threshold is given to show how the ‘positive’ or ‘negative’ inherent interactions affect the choice of the communication graph and the feedback gain. Finally, a more practical flexible link robotic arm example is provided to illustrate the effectiveness of the theoretical analysis.

The authors discuss an incentive Stackelberg game with one leader and multiple non-cooperative followers, for a class of discrete-time stochastic systems with an external disturbance. In this game, the leader achieves a team-optimal solution by attenuating the external disturbance under their constraint, whereas the followers adopt Nash equilibrium strategies according to the leader's incentive Stackelberg strategy set (declared in advance) while considering the worst-case disturbance. Using our proposed method, we demonstrate that the incentive Stackelberg strategy set can be found by solving a set of matrix-valued equations. Techniques are presented for both the finite- and infinite-horizon cases. In addition, through an academic and a practical numerical examples, we verify the efficacy of the proposed method in providing the incentive Stackelberg strategy set.

In this study, the authors address the two-player zero-sum differential game problem for non-linear dynamical systems with non-linear-non-quadratic cost functions over the infinite time horizon. The pursuer's goal is to minimise the cost function and guarantee asymptotic stability of the closed-loop system, whereas the evader's goal is to maximise the cost function. Closed-loop asymptotic stability is certified by continuous Lyapunov functions that are viscosity solutions of the steady-state Hamilton–Jacobi–Isaacs equation for the controlled system. Since it is difficult to find viscosity solutions of partial differential equations for numerous problems of practical interest, they extend an inverse optimality framework to provide explicit closed-form solutions of differential game problems, which involve affine in the controls dynamical systems with quadratic cost functions and linear dynamical systems with Lagrangians in polynomial form. The authors' framework allows also to solve optimal robust control problems involving non-linear dynamical systems with non-linear-non-quadratic cost functionals and provides a generalisation of the mixed-norm optimal robust control framework. Two numerical examples illustrate the applicability of theoretical results provided.

In this paper, a cooperative distributed model predictive control is proposed for a class of large-scale systems composed of discrete-time linear subsystems which are coupled via states. The subsystems communicate with each other through a network with communication delays and they do not have direct access to their local states. In the proposed scheme, each subsystem is associated with a local MPC unit, a local predictor and a local observer. The local model predictive controllers exchange predicted input sequences via a delayed communication network. The local predictor uses the explicit model of the subsystems and predicts those states which are coupled between subsystems and their actual values are not available due to delays. The states of each subsystem are estimated from local measurements by designing a local observer. Convergence analysis of the proposed estimation methodology is performed and it is shown that the observer and predictor have exponential convergence. Furthermore, the exponential stability of the closed-loop system is existed. Finally, the theoretical results are verified by a simulation study.

This study presents a study on delay-dependent algebraic Riccati equations (DAREs) derived from linear quadratic optimisation and stabilisation problems of networked control systems (NCSs) that endure both transmission delay and packet dropout. By applying the operator spectrum theory, two sets of fundamental results are obtained for such DARE: first, it is shown that the stabilising solution to a DARE, if it exists, is unique and coincides with a maximal solution. Moreover, under the assumption of detectability or observability, it is shown that the unique stabilising solution exists if and only if the associated NCS is stabilisable. Second, an iterative algorithm for computing the stabilising solution is proposed. The proof of convergence of the algorithm is presented. To confirm the validity of our theoretic results, two illustrative examples are included in this study. One of the example is motivated by a pursuit–evasion problem.

This study introduces the use of model predictive control (MPC) to improve the performance of pre-compensated power supplies, and in particular of DC–DC converters, by dynamically modifying their output voltage reference. The importance of developing controllers for pre-compensated converters is twofold. First, the hierarchical structure is particularly useful when the primal controller is already coded, or hardware based, and cannot be changed. Second, the double-loop and, possible, multi-rate structure represents a computationally cheaper alternative to a direct MPC that would replace the primal controller and would require a much higher sampling frequency. In this study a MPC controller has been applied for the regulation of a pre-compensated synchronous DC–DC buck converter. The aim is to improve the performance of standard voltage mode control (VMC), without replacing the linear controller and without drastically affecting the computational burden. The algorithm has been tested both in simulation and experimentally, on commercially available hardware. The results show the performance improvement with respect to the standard VMC, as well as the feasibility of the proposed approach in an embedded platform. Tests with different primal controller tunings, and unknown varying loads, confirm the advantages of the method.

Focusing on multidimensional stochastic Lotka–Volterra type ecosystems in which multiple species are interacting, this study aims developing optimal harvesting strategies. The underlying systems are controlled regime-switching diffusions. Dealing with such a class of singular controls, the authors' objective is to maximise the total expected discounted rewards by using the ideas from singular control theory. In this study, the finiteness of the value function is obtained. The value function is characterised as a viscosity solution of the associated coupled systems of quasi-variational inequalities. Chattering policies are developed, which provide candidates for lower bounds of value functions. The impact of large noise on harvesting is studied by using certain upper bounds.

In this study, a novel event-based model-free adaptive control (MFAC) algorithm for discrete-time non-linear systems is presented. Different from the traditional MFAC scheme which calculates the control signal at fixed sampling instants, an event-based sampling scheme is given to calculate the new control signal only when the input/output (I/O) data sufficiently changes. The event-triggered MFAC can obviously reduce the computational load and network communication. The closed-loop system is proven to be ultimately bounded by using the Lyapunov technique. Finally, the simulation examples indicate the effectiveness and applicability of the proposed event-trigger model-free adaptive control algorithm.

The problem of adaptive tracking control is studied for a class of switched non-strict-feedback non-linear systems with unknown control direction and asymmetric saturation actuators under arbitrary switchings. The main technical difficulty comes from developing a common adaptive control scheme in the presence of unknown control direction and unknown asymmetric saturation non-linearities. A linear state transformation is exploited to deal with the unknown control coefficients and a Gaussian error function-based smooth model is used to approximate the asymmetric saturation non-linearity. Based on an input-driven observer, a common adaptive output-feedback control strategy containing only one adaptive parameter is developed for such systems via a novel combination of common Lyapunov function method, backstepping technique, variable separation approach and neural network approximation. Under the proposed control scheme, the tracking error converges to an adjustable neighbourhood of the origin. Finally, two illustrative examples are included to verify the effectiveness of the proposed control design.

In this study, the distributed optimisation problem is investigated by using the framework of second-order multi-agent systems (MASs) over a directed communication topology. A distributed algorithm is proposed for the MASs to seek the solution of the optimisation problem. The proposed algorithm contains two layers, the cooperative compensator and the local optimiser, where the former layer is to compensate the cooperative errors and the latter will lead the agents to the optimal solution. In the algorithm, each agent only uses the position information from its neighbours in the presence of delay. By utilising the Lyapunov–Krasovskii functional, delay-dependent conditions are derived for the slowly-varying and fast-varying delays, respectively, to guarantee the algorithm converges to the optimal solution. Furthermore, a criterion on solving the optimisation problem through the MASs with discrete-time communication is also proposed directly from the result of the fast-varying delay. Finally, a numerical simulation example is presented to illustrate the persuasive effectiveness of the theoretical results.

This study proposes a non-linear saturation-aware controller for dual-stage micro–nano actuators. Dual-stage motion systems use two actuators in series in order to achieve an improved performance: a micro actuator responsible for a large range of actuation, and a nano actuator (NA) able to achieve a high bandwidth. The NA is commonly driven by flexure-based piezoelectric actuators subject to a limited range which presents large oscillations in the presence of output saturation. In order to avoid these oscillations, a non-linear smooth switching function that limits the actuation of the NA to only track references within its range is proposed. Experimental results demonstrate the effectiveness of the proposed approach, which is able to reduce oscillations and energy consumption without compromising settling time performance.

The consensus problem of discrete time multi-agent systems with linear dynamic models is investigated. To reduce the controller update times and communication among agents, an event-based dynamic feedback scheme is proposed. For each agent, the controller update instants are determined by a state-dependent threshold. It is shown that the controller update for each agent is only dependent on its own event times. Some sufficient conditions are obtained for consensus. Observing the current states of its neighbour agents as well as its own state at every discrete-time is also avoided. Furthermore, certain conditions are given to exclude the Zeno-like behaviour of the triggering time sequence. Finally, a numerical example is given to illustrate the efficiency of the proposed control strategy.

This study addresses the problem of stabilising a desired trajectory (also referred to as the trajectory tracking problem) for underactuated surface vessels. The desired trajectory does not need to be a particular type (e.g. feasible trajectory) and can be any sufficiently smooth curve parameterised by time. To overcome difficulties caused by underactuation, the authors apply the transverse function approach to introduce an additional control input in backstepping design procedure. They give the calculation of transverse functions accordingly. To compensate for the effects of the external disturbances, they employ disturbance observer to estimate the unknown time-varying disturbances. Subsequently, disturbance-observer-based tracking control is designed that achieves practical stabilisation of any smooth reference trajectory (i.e. the vessel position and orientation tracking errors converge to a small neighbourhood of zero). A noticeable feature of the design technique is that the desired reference trajectory allows to be feasible or non-feasible. Besides the nominal case where exact knowledge of the vessel model is available, they also deal with scenarios wherein modelling uncertainties are present. The proposed control is robust not only to modelling uncertainties but also to external disturbances. Simulation studies are performed to demonstrate the effectiveness of the proposed design technique.

This study investigates the finite-time formation tracking control problem for multi-agent systems. The objective is to control all the follower agents to converge into the desired formation in finite time while the geometric centre of the follower agents tracks the leader agent's trajectory in finite time simultaneously. Then, the distributed finite-time formation tracking protocols are proposed via the fast terminal sliding mode control (FTSMC) scheme. On the basis of algebraic graph theory, properties of the Laplacian matrix and finite-time stability theory, it is shown that the distributed formation tracking can be achieved in finite time under the proposed control protocol. Two numerical simulation examples are employed to illustrate the effectiveness of our theoretical results.

This study proposes a direct parameter estimation approach from observed input–output data of a stochastic single-input–single-output fractional-order continuous-time Hammerstein–Wiener model by extending a well known iterative simplified refined instrumental variable method. The method is an extension of the simplified refined instrumental variable method developed for the linear fractional-order continuous-time system, denoted. The advantage of this novel extension, compared with published methods, is that the static output non-linearity of the Wiener model part does not need to be invertible. The input and output static non-linear functions are represented by a sum of the known basis functions. The proposed approach estimates the parameters of the linear fractional-order continuous-time subsystem and the input and output static non-linear functions from the sampled input–output data by considering the system to be a multi-input–single-output linear fractional-order continuous-time model. These extra inputs represent the basis functions of the static input and output non-linearity, where the output basis functions are simulated according to the previous estimates of the fractional-order linear subsystem and the static input non-linear function at every iteration. It is also possible to estimate the classical integer-order model counterparts as a special case. Subsequently, the proposed extension to the simplified refined instrumental variable method is considered in the classical integer-order continuous-time Hammerstein–Wiener case. In this paper, a Monte Carlo simulation analysis is applied for demonstrating the performance of the proposed approach to estimate the parameters of a fractional-order Hammerstein–Wiener output model.

A novel tracking control strategy is proposed for a hypersonic vehicle based on model predictive control and the extended linearisation method. Unlike the general linearisation techniques, the state-dependent coefficient parameterisation method is used to establish a linear structure of non-linear dynamics. Based on the acquired linear system, two predictive controllers are designed for the velocity and altitude tracking in the presence of constraints. Compared with the conventional model predictive control which consumes a large amount of computer resources due to the online constrained optimisation, the predictive functional control adopts the heuristic approach to deal with constraints hence suiting fast systems more. Simulation results show the designed controllers not only meet constraint requirements but also ensure the fast response and tracking performance, and the resulting closed-loop system is robust with respect to the parameter variations and external disturbances.

This study addresses distributed state estimation problems for a power system subject to imperfect measurements over a finite horizon. The power system under discussion is assumed to be a time-variant model with varying delays, random non-linearity, and external disturbances. Imperfect measurements through the sensor network include both sensor saturations and signal quantisation. A set of novel distributed state estimators were designed, where each of them utilises the information from both the local sensor node and its neighbours according to the topology. To cater for the various package dropouts that are possible, a random process is introduced during the information transmission between each sensor node and the local estimator. In addition, a novel event-triggered mechanism is also developed for energy reduction. The main work focuses on the analysis and synthesis of event-triggered robust state estimators for the system being addressed, such that the estimation error is bounded in the mean square. In comparison to the existing literature, the transient performances over a finite horizon are emphasised here and a recursive algorithm is provided to obtain the estimator gains. Finally, a power system example is presented to validate the proposed estimator design laws.

A simple non-linear system modelling algorithm designed to work with limited a priori knowledge and short data records, is examined. It creates an empirical Volterra series-based model of a system using an -constrained least squares algorithm with . If the system is a continuous and bounded map with a finite memory no longer than some known , then (for a D parameter model and for a number of measurements N) the difference between the resulting model of the system and the best possible theoretical one is guaranteed to be of order , even for . The performance of models obtained for and 2 is tested on the Wiener–Hammerstein benchmark system. The results suggest that the models obtained for are better suited to characterise the nature of the system, while the sparse solutions obtained for yield smaller error values in terms of input-output behaviour.

The cluster formation problem of the multi-agent system in the presence of disturbances and unmodelled uncertainties has been studied. Agents in the system are partitioned into multiple clusters and each cluster is required to maintain a predefined time-varying sub-formation, where the sub-formations can be different from each other. An identifier-based robust control algorithm using the neighbouring relative information has been proposed to accomplish the time-varying cluster formation. Some sufficient conditions for the second-order multi-agent system to achieve the control objective have been proposed based on the graph theory and the Lyapunov method. Numerical simulations are provided to testify the validity of the algorithm. Compared to the previous work on cluster formation control, the novel feature of this study is that disturbances and unmodelled uncertainties are taken into consideration and the authors propose a robust cluster formation control algorithm based on a non-linear identifier to eliminate the adverse effects of disturbances and unmodelled uncertainties.

In this study, neural networks approximation-based command filtered adaptive control is studied for induction motors with input saturation. The neural networks are utilised to approximate the non-linearities, and the command filtering technology is used to deal with the ‘explosion of complexity’ problem caused by the derivative of virtual controllers in the conventional backstepping design. The compensating signals are further exploited to get rid of the drawback caused by the dynamics surface technology. It is verified that the adaptive neural controller guarantees that the tracking error can converge to a small neighbourhood of the origin. At last, the effectiveness and advantages of the proposed method are intuitively illustrated by simulation results.

In this study, a dynamic output-feedback stabilisation problem for Markovian jump systems (MJSs) with incomplete transition description and input quantisation is investigated. While the previous researches about output-feedback stabilisation for MJSs assumed that the transition rates are completely known, a more general situation where the transition rates are partly unknown is considered. Moreover, the proposed controller includes non-linear control part to eliminate the effect of input quantisation. Two numerical examples are provided to demonstrate the feasibility of the proposed dynamic output-feedback controller.

This study considers the cooperative global output regulation problem for a class of non-linear multi-agent systems. In particular, the authors consider the case that the exosystem is of a non-linear form. With a distributed non-linear observer of the exosystem and the solvability assumption of the regulator equations, the authors convert the problem into a global cooperative stabilisation problem. Sufficient conditions are derived for the global cooperative stabilisation problem under fixed directed network topologies and switching undirected network topologies, respectively. Finally, the validity of the proposed approach is illustrated by simulation results.

The infinite horizon linear quadratic differential games for positive linear systems with Markovian jumping is considered. The authors' goal is to propose a set of sufficient conditions that guarantee the existence of the stabilising solution of a system of game theoretic algebraic Riccati type equations associated to the considered differential game. To this end the authors' introduce a new type of solution of the Riccati equation namely the strong stabilising solution and they prove that this strong stabilising solution is just a stabilising solution of this kind of Riccati equation. The main contribution is the formulation of a set of sufficient conditions which guarantee the convergence of the proposed iterative procedure to the stabilising solution of game theoretic algebraic Riccati type equation. Finally, a numerical example shows the performance of the proposed algorithm.

This note presents important aspects that should be taken into account in the comparative study on stability conditions of switched affine systems with performance presented in the aforementioned paper. Using a numerical example, it is demonstrated that stability conditions for switched affine systems obtained from a max-type composition to define both the Lyapunov function and switching rule are not necessarily more conservative than the ones obtained from a quadratic Lyapunov function and a min-type composition to define the switching rule.

The authors present some aspects that worth to be taken into account in a comparative study on performance derived from min-type and max-type switching functions for continuous-time switched affine systems. In this direction, this note puts in evidence the comparisons made by Deaecto and Santos in 2015 about the results of Trofino et al. in 2012 whose illustrative example was enhanced by Scharlau et al. in 2017 by optimising some free parameters. With the optimisation, the guaranteed costs became smaller than the ones of Deaecto and Santos in 2015 for the case where the switching function depends only on the state variable. It is shown that this situation can occur and it is in complete accordance with the theoretical results reported by Deaecto and Santos in 2015.