This study presents a self-triggered distributed model predictive control algorithm for the flock of a multi-agent system. All the agents in a flock are endowed with the capability of determining the sampling time adaptively to reduce the unnecessary energy consumption in communication and control updates. The agents are dynamically decoupled in a flock, and each agent is driven by a local model predictive controller, which is designed by minimising the position irregularity between the agent and its neighbours, velocity tracking errors as well as its control efforts. Moreover, the collision avoidance is considered by introducing constraints in the model predictive minimisation problem. In order to adaptively determine the sampling time, a self-triggered algorithm is designed by guaranteeing the decrease of the Lyapunov function. Finally, numerical simulations are given to demonstrate the feasibility of the proposed flocking algorithm.

This study establishes an approximate optimal critic learning algorithm based on single-network adaptive dynamic programming aiming at solutions to continuous-time two-player zero-sum games in the absence of initial stabilising control policies. Single-network means one critic neural network, which is utilised to derive the saddle-point equilibrium of a zero-sum differential game by approximately learning the value function. First, the authors elaborate mathematically two-player zero-sum game problems and analyse the similarity of the zero-sum game problem between linear and non-linear systems. Then, this adaptive learning scheme is implemented as a critic structure that derives control and disturbance policies by learning the optimal value, and a novel weight tuning law involving a stable operator is proposed to ensure convergence and stability. Moreover, the uniform ultimate bounded stability of the whole system is rigorously proved by Lyapunov theory. Finally, reasonable simulation results are provided to confirm the effectiveness of the improved approximate optimal control technique in solving equations for a complex linear system and a non-linear system.

In this study, a composite robust control approach with non-singular terminal sliding mode control and fixed-time disturbance observer (FxTDO) is proposed for a class of second-order non-linear systems in the presence of matched uncertain disturbances. A bi-limit-weighted homogeneous FxTDO is designed based on the efficient utilisation of power functions obtained by the differentiation error amplification strategy. The FxTDO enjoys a fast convergence rate and simple parameters tuning process. By introducing the disturbance estimation to directly compensate the total disturbance in the composite control law, only a particular small gain-based discontinuous control term is needed to guarantee the existence of sliding mode, and chattering phenomenon can be attenuated. The simulation results revealed the effectiveness of the proposed method.

This study proposes a novel multi-rate model predictive control (MPC) scheme for linear discrete-time systems subject to input constraints. The proposed scheme consists of two control layers, acting at two different timescales. At a slow timescale, the outputs associated with the slow dynamics are steered to their reference values while at a fast timescale, a shrinking horizon MPC regulator is designed to refine the control action computed at the slow timescale. The proposed control scheme shows to be particularly useful, not only to control systems with different open-loop dynamics but also in cases when the controlled variables are required to have different responsiveness in a closed loop. Simulation results on a fire tube boiler example are reported, which indeed show that different dynamics can be efficiently imposed on the controlled variables, i.e. the boiler pressure and the water level, in the presence of variations of the disturbance represented by the steam output flow rate.

An improved frequency-domain method for the fractional order controller design is proposed in this study. A proportional relation between the integral gain and derivative gain of the controller is built, while the derivative order is set to be equal to the integral order. Applying the improved method, the controller parameters can be calculated analytically according to different design requirements. The proportional coefficient between the integral and derivative gains is studied and then the model of the optimal proportional coefficient for the commonly used permanent magnet synchronous motor speed control system is built. Based on the established model, the optimal controllers are obtained analytically applying the proposed method. Motor speed control simulations and experiments are performed, comparing the performance of the controllers obtained using the proposed method and those obtained using the current frequency-domain method and other design methods. Simulation and experimental results show that the control system obtained using the proposed method achieves the specified stability, robustness to gain variations and the optimal dynamic performance.

This study focuses on the asymptotical consensus and synchronisation for coupled uncertain parabolic partial differential equation (PDE) agents with Neumann boundary condition (or Dirichlet boundary condition) and subject to a distributed disturbance whose norm is bounded by a constant which is not known a priori. Based on adaptive distributed unit-vector control scheme and Lyapunov functional scheme, the distributed unit-vector controller with adaptive gain is suggested to provide for the leader–following tracking of uncertain parabolic PDE agents. The suggested gradient-based and mono-directional gain adaptation provides convergence without requiring the knowledge of an upper bound to the norm of the external disturbance. The simulation is proposed to account for the effectiveness and robustness of the provided method.

A reduced-order non-linear generalised minimum variance (NGMV) controller is introduced. The NGMV controller is one of the simplest control solutions for non-linear systems, with flexibility regarding the form of the non-linear system and the type of cost-function that may include non-linear elements. The new element is to introduce a pre-specified low-order controller structure. The motivation was the need to develop a non-linear industrial controller that has a simple structure and is easy to understand. The optimisation problem is to generate the optimal feedback controller gains or controller parameters on-line. These computations involve background processing to optimise gains or parameters. The gains vary as setpoints or disturbances change but for much of the time these are approximately constant. The approach provides a model-based optimal control solution, but in a form where classically trained engineers can easily retune if needed.

Information sharing among local controllers is the key feature of any distributed model predictive control (DMPC) strategy. This study addresses the problem of communication failures in DMPC strategies and proposes a distributed solution to cope with them. The proposal consists in an information-exchange protocol that is based on distributed projection dynamics. By applying this protocol as a complementary plug-in to a DMPC strategy, the controllers improve the resilience against communication failures and relax the requirements of the communication network. Furthermore, a reconfiguration algorithm, which is a contingency procedure to maintain the connectivity of the network, and a discussion on the selection criteria of the information-sharing network are also presented. In order to demonstrate the performance and advantages of the proposed approach when it is applied to a DMPC strategy, a case study of a power-network control problem is provided.

This work explores the consensus problems under the directed graph, variable learning gains, fast convergence and data-driven control framework comprehensively and proposes an adaptive estimation-based terminal iterative learning control for a nonlinear discrete-time multi-agent system (MAS) with a constant control input. A linear iteration-incremental model is built by using an iterative dynamic linearisation where the unknown partial derivatives are estimated iteratively using I/O data. The learning control law is designed with both a constant learning gain and an iteration-time-varying learning gain. The constant one can be selected properly according to the estimation of partial derivatives and the varying one can be estimated from iteratively utilising I/O data. The result has also been extended to the nonlinear MAS with time-varying control input and an extended adaptive estimation-based TILC is developed by using time-varying control input to enhance the control performance. A fast convergence of both the proposed methods is achieved by removing the unnecessary error constraints at other time instants than the endpoint. Both the proposed methods is apparently data-driven since no model information is involved. The proposed finite time consensus control methods are confirmed to be effective under the directed graph through mathematic proof and extensive simulations.

In this note, a novel adaptive constrained control algorithm is proposed for dynamic positioning vessels in the presence of input amplitude and rate saturations. In the scheme, both kinematics and kinetics loops are augmented by the auxiliary system to deal with the saturation impact. Meanwhile, for merits of the command filters and minimal leering parameter technique, the cumbersome analytic derivatives of the virtual control law need not be required in the control design, and only two adaptive parameters are updated online to stabilise the effect of the model uncertainty and the external disturbance for each subsystem. Using the Lyapunov theory, the semi-global uniformly ultimately bounded is proved for the closed-loop system. The effectiveness and robustness of the proposed algorithm are demonstrated by the numerical example in the presence of the simulated marine disturbance.

This work studies the conditions on which the outputs of linear heterogeneous (i.e. non-identical) agents are asymptotically synchronised, where the dynamics of the agents and the dimensions of the state variables might widely differ among themselves. With the constraint that the relative outputs of the agents are the only measurements, it is shown that the reflexive generalised inverses play a key role in characterising the conditions, and give rise to the synchronisation stability of the agents. Together with the internal model principle for synchronisation, this results in a necessary and sufficient condition for reaching the asymptotic output synchronisation. This necessary and sufficient characterisation has its own geometric interpretation as the reflexive generalised inverses are related to the projections onto subspaces. Finally, it is shown that the condition is in fact a natural generalisation of the state synchronisability of homogeneous (i.e. identical) linear agents. A computer simulation is also provided to verify the result.

Methods for the design of static output feedback controllers for linear discrete-time systems subject to state and control constraints, additive disturbance and measurement noise are proposed in this study. First, the authors show how the design can be performed through the construction of an output feedback controlled invariant set together with the solution of several multiparametric linear programming (mp-LP) problems. This technique is commonly used to characterise the optimal control action as a piecewise affine (PWA) function over polyhedral regions. However, when applied to constrained multiple output systems, it may require high online computational cost and large memory capacity, due to the number of polyhedral regions resulting from the mp-LP solution. Within this context, the authors present a new approach to compute a PWA static output feedback control law over a smaller number of polyhedral regions using the K q-flat data cluster analysis algorithm. Optimisation problems to compute PWA sub-optimal static output feedback control laws over an even smaller number of regions are also proposed, and illustrated by numerical examples.

This study is concerned with the event-triggered state estimation problem for a class of stochastic hybrid systems with missing measurements in a networked environment. Two independent Markov chains are introduced to, respectively, characterise the stochastic measurement missing and the possible modal (or mode) transition of the system. In consideration of the constrained bandwidth and limited power resources of networked systems, a closed-loop event-triggered mechanism based on the measurement innovation is designed to trigger data transmission only when trigger conditions are satisfied. To keep the exponentially increasing number of full hypothesis sequences in optimal estimation to bounded computational complexity, the interacting multiple model framework is extended to tackle event-triggered sampling with the statistical information implicit in event-triggered conditions sufficiently explored and the possible measurement missing taken into account. A Monte Carlo simulation involving tracking a two-dimensional manoeuvring target with two operational modes is provided to demonstrate the effectiveness and efficiency of the proposed event-triggered hybrid state estimation in the presence of missing measurements.

A Luenberger-like functional interval observer for the linear systems with time-varying disturbances is developed in this study. First, as an extension of the definition of the general interval observer, a new definition of the functional interval observer is provided. Then the sufficient conditions for the existence of such an observer are introduced in terms of the properties of positive systems. Simultaneously, on the basis of the proposed existence conditions, the parametric design method of the interval observer for the linear functional of the states in the systems is presented by employing the solution of the Sylvester equations. Eventually, the correctness and efficiency of the obtained results are illustrated by a numerical example.

This study addresses the problem of distributed formation control for a multi-agent system with collision avoidance between agents and with obstacles, in the presence of various constraints. The authors proposed solution incorporates a control Lyapunov function (CLF) into a distributed model predictive control scheme, which inherits the strong stability property of the CLF and optimises the formation performance. For each agent, the formation tracking objective is formulated through the CLF, while the collision avoidance objective being explicitly considered as constraints. A relaxation parameter is introduced into the CLF condition to make the trade-off between the two conflicting objectives. The terminal constraint is constructed based on the concept of velocity obstacle, which characterises the set of states that lead to collisions. They show that the terminal constraint together with the relaxed CLF-based constraint guarantees the recursive feasibility and stability of the multi-agent system for almost any prediction horizon. Furthermore, the theoretical effectiveness and advantageous implementation properties are demonstrated through simulation for multi-agent formation control with several obstacles.

The problem of fixed-time stabilisation for a class of high-order non-linear systems is studied. By introducing the manipulation of sign functions and revamping by adding a power integrator technique, a novel approach is proposed to construct a continuous stabiliser as well as a continuously differentiable Lyapunov function, which is crucial for proving fixed-time stability. The novelty of this study is the development of a systematic design method that provides a delicate solution to the problem of fixed-time stabilisation for high-order non-linear systems.

In this study, based on the finite-time sliding mode control method, an antiswing control law is designed for the underactuated crane systems in two-dimensional space with external disturbance. The finite-time disturbance observer is utilised to estimate the external disturbance and develop the finite-time control law. The designed controller can regulate the trolley to the planned trajectory within a finite time in the presence of external disturbance. Then it can be shown that the proposed control approach can achieve precise trolley positioning and swing suppression. Simulation results are provided to show the satisfactory control performances of the presented control method in terms of working efficiency as well as robustness with respect to external disturbance.

In this study, a novel idea is proposed for fixed-time recursive surface structure design for arbitrary-order system. The stability of controller design methodology is verified by using Lyapunov analysis. The primary benefit behind formulating the proposed surface structure is in achieving fixed-time convergence during sliding. Moreover, the control structure is designed to get fixed-time convergence during reaching as well. The approximate convergence time has been calculated mathematically and is verified using simulations. The sliding mode control is formulated for single-input-single–output non-linear dynamical systems. The proposed control scheme is robust and the singularity is avoided. The conditions to ensure stability during reaching phase are derived and are shown to depend only on the design of surface parameters. The detailed simulation results of a general third-order dynamic system show the efficacy of the proposed scheme. Finally, the proposed method is implemented for automatic generation control (AGC) of a multi-area interconnected power system while considering the non-linearity in the dynamic system. For the first time, fixed-time convergence is assured for AGC. To the best of the authors' knowledge, no such structure is proposed yet for AGC. The results are also compared with the traditional proportional–integral controller.