This article provides a short note on the research work and academic life of the late Professor J.C. West as an introduction to a reprint of his Presidential Address as President of the IEE in 1984.

The large number of control devices which had been invented over the previous two centuries led, by about 1930, to the conception of a control theory with fundamental principles basic to all forms of control. The last war saw the use of this theory to develop sophisticated mechanisms of high precision. The study gives the development of the science and engineering of control over the last 40 years. In engineering, the increasing importance of the effects of non-linearity is emphasised, and the spinoff resulting in unconventional electrical machines is described including the development of magnetic levitation. During this period control theory has also been introduced into a wide variety of other branches of knowledge. The greatest impact has probably been in medicine, with the body now being regarded functionally as a complex, dynamic control system. The heart–lung combination was eventually seen to be a ‘self-adaptive’ system, and the study had an effect on engineering design. Other areas described include sociology, economics and management. The basic tenets of the accuracy of measurement, the speed of measurement and ‘dead time’, well established in engineering, are shown to be equally fundamental in management and economics.

This study is concerned with the problem of stability analysis of two-dimensional (2D) discrete-time Roesser systems with time-varying delays. First, based on an augmented Lyapunov–Krosovskii functional, a less conservative stability criterion incorporating time-varying terms is established by utilising a general free-matrix-based inequality. Next, in order to eliminate the time-varying terms without introducing redundant constraints, a quasi-convex combination method is proposed. Then, compared with the criteria derived via the other inequalities, the conservatism analysis is given to prove the proposed criterion can lead to a better result theoretically. Finally, a numerical example is presented to illustrate the advantage of the presented method.

This study addresses the problem of distributed sampled-data fuzzy controller design for a class of non-linear distributed parameter systems which are described by first-order hyperbolic partial differential equations (PDEs). To achieve this goal, first, the non-linear system is modelled by a continuous-time Takagi–Sugeno first-order hyperbolic PDE fuzzy model. Subsequently, the authors design a new distributed sampled-data fuzzy controller that generates a zero-order hold sampled-data control signal appropriate for the PDE systems. Then, a new Lyapunov–Krasovskii functional is suggested to provide the stability analysis conditions of the closed-loop control system. Moreover, the stabilisation conditions are obtained and converted to linear matrix inequalities using some new null terms. The proposed technique has removed the structural constraints on the convection and Lyapunov matrices. Finally, the proposed approach is applied on a biological system and a non-isothermal plug flow reactor .

The output feedback robust controller is proposed for a class of non-linear systems with integral input-to-state stable inverse dynamics and external disturbance. The investigated systems represent more general classes of non-linear uncertain systems. An extended state observer (ESO) is designed to estimate both the system states and the external disturbance by use of the disturbance as a generalised state. Based on the given reduced-order ESO, a new error dynamic system is constructed. The global asymptotic regulation is guaranteed under the presented anti-disturbance controller by the combined approach of backstepping and linear matrix inequality. The simulation result demonstrates the effectiveness of the given algorithm.

In this study, the authors address the problem of reaching a given percentage of an optimal cost, so as to guarantee a known reserve with respect to the optimum. This reserve aims to counteract fast changes in the operating conditions. The authors assume that the analytical expression of the cost function is not available. To tackle this problem, they propose a novel extremum seeking scheme, the sub-optimal extremum seeking, that is able to keep a given margin with respect to the estimated optimal cost. Stability properties of the control scheme are proved and the effectiveness of the approach is validated in simulation.

This study investigates the group consensus problem for heterogeneous multi-agent systems composed of discrete-time first- and second-order agents. Two kinds of distributed group consensus protocols are proposed based on the information of the agent itself and its neighbours. Model transformation is introduced and some sufficient conditions are derived for heterogeneous multi-agent systems with directed communication topology to reach group consensus by utilising the matrix theory and the graph theory. Finally, simulation examples are given to validate the effectiveness of the theoretical results.

To assess the performance of a control loop based on the minimum variance (MV) benchmark, we need to calculate MV lower bound (MVLB). Even though there is a plethora of literature available for calculating MVLB for the linear systems, these methods are not suitable for non-linear systems. Furthermore, almost all of the real-world applications have been encountered with input variance constraints. These constraints limit controllers' abilities in decreasing the output variability. Therefore, existing MVLB computation methods, which do not account for input constraints, are not realistic when applied to constrained systems. The authors propose a novel approach to estimate MVLB by employing properties of dual Lagrangian functions to address these issues simultaneously in this study. Furthermore, to design the constrained non-linear MV controller (MVC), they propose to use the recurrent neural network for accommodating non-linearities and the input constraints. Then, control loop stability, optimality with respect to MVLB as well as the global convergence of the proposed controller are analytically proved for convex-non-linear systems with input constraints. The proposed control strategy is verified through simulations performed on a non-linear quadruple-tank system. The results indicate that the proposed design provides satisfactory results in decreasing output variance while satisfying the constraints.

An L-shaped arm with unknown load driven by a linear pulse motor is studied in this work. To control the motor motion and the arm vibration, an operator-based non-linear control is designed using an on-line discrete wavelet transform (DWT). First, the dynamics of the L-shaped arm vibration is modelled by considering the arm as a two-dimensional Euler–Bernoulli beam. The relationship between the load and the arm vibration is given. Second, by using the on-line DWT in the operator-based non-linear control, the proposed control for the system is designed. The wavelet transform is used to estimate the load and remove the influence of some undesired uncertainties. The operator-based right coprime factorisation method is used to guarantee the robust stability of the motor-arm system. The piezoelectric actuator is utilised to further reduce the arm vibration. The hysteresis of the piezoelectric actuator is compensated by using a Prandtl–Ishlinskii hysteresis model. Finally, simulation results are demonstrated to validate the proposed control.

In this study, the asymptotic tracking control problem is addressed for known and unknown non-linear systems in the strict-feedback form with time-varying output constraints, input saturation, and external disturbances. A barrier Lyapunov function is employed to prevent transgression of the output constraints. Neural networks are applied to approximate the unknown functions. To deal with the input saturation effects and/or neural networks reconstruction errors, the Nussbaum gain technique is suggested. The proposed approach guarantees the boundedness of all the closed-loop signals, and for the first time, the asymptotic tracking property is achieved for the strict-feedback non-linear systems, while the actual output remains in the output constraints, despite input saturation and external disturbances. Two simulation examples have validated the effectiveness of the proposed results.

This study investigates the problem of delay-dependent stability and stabilisation of uncertain delta operator systems with time-varying delay. A new model transformation is proposed using a three-term approximation, which has a smaller approximation error than the existing methods based on one or two terms. On the basis of scaled small gain theorem (scaled small gain) and an appropriate Lyapunov–Krasovskii functional, a new stability criterion is proposed in terms of linear matrix inequalities. Finally, numerical examples are presented to illustrate the effectiveness of the proposed method.

This study investigates the stabilisation of a class of continuous-time two-dimensional (2D) switched non-linear Roesser model with all modes unstable. Other than design controllers for the system, the authors would like to schedule the switching signal to achieve the asymptotical stability of the system. The main idea in this study is to utilise the alternative running of different subsystems to compensate the divergence of each subsystem, which thus achieves the stabilisation goal. By taking advantage of mode-dependent average dwell time property and a piecewise continuous Lyapunov function method, a general criterion is developed to guarantee the stability of the continuous-time switched 2D non-linear system with a designed switching law. The obtained result is further used to deal with switched 2D linear system. Finally, the effectiveness and superiority of the proposed methods are illustrated by two numerical examples.

In this brief, a non-identical gain based control design scheme is proposed to stabilise balanced collective formation in multi-vehicle systems, modelled with non-holonomic unicycle dynamics. Balanced collective formation refers to a situation in which the vehicles' motion causes their positional centroid to become stationary. This study mainly focuses on achieving stable balanced collective formation about the prescribed location of the collective centroid along with desired orientations of the vehicles. It is assumed that the vehicles are moving in a force field which is controlled externally. The proposed control algorithm consists of two controls – one of the controls, pertaining to the external force field, is directly applied to the system, and assumes the same value for all the vehicles. While the other control, which operates with heterogeneous gains, provides the steering force to the vehicles and is derived using Lyapunov analysis. Theoretical findings are validated through numerical simulations.

A class of discrete-time non-linear positive time-delay switched systems with sector-type non-linearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov–Krasovskii (L–K) functionals for this system class are derived; these are expressed as feasibility conditions for systems of linear algebraic inequalities. Corresponding spectral conditions for the existence of common L–K functionals are also described. Furthermore, it is shown that the proposed approaches can be applied to discrete-time models of digital filters and neural networks. Finally, a numerical example is given to illustrate the effectiveness of theoretical results.

This study presents a novel non-linear mapping-based feedback technique for controlling chaotic permanent magnet synchronous motor (PMSM) using dynamic surface control (DSC), neural approximation and parameter identification. Neural networks are utilised to online approximating the unknown system dynamics, adaptive parameter identification is designed to estimate the unknown parameter, and DSC technique circumvents the problem of ‘explosion of complexity’ in the traditional backstepping methodology. The major feature of the non-linear mapping-based feedback technique lies in that the merits of high-gain and low-gain control are synthesised by virtue of a novel non-linear continuous differentiable mapping feedback function, and a novel non-quadratic Lyapunov function is used to analyse the closed-loop system stability caused by the compound function of non-linear feedback. Finally, unprejudiced comparative results are given to demonstrate the effectiveness and advantages of the proposed control scheme.

This work studies the delayed output feedback (DOF) of discrete-time systems with input and output delays that are arbitrarily large, bounded, and exactly known. The significance of the DOF is that only the present and delayed inputs and outputs are used for feedback. For systems with a single input delay and multiple output delays, the idea of state prediction is utilised to construct the DOF controller. While for systems with multiple input and output delays, the DOF controller is designed by firstly reducing the original system to a delay-free one. It is shown in both cases that the closed-loop systems controlled by DOF are asymptotically stable and act like delay-free systems with the same dimensions as open-loop systems. Compared with the continuous-time case, the DOF controllers for discrete-time systems do not contain distributed delay terms and the implementation problems can be avoided. The DOF is used to stabilise the spacecraft rendezvous system with input and output delays and simulations show the effectiveness of the proposed approach.

In this study, a geometrically incremental dissipativity is proposed for switched discrete-time non-linear systems using multiple storage functions and multiple supply rates. The uniform incremental stability conditions are derived for geometrically incrementally dissipative discrete-time switched systems by using multiple Lyapunov functions approach and average dwell-time technique. The geometrically incremental dissipativity is preserved for the feedback interconnected switched non-linear systems with a composite switching law, while uniform incremental stability is preserved under some certain conditions. Two numerical examples are given to illustrate the validity of the authors' results.