In this study, a consensus algorithm for multiple non-linear Euler–Lagrange systems is presented. This controller guarantees that all agents can reach a common state in the workspace. External disturbances acting on the system are included in the closed-loop stability analysis, and the input-to-state properties of the proposed controller are investigated based on the concept of input-to-state consensus. Moreover, the influence of structural uncertainty is further discussed on the basis of passivity theory. The robustness of the proposed consensus algorithm is then demonstrated in the presence of both external disturbances and structural uncertainty. Experiments are conducted to validate the effectiveness of the proposed consensus algorithm.

A miniature capsule robot (capsubot) – which has no external moving parts whereas a conventional robot has legs and/or wheels – is suitable for in-vivo applications, engineering diagnosis and pipe inspection. This study addresses the trajectory-tracking problem of an underactuated planar capsubot. A combining piecewise and behaviour-based control algorithm is proposed for trajectory tracking. This study also proposes four motion behaviours, four switching behaviours and one stationary behaviour. A selection algorithm for behaviour-based control and rules for inner mass (IM) motion control in all the behaviours are developed. The partial feedback linearisation control is used for low-level IM motion control while the piecewise and behaviour-based control is used for the capsubot trajectory tracking control.

This study presents the concept of structural weight-balanceability of network systems as a useful method to examine the average consensus of the systems. The authors introduce the notion of structurally unobservable node based on structural observability concept to determine the structural weight-balanceability of a network. They propose a simple technique to identify structurally unobservable nodes, and consequently infer on structural weight-balanceability of the network. A mathematical method based on principal minors of the associated Laplacian matrix of the network is developed to modify a structurally weight-balanceable network into a weight-balanced one. A distributed method is presented to compute normalised principal minors in a large-scale network system with directed communication topology. This is the first work that provides a rigorous mathematical formulation to check the structural weight-balanceability of network systems and make a structurally weight-balanceable network, weight-balanced. Finally, simulation results are presented to illustrate the performance of the proposed method in dealing with networks with a large number of nodes.

This study studies the consensus of multi-agent systems on time-varying network topologies. It is shown that this consensus reaching is equivalent to the corresponding weak ergodicity of the Markov process. A very mild sufficient condition of the consensus reaching that allows the communication among agents to be time-dependent and directed is obtained by estimating the Dobrushin coefficient of ergodicity. It is also shown that the notion of in-branching spanning tree plays a central role in the reaching of consensus. Moreover, sufficient conditions for (almost sure) consensus are presented for the case of time-varying networks.

This study aims to address the regulation problem for the unicycle model while guaranteeing prescribed performance. Different controllers based either on polar coordinates or time-varying laws are proposed. The main contribution is the combination of the standard control laws that allow to achieve posture regulation for the unicycle, with the prescribed performance control technique that imposes time-varying constraints to the system coordinates. To apply prescribed performance to the unicycle system which is subject to a non-holonomic constraint, the authors design a specific transformation function that is instrumental in the proof of asymptotic convergence with prescribed guaranties.

This study is concerned with the low-frequency (LF) integral quadratic constraints (IQC) of the linear singularly perturbed model (SPM). The conditions satisfying LF IQC are derived in terms of linear matrix inequalities by using the generalised Kalman–Yakubovich–Popov lemma. As special cases of LF IQC, LF bounded realness and LF positive realness are exploited in detail. In addition, upper bound of the small perturbation parameter, which relates to the robustness of SPM, can be estimated. Numerical simulations demonstrate that the proposed method can reduce the conservatism and characterise the SPM more specifically by ignoring the unrelated frequency range.

Selective catalytic reduction (SCR) systems are commonly used for exhaust gas aftertreatment in many applications. For optimal NO _x reduction using the SCR technique a certain temperature must be reached. This study deals with modelling and control of the temperature inside the SCR system for optimal catalyst operation. A first principle-based model is described for the propagation of the temperature inside the catalyst. The model is described in linear parameter varying (LPV) state-space form and used for control of the temperature using a linear-quadratic-Gaussian (LQG) controller. Necessary conditions for obtaining an optimal controller without complete state information are defined. This leads to a discrete-time LQG controller for LPV systems. The results obtained for the controller are based on several assumptions to ensure the stability of the controller. The states of the proposed model are not measurable. For this purpose, a Kalman filter-based observer is designed for estimation of the states that are used for state feedback in the controller. The observer is designed for discrete-time LPV systems and necessary assumptions for the observer are derived in the work. The resulting model of the temperature gives a model fit of up to 77% for validation data and the controller requirements are met using the proposed controller applied in a simulator environment.

This study is concerned with the non-fragile H _∞ control problem for a class of discrete-time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite-distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time-delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non-fragile H _∞ output-feedback controller such that the closed-loop control system is stochastically stable with a prescribed H _∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H _∞ disturbance attenuation, and the addressed non-fragile control problem is then recast as a convex optimisation problem solvable via the semi-definite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method.

The design approach of robust sliding-mode output-feedback (SMOF) controller in static nature is proposed for a class of uncertain systems with mismatched uncertainty in the state matrix. The main contribution of the approach is in that the quadratic performance can be optimised with guaranteed cost. At first, a new existence condition of linear sliding surface with guaranteed cost is derived, which only involves the original system parameters. Secondly, based on the existence condition, an iterative linear matrix inequality approach is proposed to optimise the quadratic performance on the sliding surface. At last, by using linear matrix inequalities approach, a design framework for synthesising the SMOF controller is presented, as a consequence, finite time convergence to the sliding mode can be guaranteed and, the quadratic performance can be optimised under input constraints. The superiority of the proposed method is verified by numeric examples.

The new algorithm presented in this study, called TRAC (trust-region reflective adaptive controller), performs online adaptive control of time-varying linear or linearisable systems subject to parametric disturbances. The process of accomplishing such adaptive control consists of feeding the measured output signal back to TRAC – which occupies the outer loop of a control scheme – as well as the reference signal. Knowing the order of the closed-loop system in the inner loop, a parametric model of the time-varying output is derived as a function of the system's variables, such as damping and natural frequencies. Using trust-region optimisation, these parameters are estimated in real-time by recursively fitting the actual output into the parametric model. This allows for the location of the actual poles to be estimated in the s-domain after the poles have been shifted by the disturbance. Accordingly, the gains are re-tuned in order to return the actual poles to their desired location and absorb the disturbance. The primary advantage of TRAC relative to the state-of-the-art is its computational simplicity which is owed to search space restriction and heuristic approximations with trust-region search. A video of a sample application describing real-time TRAC-based control can be found on the IET's Digital Library.

A challenging problem in automotive industry is the torque control of permanent magnet synchronous machines employed in automotive electrical traction drives. These applications are characterised by fast dynamics that are subject to physical and computational constraints. The goal of this study is to provide a controller synthesis method that can deal with these challenges. To this end, a one step ahead model predictive state-feedback control scheme based on flexible Lyapunov functions concept was designed. The existing constraints related to the system states and control inputs are approximated with polytopic constraints, which are linear constraints. Moreover, the rotor temperature behaviour, which is crucial in automotive electrical drives, is taken into account directly in the controller synthesis methodology. As a result, the derived model predictive control problem is reduced to a linear program that can be solved on-line at each sample instant. Then, the obtained control solution is implemented in a real electronic control unit and tested in real-time using an industrial hardware-in-the-loop test-bench. Real-time results are reported and analysed and show significant improvement compared with the classical proportonal–integral approach.

The authors study here the problem of adaptive ‘soft-landing’ control for electromagnetic actuators. The soft landing requires accurate control of the actuator's moving element between two desired positions. They propose a non-linear adaptive controller to solve the problem of robust trajectory tracking for the moving element, when considering model uncertainties with linear parametrisation. The controller is an integral input-to-state stability (iISS) backstepping controller, merged with gradient descent estimation filters to estimate model uncertainties with linear parametrisation. They show that it ensures bounded tracking errors for bounded estimation errors. Furthermore, iISS result allows us to represent the bound on tracking error as a decreasing function of the estimation error. They demonstrate the effectiveness of this controller with numerical tests.

The efficient coupling driving control is a key technique that affects both the fuel economy and drivability of the hybrid electric bus (HEB). However, the uncertainties resulting from the complex driving condition and the powertrain would affect the control performance. To solve this problem, this study proposes a novel control approach, which is elaborately integrated with multi-controllers under the consideration of properties of the city-bus-route and the hybrid powertrain configuration. First, a torque split strategy with the automated mechanical transmission (AMT) gear-shifting strategy is employed to adapt the driving intention quantified by fuzzy logic. Then the coordinated control mechanism is constructed through utilising the electric machine (EM) to compensate the response deviation of engine torque, meanwhile a robust controller is designed to withstand parameter perturbation and external disturbance existing in EM. Simulation results show that the operating points of the engine and EM are adjusted into the high-efficiency areas with the assistance of AMT gear-shifting, and the EM torque tracking performance especially when parameter perturbation and external disturbance appear. Moreover, the strategy adaptively distributed the driving torque in the predefined working modes for different driver's intentions. Thus, the efficient coupling driving of HEB might be implemented by the proposed method.

This study considers the global output-feedback control for a class of switched stochastic non-linear time-delay systems under arbitrary switchings. By using the backstepping technique and choosing an appropriate Lyapunov–Krasoviskii functional, an output-feedback controller independent of switching signals is constructed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. Two simulation examples are provided to show the effectiveness of the designed controller.

This study presents a time-delay-independent fault detection and adaptive accommodation control scheme for strict-feedback systems with unknown multiple time-delayed non-linear faults. The magnitude and occurrence time of the multiple faults with unknown time-varying delays are unknown. First, a detection threshold is derived to design a time-delay-independent fault detection scheme for the time-delay systems and the fault detectability is analysed. Second, an adaptive approximation design for a time-delay-independent fault accommodation control is addressed. The adaptation technique is applied to learn weights of function approximators and thus the multiple faults can be compensated after the detection of the first fault. It is shown that all signals of the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to an adjustable neighbourhood of the origin.

In this study, the authors investigate the exponential stability and L ₂-gain for a class of non-linear switched impulsive systems with time-varying disturbances. Using the concept of average impulsive interval incorporated with a piecewise Lyapunov function, some new stability criteria and disturbance attenuation properties are presented. The derived criteria are theoretically proved to be less conservative than some existing results. A numerical example as well as its simulation is given to illustrate the effectiveness of the obtained results.