Aircraft are highly non-linear systems, but flight control laws are traditionally designed from a set of linearised models. Due to the application of linear control laws on a non-linear system, the real performance ability of the aircraft is not fully utilised. In addition, in adverse situations like near stall, the aircraft develops significant non-linearities, and linear control laws do not perform well. This study therefore considers the design of a longitudinal flight controller for a fixed-wing aircraft using non-linear dynamic inversion technique or, in terms of control theory, partial exact feedback linearisation. A novel contribution of this study is the proposed combination of three different automatic flight controllers that provide complete 3-DOF longitudinal control. A detailed analysis of the internal dynamics for each controller is also presented. It has been shown that for each controller the internal dynamics are stable. This makes the controller suitable for various flight conditions. The aims of these flight controllers are threefold. First, to provide control of the flight path angle by tracking the pitch angle and the angle of attack. Second, to provide high attitude (pitch up or down) manoeuvrability. Finally, to provide automatic adverse attitude recovery of the aircraft in situations like stall, the switching strategy between the controllers are also discussed. A simulation carried out on a non-linear model of a multi-role fighter aircraft verified the proposed theoretical results confirming the suitability of the controllers.

This study addresses a stochastic model predictive tracking problem for linear parameter-varying (LPV) systems described by affine parameter-dependent state-space representations and additive stochastic uncertainties. The reference trajectory is considered as a piecewise constant signal and assumed to be known at all time instants. To obtain prediction equations, the scheduling signal is usually assumed to be constant or its variation is assumed to belong to a convex set. In this study, the underlying scheduling signal is given a stochastic description during the prediction horizon, which aims to overcome the shortcomings of the two former characterisations, namely restrictiveness and conservativeness. Hence, the overall LPV system dynamics consists of additive and multiplicative noise terms up to second order. Due to the presence of stochastic disturbances, probabilistic state constraints are considered. Since the disturbances make the computation of prediction dynamics difficult, augmented state prediction dynamics are considered, by which, feasibility of probabilistic constraints and closed-loop stability are addressed. The overall approach is illustrated using a tank system model.

This study concerns an n-link underactuated planar robot connected to a fixed base by n revolute joints in a vertical plane. The linear strong structural controllability and observability of such a robot around the upright equilibrium point, where all the links are in the upright position, are investigated. This study aims to solve an open problem regarding the linear strong structural controllability and observability of such a robot with only active intermediate links rather than the first or last link. This paper proves that it is linearly strongly structurally controllable and observable (linearly controllable and observable regardless of its mechanical parameters), if and only if there are at least two active adjacent links among the intermediate links with measurable corresponding link angles. Specifically, first, if there are two active adjacent links among the intermediate links with measurable corresponding link angles, without making any other assumptions about any link of the robot, this paper proves that the robot is linearly strongly structurally controllable and observable. Second, when the robot only has two or more active intermediate links with measurable corresponding link angles, if there are no active intermediate adjacent links, this study proves that the robot is linearly strongly structurally uncontrollable and unobservable by presenting a constructive example to show that there always exists a set of mechanical parameters that renders the robot linearly uncontrollable and unobservable.

State-dependent intermittent control is presented to investigate the exponential stabilisation issue for a class of non-linear systems. The so-called state-dependent intermittent control means that whether control signals are imposed on a plant or not is related to system dynamics. Based on the concept, the mathematical description of a state-dependent intermittent controller is initially introduced. Then, in the framework of it, the globally exponential stability is analysed in detail for the deduced state-dependent intermittent control system with the pre-given state-dependent regions. It is worth mentioning that parameters in the pre-given state-dependent regions are tunable, which makes it flexible to design. Furthermore, a state-dependent intermittent controller can be designed for the concerned non-linear system according to the established exponential stabilisation criterion. Here, the designed state-dependent intermittent controller can not only avoid chattering effectively but also control switching frequency by adjusting values of parameters in the pre-given state-dependent regions. Finally, two examples are given to show the effectiveness and superiority of the proposed method.

In this study, actuator fault diagnosis of singular delayed linear parameter varying (SDLPV) systems is considered. The considered system has a time-varying state delay and its matrices are dependent on some parameters that are measurable online. It is assumed that the measured parameters are inexact due to the existence of noise in real situations. The system with inexact measured parameters is converted to an uncertain system. Actuator fault diagnosis is carried out based on fault size estimation. For this purpose, the system is transformed to a polytopic representation and then a polytopic proportional integral unknown input observer (PI-UIO) is designed. The proposed observer provides simultaneous state and actuator fault estimation while attenuating, in the sense, the effects of input disturbance, output noise and the uncertainty caused by inexact measured parameters. The design procedure of PI-UIO is formulated as a convex optimisation problem with a set of Linear Matrix Inequality (LMI) constraints in the vertices of the parameter domain, guaranteeing robust exponential convergence of the PI-UIO. The efficiency of the proposed method is illustrated with an electrical circuit example modelled as an SDLPV system.

This study investigates the sampled-data reliable control for a class of Takagi-Sugeno (T-S) fuzzy semi-Markovian jump system (FSMJS). The system under consideration involves semi-Markov stochastic process that is described by the property of cumulative distribution function. To relax the difficulty of finding upper bounds in sample-and-hold behaviour of the FSMJS, a novel method named mismatched membership function is presented. Sufficient conditions that can guarantee the T–S FSMJS to be stochastically stable are given. More precisely, the reliable sampled-data controller is designed in terms of linear matrix inequalities. Finally, the validity of the presented approach is demonstrated by a controller design for a single-link robot arm model.

The authors study the stabilisation problem of switched linear systems with sampled and quantised output feedback. They assume that every mode of the plant is stabilisable and observable and that a feedback gain is given for each mode. The controller receives the information about the active mode of the plant only at each sampling instant. Therefore, the controller mode may not synchronise with the plant mode after intersample switching. They construct update rules of quantisation scales to avoid the saturation of the quantiser due to mode mismatches. An encoding and control strategy is designed to guarantee asymptotic stability of the closed-loop system under slow-switching assumption described by dwell time and average dwell time.

A class of switched multi-agent tracking problems with variable tracking number is explored. During the whole tracking course, tracking agents switch and the tracking number varies over different time intervals. Consequently, tracking errors jump and the dimension of Laplacian matrix of the multi-agent system changes, which increase the difficulty of analysis. To solve this problem, the authors proposed a switched tracking strategy and designed an average norm of tracking errors as a Lyapunov function. Thereafter, conditions guaranteeing the stability of each subsystem and overall stability of the switched tracking system are obtained. Finally, the effectiveness of the proposed tracking strategy and validity of the theoretical results are verified by a numerical simulation.

This study investigates the cooperative containment control problem for heterogeneous discrete-time linear multi-agent systems. The structures of the systems are uncertain, and there exists more than one leader in the authors' systems. For these leaders, it is unnecessary to establish links exchanging information between them. Instead, the authors assume that at least one leader has directed paths to all the follower nodes. A distributed discrete-time compensator is presented to estimate the convex hull information of the leaders. Then, based on the estimation of the convex hull information of the reference outputs, they design a novel distributed internal model compensator to tackle the uncertain parts of the dynamics. Finally, a distributed dynamic output feedback approach is utilised to study the distributed systems with external disturbance under the directed communication topology. A numerical example is provided to illustrate the validity of the theoretical results.

This study improves a recently proposed gain scheduling predictive control strategy for the ACUREX solar collector field at the Plataforma Solar de Almería, Spain. Measured disturbances are an integral part of the plant and while simple classical, series and parallel, feedforward approaches have been proposed and used extensively in the literature, the proposed approach incorporates a feedforward systematically into the predictive control strategy by including the effects of the measured disturbances into the predictions of future outputs. Models of the measured disturbances are estimated around a family of operating points directly from input–output data and using a subspace identification method while taking into account the frequency response of the plant. Input–output data are obtained from a validated non-linear simulation model of the plant. The non-linear simulation model is validated against measured data obtained from the ACUREX plant and the effectiveness of the proposed control approach is evaluated in the same non-linear simulation environment. The study also considers related issues such as the significance of sufficient modelling of the measured disturbances and the impact of incorporating the expected future behaviour of a measured disturbance along a given prediction horizon, a theme which has received little attention in the literature.

This study investigates the problem of adaptive fuzzy output feedback control for a class of switched uncertain non-linear systems with input quantisation. The considered system contains unknown non-linearities, the switching signals, hysteretic quantised input and immeasurable states. Fuzzy logic systems are used to approximate the unknown non-linearities and a fuzzy switched state observer is designed to estimate the unmeasured states. The hysteretic quantised input is divided into two bounded non-linear functions in the control design to avoid chattering problem. By incorporating command filter into the backstepping design procedure, a fuzzy adaptive control scheme is developed, which solves the ‘explosion of complexity’ problem in conventional backstepping control schemes. Finally, the stability of the closed loop and convergence of the tracking error are proved via average dwell time and multiple Lyapunov functions methods. The effectiveness of the proposed approach is verified by a numerical simulation example.

An integrated integral sliding mode fault tolerant control scheme is proposed for the linear parameter varying (LPV) plants in the output feedback framework. To estimate the unavailable plant states, an unknown input LPV observer is employed. The feedback and observer gains are designed using linear matrix inequalities approach to ensure closed-loop stability nominally and in the situation of actuator faults/failures. An integral sliding modes approach in the LPV framework together with control allocation maintains the nominal performance in the presence of permissible set of actuator faults/failures. A rigorous closed-loop stability analysis is carried out and to show the feasibility of the proposed approach it is tested in simulations on the non-linear plant of a passenger aircraft.

Finite-time stabilisation involves finding state feedback controllers which stabilise the closed-loop system in a finite-time interval. This paper deals with robust finite-time stabilisation of linear singular systems with interval time-varying delay. Based on singular value decomposition method and a generalised Jensen inequality, we provide sufficient conditions for the design of such controllers guaranteeing the finite-time stability of the closed-loop system. The proposed conditions are expressed in terms of linear matrix inequalities. Numerical examples are given to illustrate the effectiveness of the proposed methods.

This study investigates the time-varying control for globally exponential stabilization of the Brockett integrator. Using the desired trajectory as a virtual control, the authors first illustrate the concept behind the control design and then propose an initial-value-dependent time-varying control. While this time-varying control offers a simple and analytic solution to the problem of exponential stabilisation for the Brockett integrator, it may fail if one of the initial states is zero. To resolve this initial-value-dependent issue, they develop a new time-varying control to globally and exponentially stabilise the Brockett integrator to the origin without using any state or input transformation. They present the stability analysis and numerical results to verify the effectiveness of the proposed time-varying stabilisation control.

In this study, the problem of robust control for spacecraft rendezvous on elliptical orbit, which contains parameter uncertainties and external disturbances, is investigated based on the implicit Lyapunov function method. A state-feedback controller is first designed, and its existence conditions are derived in terms of linear matrix inequalities (LMIs) which should be solved in real time. An analytical solution to these LMIs is provided to greatly reduce the computational burden. On the basis of the state-feedback analysis, an observer-based output-feedback controller is proposed, and it is proved finite-time stable by constructing an analytical solution to the parameterised nonlinear matrix inequalities (NLMIs). The advantage brought by the proposed analytical solution is that whether these NLMIs hold only need to be checked at two points, while in previous researches they were supposed to be checked at infinite points. The effectiveness of the theoretical results is illustrated by simulation examples.

The authors are concerned with the stability of hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Under some reasonable conditions, they establish an upper bound on the duration between two consecutive state observations. Moreover, we can design the discrete-time state feedback control to stabilise the given hybrid stochastic differential equations in the sense of pth moment exponential stability by developing a new theory. In comparison to the results given in the previous literature, this study has two new characteristics: (i) the stability criterion concerns pth moment exponential stability, which is different from the existing works; (ii) discrete-time state observations depend on time delays.

Extended linear matrix inequality (LMI) conditions, ensuring the stability of commensurate fractional-order linear systems by static-output feedbacks, are given. It is assumed that the system uncertainties are constant and possibly present in all the system matrices. The stabilising static-output feedback is conceived to overcome the system uncertainty and place the poles of the closed-loop system in a well-defined domain that is formed by the intersection of many regions in the complex plane. The control design is formulated as the solution of a set of linear matrix inequality conditions. The validity of the obtained results is testified through an example of a fractional-order system with polytopic uncertainties.

This study deals with the robust output regulation problem for a class of uncertain systems in a linear fractional transformation form. The problem is addressed under a measurement output-feedback framework, i.e. no full information of both plant and exosystem states is assumed for feedback control use. A new robust control law with a novel output regulator structure is proposed, based on which sufficient conditions for robust output regulability and stability are established in terms of linear matrix equations plus a set of linear matrix inequalities. As a result, the optimal output regulation control solution can be synthesised effectively via convex optimisation. Finally, the proposed robust output regulation design scheme will be applied to solve the chaos tracking control problem for the non-linear Chua's circuit.

In this study, a new distributed fast terminal sliding mode exactly tracking control method is proposed for a class of non-integral cascade high-order uncertain non-linear systems. Based on the concept of hierarchical design, a series of decentralised sliding mode surfaces are first developed in the authors' design scheme. Every sliding mode surface is independent of each other, besides, on this designed sliding mode surface, finite-time convergence characteristic can be guaranteed. By using backstepping technology and dynamic surface control method, a finite-time exact tracking controller is finally developed. Based on Lyapunov stability theory, the stability of system has been theoretically proved, and in finite time, all the closed-loop system signals ultimately converge to the origin. Simulation results verify the effectiveness of the proposed approach.

This study is concerned with the safe implementation of delayed output feedback (DOF) for linear systems with multiple input delays. It is observed that the numerical implementation of the distributed delay terms involved in the DOF controller may lead to instability of the closed-loop system. To solve this problem, a generalised low-pass filter (LPF) is introduced into the control loop. It is shown that the stability of the closed-loop system can be maintained if the numerical integration is sufficiently precise. An augmented system is then constructed to design the LPF by applying the traditional pole assignment algorithm for linear systems without delay. Two illustrative examples are worked out to show the effectiveness of the proposed approach.