In this study, the problem of reachable set estimation of switched positive systems with discrete and distributed delays subject to bounded disturbances is studied. The authors first investigate the reachable set of unswitched positive systems. Then, applying a new approach which is different from the Lyapunov functional method, they give a sufficient condition for the existence of a ball such that all the solutions of the switched positive system converge exponentially within it under certain switching rules. In addition, a precise estimation of the decay rate is also presented. Finally, the effectiveness of the theoretical result is illustrated by a numerical example.

Charge–discharge schedules of photovoltaic (PV) batteries are planned based on the prediction of solar irradiance, and various methods have been studied to cope with prediction uncertainty. Among them, the switching of charge–discharge schedules could be a measure for keeping supply–demand balance against abrupt weather changes. Those methods motivate a PV battery operation problem to retain the trackability of the secondary reference even when the primary schedule is ongoing. This study addresses the periodic operation of PV battery systems subject to the reference switching, and designs a switching model predictive control (MPC) to track the primary and secondary references with guaranteed feasibility. The proposed MPC design also incorporates the constraint-tightening technique, by which the operational limits are kept under the prediction error associated with each of the schedules. In order to utilise the design freedom in compensating the prediction error, the authors construct the constraint-tightening gain based on economic dispatching control, and discuss the features in terms of design simplicity and fuel cost efficiency.

Different real-world processes can be described by a linear model parameterised with respect to the process operating point, as an uncertain parameter. The family of transport processes with long memory is a kind of these processes which are characterised by the parameterised time-fractional diffusion equations. This study proposes a generalised iso-damping feature for achieving the phase margin invariance regardless of the uncertain parameter variations in control of time-fractional diffusion processes. Also, the study suggests an analytical method to tune stabilising fractional-order proportional–integral/proportional–derivative controllers for adjusting a desired value for the phase margin at a desired gain crossover frequency, while the proposed robustness criterion is satisfied in control of time-fractional diffusion processes. Furthermore, conditions for solvability of the problem and stability of the obtained control system are analytically derived. Finally, an example on robust temperature control of the cutting edge in alpha silicon carbide cutting tools is presented to confirm the effectiveness of the obtained achievements.

A novel adaptive model-based predictive controller for attitude and trajectory tracking of a vertical take-off and landing (VTOL) aircraft in the simultaneous presence of model uncertainties and external disturbances is introduced in this study. An important challenge of designing the model-based controllers is developing an accurate model, especially in the presence of model uncertainties. In this study, first, the nominal model of a ducted-fan air vehicle, which is a multi-input multi-output nonlinear system with non-minimum phase behaviour, is given as the test case of this research. After that, two modified robust and adaptive model predictive controllers are proposed for tracking a predefined path in the presence of external gusts and model uncertainties. The design is performed by introducing two novel observers to estimate the model uncertainties and external disturbances, simultaneously. Different types of input constraints, as well as the time delay of the system inputs, can be considered effectively in the design steps of the proposed control strategy. The stability of the closed-loop system is proved under a few realistic assumptions. The simulation results demonstrate the great capability of the proposed method for attitude and trajectory tracking of the VTOL aircraft under model uncertainties and wind turbulence.

This study investigates the stability of a class of neutral stochastic functional differential equations with Markovian switching. Some novel stability criteria are first established, including boundedness, pth moment exponential stability and almost sure exponential stability, based on multiple Lyapunov functions, generalised Itô formula and non-negative semi-martingale convergence theorem. Concretely, the authors generalise the existing results under the essential neutral term and improve the diffusion operators from being controlled by two auxiliary functions to other multiple auxiliary functions with not only constant coefficients but also time-varying coefficients. Some numerical examples are presented to illustrate the effectiveness of the obtained results.

The leader-following guaranteed-performance consensus problems for second-order multi-agent systems with and without communication time delays are investigated, where a guaranteed performance function is proposed to consider the consensus regulation performance. For the case without the time delay, the coupling gain and pinning strength are carefully considered. When the time delays exist in the communication, we find that the inequality (Seuret and Gouaisbaut) cannot be used to investigate the consensus problems proposed in the study since the obtained conditions cannot be satisfied. Therefore, Jensen's inequality and Newton–Leibniz formula, which can solve this issue well, are introduced. By using the state space decomposition approach, linear matrix inequality and Lyapunov stability theory, some sufficient conditions are derived for achieving the guaranteed performance consensus. Moreover, the upper bound of the performance function is determined. Finally, two examples are shown to verify the validity of the theoretical results.

This study considers the coordination control problem of a group of moving rigid bodies. Each rigid body communicates with other bodies via the distance-induced neighbour graphs. The authors design the distributed control laws for the angular velocity and linear velocity of rigid bodies, and establish sufficient conditions without relying on the dynamical properties of neighbour graphs, to guarantee that the rigid bodies reach the attitude synchronisation and avoid collision with nearby bodies while the communication networks keep connected. Moreover, they introduce a leader into the system to guide all rigid bodies to the desired attitude. Simulation examples are given to illustrate the authors' results.

A fault reconstruction method based on a robust adaptive observer is proposed to handle the actuator additive faults that exist in a non-linear descriptor system that satisfies the Lipschitz conditions. First, a robust adaptive fault reconstruction observer is proposed. This method has the desired robust performance and can achieve accurate reconstructions of both abrupt and time-varying faults in the presence of an external unknown disturbance. Then, to improve the transition process of fault reconstruction, an improved robust adaptive fault reconstruction observer is proposed. The improved robust adaptive fault reconstruction algorithm, which uses different coefficients for the proportion output errors and the derivative output errors, can enhance the rapidity and accuracy of fault reconstruction. The robust adaptive and improved robust adaptive observers are based on the linear matrix inequality technique. According to the Lyapunov stability theory, the stability conditions of the methods are derived. Additionally, the influence of an external unknown disturbance on the actuator fault reconstruction is suppressed using a robust method. Finally, two different examples are used to demonstrate the effectiveness of the proposed fault reconstruction methods.

Robust output tracking control of Van der Pol oscillator is an important practical problem from an application point of view. Output feedback-based robust tracking control strategies are proposed in this work for that purpose. First, a high-order sliding-mode observer is used to estimate the oscillator states from the measurable output and to identify some types of disturbances. Then, five different continuous sliding-modes controllers (Continuous-SMCs) are provided to robustly track a desired time-varying trajectory, exponentially or in a finite time, for the Van der Pol oscillator despite the presence of external disturbances. The closed-loop stability for each Continuous-SMC is given based on input-to-state stability properties. Finally, experimental validations are also provided to show the feasibility of the proposed controllers in real time.

In this study, the authors are concerned with a finite-dimensional guaranteed cost sampled-data fuzzy control problem, which is addressed for a class of non-linear Markov jump parabolic partial differential equation (MJPPDE) systems. Applying the Galerkin's method to the MJPPDE system, a non-linear Markov jump ordinary differential equation (MJODE) system is derived. The resulting non-linear MJODE system can describe the dominant dynamics of the MJPPDE system, which is subsequently expressed by the Takagi–Sugeno (T–S) fuzzy model. Then, a guaranteed cost sampled-data fuzzy controller is developed to stabilise the closed-loop slow fuzzy system exponentially in the mean-square sense while providing an upper bound for the quadratic cost function. Making full use of their special features, they will be able to establish the bound on . The authors' theory enables us to guarantee the existence of the feedback controller and to judge the effectiveness of the feedback control based on the sampled-data to stabilise the given system in the sense of mean-square exponential stability.

This study proposes a finite-time integral backstepping control for a class of non-linear systems considering practical aspects including saturation constraints, actuator fault, external disturbances and system uncertainties in order to achieve strong robustness, fast response and high-precision tracking performance. An adaptive version of the controller is then developed to deal with the total uncertainties in the system. The main property of the suggested controller is that there is no need for the knowledge of the actuator fault, external disturbances and system uncertainties to be available. Not only are all the closed-loop system states ensured to be globally finite-time stable within a given settling time, but the actuator faults are accommodated. The proposed controller is then applied to a two-link rigid robot manipulator. The simulation results verify the effectiveness of the proposed finite-time fault-tolerant adaptive control in terms of precision of tracking, convergent speed and robustness.

This study presents an output feedback-based sliding mode control approach for motion control systems with mismatched/matched disturbances. The key idea of this study is to reconstruct the unmeasured auxiliary states and disturbances synchronously online by constructing a higher-order extended state observer (HOESO). It is shown that the resulting sliding mode controller based on HOESO can drive the system output to an ultimately bounded region, which can be regulated arbitrarily small by assigning a sufficiently large scaling gain. Different from the existing extended state observer methods, the newly proposed HOESO treats the known dynamics satisfying the Lipschitz condition and the unknown higher-order disturbances separately. As such, it provides a feasible way for higher-precision states/disturbance estimation. Thanks to the utilisation of HOESO, the upper bound of disturbances is not necessarily required as a priori and the switching gain is adaptively chosen based on the estimation error such that the chattering effects can be significantly reduced. Experiments for speed regulation of a brushless DC motor are conducted to verify the effectiveness of the proposed method.

In this study, the problem of finite-time feedback stabilisation for switched linear input-delay systems with saturating actuators is addressed by virtue of the comparison-function-like method. Finite-time state feedback stabilisation is discussed and controllers are designed to make the closed-loop systems finite-time stable. Moreover, for the case that the states are unmeasured, observers are constructed to estimate the unavailable states and the observer–controller compensator strategy is proposed. Based on the results proposed in this study, information of transient performance of the controlled switched systems can be obtained and bounds of system trajectory are estimated. An example is employed to illustrate the effectiveness of the proposed approach.

The additional threshold of a mixed event-triggering mechanism (ETM) makes it impossible to guarantee the requirement of asymptotic stability. As a consequence, it is necessary to investigate input-to-state practically stable (ISpS) which is a mild stability property. In this study, the authors firstly model the closed-loop event-triggered control system as a delayed linear parameter-varying (LPV) systems with a mixed ETM and parameter uncertainty. Then, a co-design condition in a sense of ISpS of controller gain and trigger parameters for the delayed LPV systems is obtained by employing the parameter-dependent Lyapunov–Krasovskii functionals and congruent transformation method. Moreover, based on the obtained co-design condition in a sense of ISpS, an optimisation algorithm for the tradeoffs between resource utilisation and robustness of the closed-loop system is further proposed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

This study develops a fuzzy finite-time command filtered position tracking control approach for induction motors with input saturation. First, the fuzzy logic systems are utilised to approximate the non-linear functions. Then, in order to avoid the ‘explosion of complexity’ in backstepping design, the finite-time command filter is employed. In addition, error compensating signals are introduced to decrease the errors produced by command filters. The fuzzy finite-time adaptive command filtered controllers can guarantee that the tracking error can converge in finite time. The results of simulation show the effectiveness of the proposed method.

Sensor fault detection of discrete-time descriptor systems with bounded disturbances is studied. The authors propose a new structure of a fault detection observer by augmenting the output, which can broaden the application scope. A criterion is used to achieve the fault sensitivity and disturbance attenuation ability of the residual simultaneously. The residual generation and time-varying threshold calculation are integrated together based on analysis. Furthermore, sufficient conditions for the performance of the proposed observer are formulated in terms of linear matrix inequalities. Numerical simulations of a direct current motor and a flight vehicle are conducted to verify the applicability of the proposed fault detection observer design method.