The problem of robust tracking and model following is considered for a class of uncertain non-linear systems with any time-varying delays and completely unknown dead-zone input non-linearity. Here, time-varying delays are assumed to be any continuous and bounded non-negative functions, and any information on their derivatives need not known. In the study, the system uncertainties assumed to be any continuous and bounded non-linear functions, and their non-linear upper bounds do not need also to be known. Based on Wu inequality, a novel design method is presented by which some simple and direct robust tracking control schemes can be easily constructed. It is shown that the tracking error between the output of an actual dynamical system and the dynamical signals of the given reference model can be guaranteed to be uniformly exponentially bounded. A numerical example is also given to describe the design procedure of the presented method, and the simulations of this numerical example are implemented to demonstrate the validity of the theoretical results.

This study focuses on the problem of constraint consensus of discrete-time multi-agent systems with high-order heterogeneity. It is assumed that the agents are of different orders in such systems ranging from order 1 to l and the velocity of each agent is constrained to lie in a non-convex set. This study proposes a distributed constraint control algorithm which guarantees the agents converge to a common point through the use of local information. Model transformations of the system matrix are performed in this study, so that the authors can utilise the properties of the stochastic matrix. Meanwhile, the boundness of state-dependent stochastic matrices and the convexity of stochastic matrices are analysed and explored in detail. Finally, a numerical example is given to illustrate the correctness of the results.

This study concentrates on the finite-time (FT) formation control problem for a class of heterogeneous second-order (SO) multi-agent systems (MASs), where disturbance may exist in the dynamics of each agent and the communication graph is directed. First of all, a basic FT formation control protocol is proposed for the nominal SO MAS and the finite convergence time is calculated. To solve the FT formation control for a class of heterogeneous SO MASs without using global information, an adaptive FT formation control is then proposed. Finally, two numerical examples are presented to validate the theoretical results.

This study investigates the event-triggered practical finite-time output feedback control for a class of switched high-order non-linear time-delay systems with uncertain control coefficients. A reduced-order observer is first constructed to estimate the unmeasurable states. By adding a power integrator technique, an event-triggered output feedback controller is designed for the nominal system. Subsequently, the constructed observer and controller are scaled with a suitable gain by homogeneous domination approach, which, together with an appropriate Lyapunov–Krasoviskii functional, can render that the uncertain switched high-order non-linear system with time-varying delay is practical finite-time stability. Finally, two examples are provided to demonstrate the validity of the proposed scheme.

This study discusses delay-dependent stability of a class of stochastic delay systems driven by G-Brownian motion in the sublinear expectation space. With the help of the degenerate Lyapunov functional, the mean square exponential stability and quasi-sure exponential stability criteria for stochastic delay systems driven by G-Brownian motion are established and an explicit upper bound of time delay is derived. In particular, for the delay-free case, the corresponding sufficient conditions are also obtained. Here, the stability conditions are directly related to the coefficients of the stochastic delay systems and are different from the existing stability conditions which are presented in terms of the G-Lyapunov function. Some examples are introduced to illustrate the delay-dependent stability criteria.

The dynamic output feedback control for a class of semi-linear distributed parameter systems with a non-constant (spatially-varying) diffusion rate described by partial differential equations is studied. The considered system is endowed with boundary actuation available and boundary feedback controllers are designed. Meanwhile, both domain-averaged and boundary-valued measurements, two different ways of output measurements, are taken into account. Based on these two different methods of measurements, the corresponding boundary feedback control laws are designed, respectively. Using Wirtinger's inequality, the resulting closed-loop systems depending on observers and controllers are obtained in terms of the Lyapunov method. With the sufficient conditions of the linear matrix inequality, the stability of the system is subsequently obtained by the designed observer and controller. The final numerical simulations are given to illustrate the validity of the results graphically.

This study investigates the problem of forcing a vertical take-off and landing (VTOL) aircraft to land on a carrier. Once we obtain the tracking error system, we take the strategies such as preliminarily treating a two-dimensional subsystem, recombining subsystems, separating out a converging term, and using the ‘converging input converging state (CICS)’ stability theory. As a consequence, we only need to stabilise a fourth-order integrator that is subject to a bounded uncertain coefficient. Then, we assign a partially-saturated controller to deal with the perturbed fourth-order integrator and particularly the uncertain coefficient. With the suggested algorithm, the carrier is allowed to evolve in three dimensions and the landing control design has a simple expression.

Non-linear model predictive control requires the use of efficient solutions and strategies for its implementation in fast/real-time systems. A popular approach for this is the real-time iteration scheme, which uses a shifting strategy, namely the initial value embedding, that shifts the solution from one sampling time to the next. However, this strategy together with other efficient strategies such as move blocking, present a recursive feasibility problem. This study proposes a novel modified shifting strategy which preserve both recursive feasibility and stability properties, as well as achieves a significant reduction in the computational burden associated with the optimisation. The proposed approach is validated through a simulation of an inverted pendulum where it clearly outperforms other standard solutions in terms of performance and recursive feasibility properties. Additionally, the approach was tested on two computing platforms: a laptop with an i7 processor and a Beaglebone Blue Linux-based computer for robotic systems, where computational gains compared to existing approaches are shown to be as high as 100 times faster.

In this study, the problem of adaptive state feedback stabilisation of switched stochastic non-linear systems is addressed. To overcome the uncertainty of arbitrary switchings, a novel common Lyapunov function is constructed in the authors' control scheme. By integrating adaptive control technique and homogeneity with monotone degrees into backstepping framework, a common state feedback control law independent of switching signal is designed recursively under weaker non-linear growth conditions. A distinct feature of non-linear conditions is that the parameters () can be chosen as different values rather than a unified value in the existing literature. Finally, a simulation example is presented to show the effectiveness of their control scheme.

This article is concerned with the optimal control of Sobolev-type Hilfer fractional non-instantaneous impulsive differential inclusion driven by Poisson jumps and Clarke subdifferential. Initially, the existence of a mild solution is established for the proposed Hilfer type fractional problem with novel ideas of non-instantaneous impulses. The non-linear alternative of Leray-Schauder type fixed point theorem, stochastic analysis, the measure of non-compactness and the multivalued analysis are applied to prove the mild solution. Further, the existence of optimal control is derived by employing Balder's theorem. Finally, the application as a stochastic dam pollution model is provided to illustrate the developed theoretical results.

The fractional-order proportional–integral–derivative (FOPID) controller has two more parameters than the integer-order proportional–integral–derivative (PID). Such characteristic makes the controller design more flexible and leads to superior performance. This study proposes a variable coefficient FOPID (VCFOPID) with optimal single step parameters, combining discrete synthesis and variable control parameters. The new algorithm is compared with previous FOPID discrete methods via several examples. Since the energy losses of the single-ended primary-inductor converter (SEPIC) cannot be ignored, the standard models are insufficient and a new model is derived using quantum-behaved particle swarm optimisation. The VCFOPID is applied to the SEPIC and both the effectiveness of the controller and the model are verified experimentally.

Since Mao in 2013 discretised the system observations for stabilisation problem of hybrid SDEs (stochastic differential equations with Markovian switching) by feedback control, the study of this topic using a constant observation frequency has been further developed. However, time-varying observation frequencies have not been considered. Particularly, an observational more efficient way is to consider the time-varying property of the system and observe a periodic SDE system at the periodic time-varying frequencies. This study investigates how to stabilise a periodic hybrid SDE by a periodic feedback control, based on periodic discrete-time observations. This study provides sufficient conditions under which the controlled system can achieve pth moment exponential stability for and almost sure exponential stability. Lyapunov's method and inequalities are main tools for derivation and analysis. The existence of observation interval sequences is verified and one way of its calculation is provided. Finally, an example is given for illustration. Their new techniques not only reduce observational cost by reducing observation frequency dramatically but also offer flexibility on system observation settings. This study allows readers to set observation frequencies according to their needs to some extent.