There is considerable interest in the study of fractional-order systems but obtaining accurate time domain responses is a difficult problem. This is because all methods reported on to date use approximations for the fractional derivative both for analytical-based computations and more relevantly in simulation studies. This means unlike in integer systems exact simulations are not available and thus for considering non-linear problems and comparisons with measured data no exact solution reference exists. In this study, the authors provide a major breakthrough for this situation by developing methods which allow the exact computation of the time responses of fractional-order systems.

The filtering problem for discrete-time linear systems with multiplicative and time-correlated additive measurement noises is considered where the multiplicative noises are zero-mean white noise sequences, and the time-correlated additive measurement noise is described by a linear system model with white noise. Using the method of measurement differencing and some results obtained in this study, a novel algorithm for optimal filtering of the system under consideration is proposed in the sense of linear minimum mean-square error. The proposed algorithm is recursive, and does not increase computation and storage load with time. The convergence of the proposed algorithm is investigated. Computer simulations are carried out to demonstrate the performance of the proposed algorithm. The simulation results show the superiority of the proposed algorithm.

A new fault detection and diagnosis method is developed in this study for a class of singular non-linear systems via the use of observers with adaptive updating rules. The Lyapunov stability theory is applied to obtain a stable observation error system and to obtain the required adaptive tuning rules for the estimation of the process faults. Based on the fault estimation information, the controller is reconfigured to keep the post-fault system stable, leading to the active fault tolerant control of the non-linear singular system. A simulated numerical example is included to demonstrate the effectiveness of the proposed approach.

In this study, the design of the optimal decentralised full-state-feedback controllers is derived for wireless networked control systems with network-induced delays. In particular, the authors formulate the optimal decentralised control problem as a non-cooperative linear quadratic game. Then, the optimal control strategy of each controller is obtained that is based on the current plant state and the last control strategies of decentralised controllers. The proposed optimal decentralised controllers reduce to the known controller under certain conditions. Moreover, the authors illustrate the application of the proposed decentralised state feedback control to load frequency control in power grid systems.

This study investigates the exponential stability problems of singular impulsive switched systems. Using the switched Lyapunov function method and algebraic inequality, sufficient conditions are expressed as arbitrary and conditioned impulsive switching has been obtained. In addition, with the introduction of the impulsive controller, several exponential stability criteria are derived when the impulsive controllers are stabilising. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed criteria.

This study investigates the tracking-control problems of the Lorenz, Chen and Lu chaotic systems. Note that the input–output linearisation method cannot solve these tracking-control problems because of the existence of singularities, at which such chaotic systems fail to have a well-defined relative degree. By combining Zhang dynamics and gradient dynamics, an effective controller-design method, termed Zhang-gradient (ZG) method, is proposed for tracking control of the three chaotic systems. This ZG method, with singularities conquered, is capable of solving the tracking-control problems of the chaotic systems. Both theoretical analyses and simulative verifications substantiate that the tracking controllers based on the ZG method can achieve satisfactory tracking accuracy and successfully conquer singularities encountered during the tracking-control process.

This study is concerned with the problem of robust H ₂ and H _∞ filtering for uncertain discrete-time linear systems. Two types of time-invariant parametric uncertainty, namely polytopic and ellipsoidal, are considered and represented by a linear fractional transformation structure. Obtained auxiliary variables by a convex optimisation problem, play the role of decoupling the Lyapunov variables and the robust filter parameters, in order to cast the problem into a linear matrix inequality-based optimisation problem. The design conditions are derived based on the quadratic separation concept and employing appropriate parameterisations for the corresponding set of multipliers. The merit of the methods presented in this study lies in their less conservatism than the existing methods for the polytopic uncertain systems, as well as presenting a new convex optimisation procedure for the robust filtering for the ellipsoidal uncertain systems.

In this study, the authors have applied a jump parameter linear optimal control technique for the Cuk converter used in photovoltaic systems. The simulation results for the Cuk converter used for maximum power point tracking are presented. The results show how the feedback gains impact the optimal performance of the two states of the Cuk converter, and indicate complete freedom in choosing the values of the duty cycle (from the optimal performance point of view). In addition, the optimal controller for the jump linear system with integral action is applied to the Cuk converter and the simulation result is compared with that for the Cuk converter averaged system. The superiority of the proposed technique can be clearly seen from the simulation results obtained. The presented technique can be used for other applications of the Cuk converter and not necessary only for the solar cells.

In this study, two well-known model reduction techniques: balanced truncation and modal truncation are compared. The comparison is based on their error bound formulas for a special class of systems derived in this study. The comparison is illustrated by a numerical example.

This study considers linear systems with state/input time-varying delays and bounded disturbances. The authors study a new problem of designing a static output feedback controller which guarantees that the state vector of the closed-loop system converges within a pre-specified polyhedron. Based on the Lyapunov–Krasovskii method combining with the free-weighting matrix technique, a new sufficient condition for the existence of a static output feedback controller is derived. The author's condition is expressed in terms of linear matrix inequalities with two parameters need to be tuned and therefore can be efficiently solved by using a two-dimensional search method combining with convex optimisation algorithms. To be able to obtain directly an output feedback control matrix from the derived condition, they propose an appropriate combination between a state transformation with a choice of a special form of the free-weighting matrices. The feasibility and effectiveness of the derived results are illustrated through five numerical examples.

In this study, the author's interest is to reduce requirements posed on communication, sensing, processing and energy resources in multi-agent networks (MANs) without compromising MAN objectives. Consequently, the hardware expenses and energy consumption are driven down while MAN multitasking, such as inter-network collaboration, is facilitated. Scenarios, in which agents of one network need to achieve a common goal, call for the study of decentralised cooperative control schemes. To accomplish this goal in an uncertain and noisy setting and to detect changes in the communication topology, agents have to exchange information. Since each transmission and reception of information necessitates energy, communication should be induced only when the goal completion can no longer be guaranteed in order to prolong the MAN mission. Thus, the authors devise an information exchange mechanism which draws upon the ideas of self-triggered communication. The proposed mechanism is inspected both theoretically and experimentally (employing off-the-shelf wireless sensor platforms) for performance against lifetime trade-offs using a single-integrator consensus case study. Their mechanism is applicable to heterogeneous agents with exogenous disturbances, to directed switching communication topologies and to both initial-condition-dependent and initial-condition-independent long-term cooperative behaviours. The investigated stability notions include ℒ_p- and input-to-state stability (with respect to a set).

This paper studies the stability and performance of a multi-agent system composed of identical linear time-invariant dynamic agents, when only a single agent in the system is controlled by an exogenous single-input–single-output controller. It is shown that a wide class of multi-agent systems can be collectively stabilised by controlling any single agent. The tracking performance of such a closed-loop system, however, has a fundamental limitation. It is also shown that generically not only the output of controlled agent but either the sum or average of all agent outputs can be used for an exogenous controller. An example is presented to illustrate theoretical results developed in this study.

To improve the vehicle driving performance, adaptive parameter estimation is studied to simultaneously estimate the road gradient, vehicle mass and other vehicle parameters, which requires the vehicle longitudinal velocity and driving force only. Different to conventional gradient and recursive least square methods, the parameter estimation error is obtained to drive the adaptive laws for estimating unknown parameters, where exponential convergence can be guaranteed under the classical persistently excitation condition. Moreover, finite-time parameter estimation is achieved by incorporating the sliding mode technique into the adaptive laws. The robustness of the proposed adaptations against bounded disturbances is studied. Simulation results illustrate that the presented methods can obtain faster transient and better steady-state performance than some available methods.

For a class of discrete-time multi-variable systems with time-varying parametric uncertainty, the parameter identification method and switching control architecture are developed in this study to implement smooth switching control. Specifically, the identification algorithm based on the least geometric mean squares is derived for the multi-variable system. In addition, the switching control system, with model reference control technique as the basis of control design for each local model, is proposed to achieve satisfactory control performance, especially to eliminate the oscillations at the switching boundaries which can be attributed to the difference in the input–output dynamics between the pre- and post-switching closed-loop subsystems. Furthermore, the switching strategy based on neural network classifier is put forward for the accurate switching among a set of model reference controllers which are correspondingly designed for the identified subsystems. Finally, the feasibility and effectiveness of the proposed identification and control schemes are verified by numerical simulations, which show that the desirable identification and control performances are guaranteed under the proposed schemes. Moreover, the advantage of the presented switching control system in terms of smooth switching is validated through comparison with other kinds of control schemes.

Global output feedback stabilisation problem for a class of stochastic feedforward non-linear systems with state time delay is investigated in this study for the first time. By introducing the homogeneous domination approach in the stochastic system, constructing an implementable homogeneous reduced-order observer and choosing an appropriate Lyapunov–Krasoviskii functional, an output feedback controller is designed to render the closed-loop system globally asymptotically stable in probability and the output can be regulated to the origin almost surely. A simulation example is provided to show the effectiveness of the designed controller.

Stabilisation is an issue of great practical importance to the ship industry. This study considers the global asymptotic stability controller for a class of underactuated surface vessel possessing non-diagonal inertia and damping matrices. For the synthesis of controller, the investigated underactuated model is first converted into two cascade connected subsystems using input and state transformations. For these subsystems, it is shown that the stabilisation problem of this study can be reduced to the one of the second subsystem. By combining the method of adding a power integrator and the direct Lyapunov approach, a finite time switching control strategy is developed guaranteeing global asymptotic convergence of the full states to origin. The simulation results testify to the effectiveness of the presented control approach.

Vertical take-off and landing (VTOL) aircraft system is a non-linear complex system with multi-variable large-disturbances. Hence it is a difficult task to control it efficiently. For the first time, this study applies the most advanced kernel-based dual heuristic programming (DHP) algorithm into solving the optimal control problems of VTOL aircraft systems successfully. Kernel-based DHP (KDHP) algorithm is developed by integrating sparse kernel machines and approximately linear dependence analysis into the critic learning of DHP algorithm. Kernel machines are used as approximation structure for the critic module in the proposed KDHP algorithm, while multilayer perceptron neural networks (MLPNNs) are used as approximation structure for conventional DHP algorithm. Compared with conventional MLPNNs with manually designed structures, kernel method can obtain better generalisation capability. Hence to a certain extent, the proposed KDHP algorithm has better learning efficiency and generalisation capability. Moreover, the simulation and experimental results of VTOL aircraft system control problems demonstrate that the optimal controller based on the proposed KDHP algorithm is effective.

The stability problem of a linear dynamic quantised system with time-varying delay and packet losses is studied in this article. An optimal dynamic quantiser which is able to minimise the maximum output error between the quantised system and unquantised systems is designed, and the minimum upper bound of the quantised error is also given. Moreover, the system is lifted into a switched system for stability analysis and a sufficient condition for asymptotic stability is developed in terms of matrix inequalities. Finally, an illustrative example demonstrates the effectiveness of the proposed method.