Operating cranes is challenging because payloads can experience large and dangerous oscillations. The oscillations are induced by both intentional motions commanded by the human operator and by external disturbances. Although significant progress has been achieved by using command shaping to reduce operator-induced vibration, less success has been achieved on reducing oscillations induced by external disturbances, such as wind. The disturbance-rejection task is more challenging because it requires accurate sensing of the crane payload. This study presents a combined command shaping and feedback control architecture. The input shaper eliminates the payload oscillation caused by human-operator commands, and the feedback controller reduces the effect of wind gusts. Simulations of a large range of motions are used to analyse the dynamic behaviour of boom cranes using the proposed controller. Experimental results obtained from a small-scale boom crane validate the simulated dynamic behaviour and the effectiveness of the controller.

A consensus problem is investigated for a group of second-order agents with an active leader where the velocity of the leader cannot be measured, and the leader as well as all the agents is governed by the same non-linear intrinsic dynamics. To achieve consensus in the sense of both position and velocity, a neighbour-based estimator design approach and a pinning-controlled algorithm are proposed for each autonomous agent. It is found that all the agents in the group can follow the leader, and the velocity tracking errors of estimators converge to zero asymptotically, without assuming that the interaction topology is strongly connected or contains a directed spanning tree. In terms of the switching topologies between the leader and the followers, similar results are obtained. Finally, these theoretical results are demonstrated by the numerical simulations.

This study examines the stabilisation problem associated with a particular type of large-scale system. This type of large-scale system consists of several non-linear subsystems, which are connected to each other via interconnections of variable weighting. Interconnections of variable weighting between two subsystems denote that the interaction strength between the two subsystems is variable. Moreover, the weight may even be zero at some times or in some cases. In this study the authors suppose that the range of weight variation between any two subsystems is known, and that the stabilisation conditions for the large-scale system are derived and that decentralised controllers which satisfy the conditions are synthesised. In the main result derivation, the Takagi–Sugeno (T–S) fuzzy model of a large-scale system is used and a parallel distribution compensation (PDC) type fuzzy controller is synthesised based on the linear-matrix-inequality (LMI) method. Finally, a numerical example is given to demonstrate that the main theorem is applicable and the synthesised controller is effective.

This study analyses the stability of aperiodically sampled-data control systems with and without communication delays by using a new augmented Lyapunov functional method. Compared with most of existing methods that commonly require each term of a Lyapunov–Krasovskii functional (LKF) to be non-negative, the proposed method waives this requirement by introducing an augmented term, which has zero value and zero derivative, into the LKF. Several stability criteria with less conservatism are obtained from the relaxation of constraint conditions for guaranteeing the non-negativeness of the LKF. These criteria are extended to investigate the stability of the systems with polytopic uncertainties and the exponential stability of the system. Three numerical examples are given to show the effectiveness of the proposed method.

The global stability of non-linear dynamical systems has been investigated extensively in recent decades. It is well known that time delay and neutral term could derail the stability of non-linear systems. This study presents new results on the robustness of the global exponential stability of non-linear systems with respect to time delay and neutral term. Given globally exponentially stable non-linear systems, the problems to be addressed herein are how much time delay and neutral term contraction coefficient are allowed so that the non-linear systems can remain to be globally exponentially stable, in the presence of time delay and neutral term. Upper bounds of allowable time delay and neutral term contraction coefficient will be derived for non-linear systems to sustain their global exponential stability. A numerical example is provided to illustrate the results.

This study investigates the problem of robust fault-tolerant control for uncertain fractional-order (FO) systems against actuator faults, whose commensurate order α is assumed to be 1 ≤ α < 2. By using reciprocal projection lemma and some properties of Kronecker product, the authors present a sufficient condition for the existence of fault-tolerant FO dynamic output feedback controllers for the FO systems with polytope-type uncertainty. The controller designed here takes the possible actuator faults into consideration and ensures the resulting closed-loop system is robustly stable. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

The present study deals with the controllability results for fractional dynamical systems with prescribed controls. Sufficient conditions for the controllability results of non-linear fractional dynamical systems are obtained using Schauder's fixed point theorem and fractional calculus. Illustrative examples are presented.

This study addresses the robust consensus tracking problem of multi-agent systems with uncertain Lur’e-type non-linear dynamics under a fixed topology. To achieve consensus tracking, a class of discontinuous control protocols are first proposed, which rely on the relative information among the neighbouring agents. Theoretical analysis indicates that the robust consensus tracking of uncertain Lur’e network can be achieved if the coupling strength and the control gain are both larger than the thresholds depending on some global information of the network. Then, an adaptive consensus tracking protocol is further designed to solve the robust consensus tracking problem as a modification of a fully distributed version without the need of any global information of the multi-agent systems. Furthermore, as an expansion of the discontinuous protocols, a new class of continuous control laws are developed based on the boundary layer concept. Finally, a couple of examples are given to illustrate the effectiveness of the theoretical results.

A robust disturbance rejection method for uncertain systems is presented in this study. It effectively rejects both matched and unmatched disturbances and guarantees robust stability of the system when there exist modelling uncertainties. First, the authors show the configuration of the system that is based on the idea of the equivalent input disturbance (EID). An EID estimator is designed to compensate disturbances without requiring their prior knowledge. Then, a robust stability condition and the method of the controller design are presented using a linear-matrix-inequality. Finally, the validity of the authors method and its superiority over a conventional control method and the sliding-mode control method are demonstrated through the simulations of a numerical example and experiments of a rotational-speed control system.

Topological structures and node dynamics of dynamical networks have important influence on their dynamical behaviours. In practical applications, not all of them can be well determined beforehand; therefore this study investigates the structure identification of an uncertain dynamical network coupled with complex-variable chaotic systems. Based on the Barbalat's lemma, corresponding network estimators are designed for identifying the unknown or uncertain topological structure and node dynamics. Notably, the node dynamics need not to be identical and the topological structure need not to be symmetric or irreducible. Furthermore, this method can also better monitor the switching topological structure of a dynamical network. Numerical simulations are provided to verify the correctness and effectiveness of the theoretical results.

This study presents the first attempt of direct continuous-time model identification using instrumental variable method for Hammerstein–Wiener systems from sampled data. Under the assumption of monotonic function for the Wiener part, the whole non-linear model is first estimated as an augmented multiple-input single-output linear model, from which the model parameters are then extracted by singular value decomposition. A refined instrumental variable method is proposed to consistently identify this non-linear system acting in a coloured noisy environment. Monte Carlo simulation analysis is presented to illustrate the effectiveness of the proposed method.

Using the energy-based Hamiltonian function method, this study investigates the decentralised saturated excitation control of multi-machine multi-load power systems based on the structure preserving dynamic model. First, a constructive procedure is proposed for the dissipative Hamiltonian realisation of non-linear differential algebraic systems and transform the power system to its equivalent dissipative Hamiltonian system. Constant feedforward control is proposed to adjust the system to the desired equilibrium point. Then, we put forward a decentralised saturated excitation controller using only the local information. Simulation results show that the proposed control scheme can effectively improve the transient stability of the power system.

This study investigates the reachability and controllability of linear switched impulsive systems in which impulsive component is independent of switching among different subsystems. Some crucial geometrical criteria are established. The authors present the fact that the reachable sets and the controllable sets may not be subspaces, if impulsive matrices are singular. While impulsive matrices are reversible, the reachable and controllable subspaces can be determined by two proposed subspace algorithms. The authors also point out that the reachable or controllable subspace is an invariant subspace of the considered systems. Finally, two simple corresponding examples are discussed to illustrate the correctness and effectiveness of the proposed theoretical results.

This study is concerned with the problem of output feedback H _∞-tracking control design for Takagi and Sugeno (T–S) fuzzy systems with immeasurable premise variables. In most of the existing results in the area of fuzzy H _∞-tracking control design, it is assumed that the information of premise variables is accessible through the measurement equations. This assumption reduces the practical applications of these results. On the other hand, there exist some recent results for control of T–S fuzzy systems with immeasurable premise variables in the literature. By combining this approach with our previous scheme in the area of fuzzy H _∞-tracking control, the authors succeed to design a single controller which leads to the stability of the closed-loop system and guarantees the required H _∞ tracking error norm to some reference and bounded signals. This single controller can be found by a search over the solutions of two linear matrix inequalities. The authors also offer a simple numerical method to find the optimal H _∞-tracking control law. One particular example is given to illustrate the effectiveness of the obtained results.

This study deals with the problem of local stability analysis and the computation of invariant subsets of the domain of attraction (DA) for discrete-time Takagi–Sugeno fuzzy systems. Based on the fuzzy Lyapunov functions, new sufficient conditions and an iterative scheme are proposed in order to prove the local stability and to estimate the DA. The mean value theorem and polytopic type bounds on the gradient of the membership functions are used to consider the relation between the membership functions at samples k and k + 1. Each step of the iterative procedure consists of linear matrix inequalities (LMIs) or single-parameter minimisation problems subject to LMI constraints, which are solvable via convex optimisations. Finally, examples compare the proposed conditions with existing tests.