In this study, the stochastic sampled-data approach is developed to deal with the H _∞ control problem for a class of linear multi-agent systems. For each agent, signals should be transmitted to the control input, including not only its own measurements, but also the output information received from the neighbour agents. The relationships of information communications between the whole multi-agents are totally reflected by a weighted directed graph with a fixed topology structure. To the addressed problem, the author's focus is to design an output feedback controller for each agent such that, for the external energy bounded disturbances, the exponential stability in the mean square sense and interference rejection ability under consideration can be guaranteed. By assuming that the sampling period of each agent switches between two values in a probabilistic way, the stochastic sampling phenomenon is well characterised in every sampling tasks. In virtue of Lyapunov theory and semi-definite programming method, sufficient conditions are derived to ensure the exponential stability as well as H _∞ performance, and the feedback controllers are also designed by solving some certain matrix inequalities. Finally, a numerical simulation is given to demonstrate the validness of the proposed control strategy.

Transmission power control constitutes a core feature required to achieve a desired quality of service in wireless networks. A practical implementation calls on the intuition of using limited resources, only when are strictly required. Thus, the appeal of an event-triggered scheme arises naturally over more traditional, but less efficient, periodic time-triggered control solutions. Motivated by these ideas, the authors present here a power allocation strategy based on an event-triggered transmission (ETT) to reduce the feedback signalling in the network. The power allocation under ETT is based on a nominal control that guarantees internal stability and performance. Hence, if the feedback signalling does not change significantly from the previous sample, no feedback transmission is assigned to reduce bandwidth usage. Two schemes are employed to define the ETT while preserving closed-loop stability: a piecewise quadratic Lyapunov argument and a perturbed linear system approach. These two approaches establish a trade-off between complexity and conservativeness. The power allocation under ETT was thoroughly evaluated under two nominal control schemes to establish a relation between performance and feedback reduction.

This study proposes a novel model predictive control (MPC) based on receding horizon particle swarm optimisation (RHPSO) for formation control of non-holonomic mobile robots by incorporating collision avoidance and control input minimisation and guaranteeing asymptotic stability. In most conventional MPC approaches, the collision avoidance constraint is imposed by the 2-norm of a relative position vector at each discrete time step. Thus, multi-robot formation control problem can be formulated as a constrained non-linear optimisation problem. In general, traditional optimisation techniques suitable for addressing constrained non-linear optimisation problems take a longer computation time with an increase in the number of constraints. The traditional approaches therefore suffer from the computational complexity problem corresponding to an increase in the prediction horizon. To address this problem without a significant increase in computational complexity, a novel strategy for collision avoidance is proposed to incorporating a particle swarm optimisation. In addition, the stability conditions are derived in simplified forms that can be satisfied by selecting appropriate constant values for control gains and weight parameters. Numerical simulations verify the effectiveness of the proposed RHPSO-based formation control.

This study considers an iterative learning control approach to achieve accurate coordination performances of the output data sequences for multiple plants that are involved in a networked environment. To realise such a desirable control objective, an update process of the input data sequence is needed to refine its output performance iteratively for each plant, which uses the local or nearest neighbour knowledge. The nominal multi-agent systems are employed as the plants’ description, for which input–output data-driven consensus problems are addressed in a hybrid networked environment given by signed directed graphs with both cooperative and antagonistic interactions. It is proved that the output data can be guaranteed to achieve bipartite consensus or remain stable for the multi-agent networks under structurally balanced or structurally unbalanced signed graphs. Moreover, the convergence conditions are derived, which need less knowledge of the agents’ plant, and the proposed consensus results can be developed to take into account the plant uncertainties and noises. Simulation tests are performed to verify the effectiveness of the learning approach in refining high input–output data-driven consensus performances of networked agents.

An output-feedback proportional–integral-derivative-type control scheme for the global position stabilisation of robot manipulators with bounded inputs is proposed. It guarantees the global regulation objective avoiding input saturation by releasing the feedback not only from the exact knowledge of the system structure and parameter values, but also from velocity measurements. With respect to previous approaches of the kind, the proposed scheme remains simple while increasing design/performance-adjustment flexibility. For instance, it does not impose the use of a specific sigmoidal function to achieve the required boundedness but involves a generalised type of saturation functions. More importantly, it is characterised by a very simple control-gain tuning criterion, the simplest hitherto obtained in the considered analytical context. Experimental tests on a 2-degree-of-freedom direct-drive manipulator corroborate the efficiency of the developed scheme.

Recently, a generalised framework for robust non-linear H _∞ filtering of uncertain Lipschitz descriptor systems has been developed by Abbaszadeh and Marquez. The main feature of the associated H _∞ filter is that it holds a general structure, which can capture both dynamic and static-gain filter structures. In this study, the authors aim to propose improved results on the general H _∞ filter synthesis for Lipschitz descriptor non-linear systems in the presence of disturbance and model uncertainties. Based on a technique to directly deal with the Lipschitz non-linear terms, new H _∞ filter synthesis conditions that guarantee asymptotic stability of the estimation error dynamics with prescribed disturbance attention level are established and formulated in terms of linear matrix inequalities. They also give some remarks on the results of Abbaszadeh and Marquez and compare them with the author's results. More precisely, it is shown that the proposed conditions are less conservative than those in the existing results. Simulation results on an example are given to numerically verify the proposed design.

This study presents a guidance law to intercept non-manoeuvring targets at a desired impact angle. The desired impact angle, defined in terms of a desired line-of-sight angle, is achieved by selecting the missile's lateral acceleration to enforce the sliding mode on a sliding surface. Then, the authors use the Lyapunov stability theory to prove the stability of the proposed non-linear sliding surface. Furthermore, they introduce the adaptive neuro-fuzzy inference system (ANFIS) to adaptively update the additional control command and reduce the high-frequency chattering of sliding mode control (SMC). The proposed guidance law, denoted ANFSMC guidance law with impact angle constraint, combines the SMC methodology with ANFIS to enhance the robustness and reduce the chattering of the system. The effectiveness of the ANFSMC guidance law is also verified by the numerical simulations.

This study considers the observer-based consensus tracking problem of linear multi-agent systems with input saturation. Existing observer-based consensus protocols are designed based on an undirected graph, and need global information, such as the network size or eigenvalue information of the Laplacian matrix. In this study, based on only the agent dynamics and the relative outputs of neighbouring agents, an adaptive consensus protocol is proposed by assigning a time-varying coupling weight to each node, and this protocol is independent of any global information and hence is fully distributed. Under the assumptions that each agent is asymptotically null controllable with bounded controls and detectable, and the topological graph has a directed spanning tree with the leader as the root node, semi-global observer-based consensus tracking of multi-agent systems can be reached despite actuator saturation occurring. The results are applied to consensus tracking control of two-mass-spring systems, which are well-known models for vibration in many mechanical systems.

This study is concerned with stability and stabilisation of switched positive systems in both continuous- and discrete-time contexts. Several criteria of Metzler/Hurwitz and non-negative/Schur matrices are presented. By using these criteria and dual system theory, a sufficient condition for stability of switched positive systems is established. On the basis of the sufficient condition, a new controller design is proposed for switched positive systems. It is shown that the proposed design reduces the conservatism of the existing approaches in the literature where the controller gain matrices always have the property of being rank one. The results are also extended to discrete-time systems. Finally, two illustrative examples verify the validity of the theoretical findings.

This study considers the problem of designing a multi-input and multi-output (MIMO) proportional-integral-derivative (PID) controller via direct optimal or suboptimal linear quadratic regulator (LQR) approach. To design the controller, first the MIMO PID design problem is transformed into a state feedback control and then the gains of the state feedback controller are chosen through an optimal or suboptimal LQR design. Given a minimal state space representation (A, B, C) of the plant, a necessary and sufficient condition (based on matrices A, C) for which the optimal problem (i.e. PID design via optimal LQR) is solvable is obtained. When this optimal problem is not solvable, a suboptimal solution (i.e. PID design via suboptimal LQR), if exists, is obtained by converting the problem into trace minimisation one, which is solved using linear matrix inequality-based method. Suitable examples are considered to illustrate the approaches.

This study considers the functional observers design for a class of discrete-time switched singular systems simultaneously subject to state delays, unknown inputs (UIs) and arbitrary switching sequences. The singular matrix E is assumed to be switching-mode-dependent, and the UIs are present in both the state and the measurement channels. A mode-dependent, delay-type observer is first constructed, then, based on the unknown input decoupling and the switched Lyapunov theory, a method is proposed to design such observer which ensures both: the total elimination of the UIs and exponential estimate of the given function of the state vector. The conditions for the existence of the proposed observer are given through algebraic matrix inequalities, and exponential stability of the observation error dynamics is derived by using a properly constructed decay-rate-dependent switched Lyapunov function and the linear matrix inequality technique. Finally, an illustrative example is given to show the effectiveness of the obtained results.

This study investigates the practical synchronisation of networked Lagrangian systems with a directed graph by pinning adaptive control. Some simple yet general algebraic criteria are proposed based on practical stability theory on dynamical systems, and the proposed criteria ensure that all the robotic agents described by Lagrangian dynamics can achieve desired practical synchronisation. The main features of the present investigation include, an efficient pinning adaptive strategy is implemented by applying local linear feedback injections to a small fraction of agents, which means that the presented control strategy does not require the prerequisite knowledge of system models. Moreover, an allowable attraction region is explicitly given by Lagrangian dynamics parameter and the controlled network structure, and so it is very convenient to application in practice. Besides, this study addresses the fundamental problems in the pinning control of networked Lagrangian systems: what kind of agents and how many agents should be pinned? As a direct application of the theoretical results, practical synchronisation of eight two-link revolute manipulators is discussed in detail. Numerical experiments verify the effectiveness of the proposed control technique.

This study focuses on the design of fixed-time consensus for first-order multi-agent systems with unknown inherent non-linear dynamics. A distributed control protocol, based on local information, is proposed to ensure the convergence of the tracking errors in finite time. Some conditions are derived to select the controller gains in order to obtain a prescribed convergence time regardless of the initial conditions. Simulations are performed to validate the theoretical results.

Finite-time stability analysis and controller synthesis for switched linear parameter-varying (LPV) systems are discussed in this paper. A new finite-time stability condition and robust finite-time controller design method are presented for switched LPV systems with two different structured uncertainty modelling assumptions (i.e. affine linear structured uncertainty or polytopic structured uncertainty). On the one hand, by using the piecewise parameter-dependent Lyapunov-like function, a less conservativeness finite-time stability condition is established. On the other hand, the new condition based on linear matrix inequalities relieves the controller design burden of dealing with specific applications. Finally, the provided design method is highly desirable to treat the problem of attitude control of bank-to-turn missiles with different channels coupling, and computer simulations demonstrate the effectiveness and superiority of the theoretical results.

This study concerns the problem of asymptotic stability analysis for neutral systems with mixed delays. Some simple and less conservative criteria are firstly proposed based on the Wirtinger-based integral inequality. Then, incorporating the delay-decomposition idea with the augmented Lyapunov–Krasovskii functional, a new augmented delay-decomposition Lyapunov–Krasovskii functional is constructed. In addition, the Wirtinger-based integral inequality is sufficiently utilised to cope with the derivative of the constructed functional. Those treatments lead to less conservatism, and an improved asymptotic stability condition is obtained. Finally, a numerical example is given to show the effectiveness and benefit of the proposed criteria.

In this study, the authors derive some new refined Jensen-based inequalities, which encompass both the Jensen inequality and its most recent improvement based on the Wirtinger integral inequality. The potential capability of this approach is demonstrated through applications to stability analysis of time-delay systems. More precisely, by using the newly derived inequalities, they establish new stability criteria for two classes of time-delay systems, namely discrete and distributed constant delays systems and interval time-varying delay systems. The resulting stability conditions are derived in terms of linear matrix inequalities, which can be efficiently solved by various convex optimisation algorithms. Numerical examples are given to show the effectiveness and least conservativeness of the results obtained in this study.