This study investigates the formation control problem for a class of multiple mobile robots considering unknown skidding and slipping, and torque saturation. The kinematics and dynamics of multiple mobile robots with skidding and slipping effects are considered. The proposed formation control scheme is derived from the dynamic surface design and virtual structure approach where the reference trajectories consisting of path parameters are employed to satisfy both the tracking control and the formation maintenance. The adaptive technique is used to compensate the unknown skidding and slipping effects. From Lyapunov-stability analysis, we prove regardless of unknown skidding and slipping that all signals of the total closed-loop system are semiglobally uniformly ultimately bounded and the point-tracking errors and the synchronisation error for the desired formation converge to an adjustable neighbourhood of the origin. In addition, it is analysed that the orientation error for each robot is related to the speed of the reference trajectory and the skidding effect. The performance and stability of the proposed approach are verified from simulation results.

This study considers the problem of directing a family of non-holonomic vehicles to formation tracking a set of closed convex planar orbits in a three-dimensional (3D) space and approach a time-varying reference orbital velocity. A novel coordinated adaptive control law based on local neighbour-to-neighbour information is proposed to estimate the desired orbital velocity, so that the assumption that every vehicle in the family has access to the reference in the literature is removed. We show how the geometric extension design, projection tracking method and consensus-based technique can be combined together to construct the formation-tracking controller under the bidirectional commutation topology. Simulation results demonstrate the effectiveness of the proposed approach.

This study proposes a new category of fuzzy-observer-based controllers to stabilise non-linear plants based on the fuzzy-model-based control approach. A fuzzy observer is proposed to estimate the system states of the non-linear plant and a fuzzy-observer-based controller using the estimated system states for feedback compensation is proposed to close the feedback loop for the control process. It does not require that the fuzzy observer and fuzzy-observer-based controller have to share the same premise membership functions and the same number of rules of the Takagi–Sugeno fuzzy model. A membership-function-dependent stability analysis approach is proposed to investigate the stability of the fuzzy-observer-based control system based on the Lyapunov method. A set of bilinear matrix inequalities (BMIs) is obtained to guarantee the system stability and control synthesis. To find a feasible solution of the BMI-based stability conditions, a solution-searching algorithm, which combines global searching algorithm and convex programming techniques, is proposed. A simulation example is provide to demonstrate its capability of relaxing control design flexibility and effectiveness.

This study is concerned with the stability, l ₂-gain analysis and ℋ_∞ control for a class of discrete-time switched linear parameter-varying systems with both mode-dependent average dwell time (MDADT) and asynchronous switching, where ‘asynchronous’ means the switching of controllers has a lag to the switching of system modes. The l ₂-gain for general switched systems with MDADT in non-linear setting is firstly derived. Based on the obtained results, the problem of asynchronous ℋ_∞ control for the studied systems is formulated under the framework of MDADT switching logic, and the conditions for the existence of admissible asynchronous ℋ_∞ controllers are deduced in the form of parameterised linear matrix inequalities. A numerical example is provided to verify the effectiveness of the acquired results.

This study is concerned with the delay-dependent H _∞ filter design for a class of discrete-time Markovian jump linear systems (MJLSs) with time-varying delay and incomplete transition descriptions. The considered systems with incomplete transition descriptions cover the MJLSs with known transition probabilities (TPs), partially unknown TPs and uncertain TPs, which are more general. A new equivalent model is proposed for the original MJLSs by employing a two-term approximation method, which formulates the filtering problem in the framework of input–output stability. Based on a Markovian Lyapunov–Krasovskii functional combined with the scaled small gain theorem, a new delay-dependent bounded real lemma for the underlying systems is established. It is shown that by using a linearisation technique, the corresponding full- and reduced-order H _∞ filter design is cast into a convex optimisation problem in terms of linear matrix inequalities. Finally, simulation examples are provided to illustrate the effectiveness and less conservatism of the proposed approach.

The problem of global robust stabilisation is investigated for a class of multi-input switched non-linear systems where each subsystem is not assumed to be asymptotically stabilisable when applying the backstepping technique. The systems under study admit a structure which includes both the p-normal form and the nested lower triangular form as special cases. By exploiting the multiple Lyapunov functions method and the adding a power integrator technique, a sufficient condition for the solvability of the global robust stabilisation problem is derived by constructing state-feedback controllers for individual subsystems and a switching law. Also, an approach is proposed to deal with individual coordinate transformations for subsystems that are required when applying the adding a power integrator technique. The effectiveness of the proposed control scheme is illustrated by its application to a two continuously stirred tank reactor system, which cannot be handled by the existing approaches.

This study is concerned with model predictive control (MPC) for discrete-time Markovian jump linear systems subject to polytopic uncertainties both in system matrices and in transition probabilities between modes. The multi-step mode-dependent state-feedback control law is utilised to minimise an upper bound on the expected worst-case infinite horizon cost function. MPC designs for three cases: unconstrained case, constrained case and constrained case with low online computational burden (LOCB) are developed, respectively. All of them are proved to guarantee mean-square stability. In the constrained case, the minimisation of the expected worst-case infinite horizon cost function and constraints handling are dealt with in a separate way. The corresponding algorithm is proved to guarantee both the mean-square stability and the satisfaction of the hard mode-dependent constraints on inputs and states. To reduce the computational complexity, an algorithm with LOCB is developed by making use of the affine property of the solution to linear matrix inequalities. Finally, a numerical example is given to illustrate the proposed results.

This study focuses on the problem of delay-dependent H _∞ filter design for non-linear interconnected systems with time-varying delays via Takagi–Sugeno fuzzy models. Based on the delay-dependent fuzzy Lyapunov–Krasovskii functional and the fuzzy-free weighting matrix technique, the delay-dependent stability and a prescribed H _∞ performance index are guaranteed for the overall filtering-error system. In addition, a sufficient condition for the existence of such a filter is established by using linear matrix inequalities that are numerically feasible. Finally, two examples are given to demonstrate the effectiveness and advantage of the proposed approach.

This study is concerned with the stability analysis and stabilisation of linear stochastic systems with Markovian switching by using the spectral technique. The notion of spectrum for Markovian jump linear stochastic systems (MJLSSs) is introduced and the relationship between the spectrum and the asymptotical mean-square stability is revealed. As applications, a necessary and sufficient condition for regional stability of MJLSSs and a result on generalised Lyapunov equations are derived. Examples are presented to illustrate the results established.

This study deals with a robust trajectory tracking control problem of discrete-time networked control systems. The systems have time-varying interval-bounded uncertainties, random network-induced delays and data dropouts in both sensor-to-controller channel and controller-to-buffer/actuator channel. A dynamic predictive feedback linearisation controller is proposed so that the system dynamics and delays caused by networked communication time and data dropouts are compensated, and the system output can perfectly track the reference trajectory when uncertainties are absent. Tracking errors caused by the time-varying parameter uncertainties are suppressed in the H _∞ sense. Finally, the proposed method is illustrated by two numerical examples which show the application procedure and effectiveness of the proposed control scheme.

This study investigates the stability of non-linear parabolic systems. Several stability conditions based on separable Lyapunov functions are provided. The new results are applied to switched non-linear parabolic systems with all stable modes or with unstable modes. An example of heat propagation control of semiconductor power chips is taken to illustrate the proposed methods.

This article studies the H _∞ control problem for single-machine infinite bus power systems with superconducting magnetic energy storage (SMES) via simultaneous design of generator excitation control and SMES control. In the control system design, the exciter dynamics and unknown external disturbances are considered for practical implementation in power systems. A new synthesis framework is proposed to address the robust control problem of power systems with SMES. First, from the energy perspective, the interconnection and damping assignment (IDA) approach is applied to improve the transient performance of power systems. Second, by introducing the idea of virtual control in the design process, the authors obtain the solution of a partial differential equation that is a crucial point and cannot be obtained by using the traditional IDA method. Third, in order to enhance the robustness of the closed-loop system, the authors study the H _∞ control design that is challenging and difficult for power systems considering the above mentioned practical considerations. In addition, the authors use a novel equivalent generator model to avoid using unmeasurable infinite bus voltage. Simulation results also show the effectiveness and advantage of the proposed controller.

In this study, the authors investigate the cluster synchronisation of coupled harmonic oscillators with multiple leaders in an undirected fixed network. Unlike many existing algorithms for cluster synchronisation of complex dynamical networks or group consensus of multi-agent systems, which require global information of the underlying network such as eigenvalues of the coupling matrix or centralised control protocols, we propose a novel decentralised adaptive cluster synchronisation protocol for coupled harmonic oscillators. By using the decentralised adaptive cluster synchronisation protocol and without using any global information of the underlying network, all oscillators in the same group asymptotically synchronise with the corresponding leader even when only one oscillator in each group has access to the information of the corresponding leader. Numerical simulation results are presented to illustrate the theoretical results.

This study is devoted to investigating the inherent relationship among the H ₂, H _∞ and H ₂/H _∞ control designs for discrete-time Markov jump systems with multiplicative noise. From a new perspective of non-zero-sum Nash game, we show that the Nash equilibrium solution may present a unified treatment approach for these three types of control design problems by taking adequate parameters in the quadratic performance indices. Moreover, a numerical example is supplied to illustrate the proposed results.