This study presents a novel robust model predictive control (MPC) method for constrained non-linear systems with control constraints and external disturbances. The control signal is obtained by optimising an objective function consisting of two terms: an integral non-squared stage cost and a non-squared terminal cost. The terminal weighting matrix is designed appropriately such that: (i) the terminal cost serves as a control Lyapunov function; and (ii) the resultant finite horizon cost can be treated as a quasi-infinite horizon cost. Provided that the Jacobian linearisation of the system to be controlled is stabilisable and the optimisation is initially feasible, sufficient conditions ensuring the recursive feasibility of the optimisation and the robust stability of the closed-loop system are established. It is shown that the conditions rely on an appropriate design of the sampling interval with respect to a certain given disturbance level. The effectiveness of the proposed method is illustrated through a numerical example.

This study considers the global adaptive control design for a class of high-order uncertain non-linear systems. Different from the existing results, the systems under investigation have serious unknowns which cannot be bounded by any known constants, and particularly have double control input channels, that is, the scalar control input directly affects two one-dimensional subsystems. Inspired by the author's recent results, by skillfully combing the method of adding a power integrator and some adaptive techniques, an adaptive controller is successfully constructed which can guarantee the asymptotical convergence of the system states for any given initial conditions. A simulation example is given to demonstrate the validity of the obtained theoretical results.

In this study, an event-triggered control strategy is proposed to achieve consensus in a multi-agent system under a directed topology. The proposed control strategy utilises a piecewise continuous control law and an event-triggering function for each agent. The control law only updates at discrete event instants computed using an event-triggering function, which depends on the states of the agents at the current and outdated event instant. This control approach is first applied to a first-order system and is further extended to a second-order system. Simulation examples are presented to illustrate the efficiency of the proposed control strategy.

Mittag–Leffler stability is a property of fractional-order dynamical systems, also called fractional Lyapunov stability, requiring the evolution of the positive-definite functions to be Mittag–Leffler, rather than the exponential meaning in Lyapunov stability theory. Similarly, fractional Lyapunov function plays an important role in the study of Mittag–Leffler stability. The aim of this study is to create closed-loop systems for commensurate fractional-order non-linear systems (FONSs) with Mittag–Leffler stability. We extend the classical backstepping to fractional-order backstepping for stabilising (uncertain) FONSs. For this purpose, several conditions of control fractional Lyapunov functions for FONSs are investigated in terms of Mittag–Leffler stability. Within this framework, (uncertain) FONSs Mittag–Leffler stabilisation is solved via fractional-order backstepping and the global convergence of closed-loop systems is guaranteed. Finally, the efficiency and applicability of the proposed fractional-order backstepping are demonstrated in several examples.

A new notion of normal positive electrical circuits is proposed. It is shown that any positive second-order electrical circuit with 2-inputs and 2-outputs is normal and a positive electrical circuit with m-inputs and p-outputs (m, p ≥ 2) is normal if its system matrix A has distinct eigenvalues or its system matrix is symmetric.

This study deals with the L ₁ analysis of stable finite-dimensional linear time-invariant (LTI) systems, by which the authors mean the computation of the L _∞-induced norm of these systems. To compute this norm, they need to integrate the absolute value of the impulse response of the given system, which corresponds to the kernel function in the convolution formula for the input/output relation. However, it is very difficult to compute this integral exactly or even approximately with an explicit upper bound and lower bound. They first review an approach named input approximation, in which the input of the LTI system is approximated by a staircase or piecewise linear function and computation methods for an upper bound and lower bound of the L _∞-induced norm are given. They further develop another approach using an idea of kernel approximation, in which the kernel function in the convolution is approximated by a staircase or piecewise linear function. These approaches are introduced through fast-lifting, by which the interval [0, h) with a sufficiently large h is divided into M subintervals with an equal width. It is then shown that the approximation errors in staircase or piecewise linear approximation are ensured to be reciprocally proportional to M or M ², respectively. The effectiveness of the proposed methods is demonstrated through numerical examples.

This study presents a state feedback adaptive controller for a class of parametric-strict-feedback non-linear systems with multiple bounded time-varying state delays and in the presence of time-varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some unknown time-varying values where the parameters, times and patterns of the failures are also unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. The adaptive state feedback control scheme is constructed based on a backstepping design method. The boundedness of all the closed-loop signals is guaranteed and the tracking error is proved to converge to a small neighbourhood of the origin. The proposed approach is employed for a second-order time delay plant as well as a two-stage chemical reactor with delayed recycle streams. The simulation results show the correctness and effectiveness of the proposed adaptive compensation in the case of actuator failures.

This study presents an effective analysis procedure to give the bounded input bounded output stability intervals of time delay for a class of commensurate delayed fractional-order systems with rational order. First, it is proposed that the analysis on multi-valued characteristic function of delayed fractional-order systems can be conducted equivalent on the consideration of the principal branch. The statement makes the generalisation of the τ-decomposition method in integer order case possible. With the convenience in studying delayed systems, the frequency-sweeping method is applied logically, and the PIRs and the cross-direction around them can be determined through the frequency-sweeping curves simultaneously. Moreover, the verification of the neutral stability condition of fractional-order delayed systems is considered in a systematic manner. At last, some examples show that the proposed strategy is practically useful in the analysis and design of feedback control for both integer and fractional-order systems with time delays.

Observer design for a Takagi–Sugeno (T–S) fuzzy system with uncertainties is extremely difficult because the estimation error is incapable of approaching zero asymptotically due to the existence of uncertainty terms. In this study, by regarding the uncertainty as an unknown input, with some particular derivation, the authors successfully synthesize a fuzzy observer which guarantees that the error will converge to zero asymptotically. Based on Lyapunov theory and linear matrix inequality tools, the main theorem is derived for the fuzzy observer synthesis. This study does not limit the size of uncertainties, but the uncertainties have to satisfy a specific matching condition in order to use the unknown input concept. Finally, a numerical example is given to show that the proposed approach is effective in estimating system's states subject to system uncertainties.

This study deals with adaptive control of non-linear systems in the strict-feedback form with parametric uncertainties and additive disturbance. The disturbance in the systems is assumed to be bounded. No knowledge of the uncertain parameters, an upper bound of the uncertain parameter vector, a bound of unknown disturbance and the differentiability of the external disturbance is required. Under the weakened assumptions, two continuous robust adaptive control schemes are proposed. In the first control scheme, a modified adaptive backstepping design procedure is proposed to remove overparameterisation. A novel damping term with the estimate of unknown disturbance bound and a positive time-varying integral function are introduced in the control law to counteract the destabilising effects of the external disturbance. In the second scheme, an alternative continuous adaptive controller is designed. Instead of the estimate of the disturbance bound, an adaptive parameter is incorporated into the control design. In both of the two control schemes, the design parameters are freely chosen to improve the control performance. It is proved that the proposed two adaptive control schemes can guarantee that the closed-loop signals are bounded and the output tracking error converges to zero asymptotically in spite of the disturbance. Finally, a numerical example is included to show the effectiveness of the presented control methods.

This study presents the framework of the acceleration reference continuous motion nominal characteristic trajectory following (AR-CM NCTF) control system, and its effectiveness in a linear motion mechanism with friction characteristics is experimentally demonstrated in comparison with the other control methods. The overall control system comprises the feedback-loops for velocity reference and acceleration reference following controls. The AR-CM NCTF control is an enhanced continuous motion NCTF (CM NCTF) control that has been proposed for high-precision motion. It has the same structure as the CM NCTF controller with additional elements for high-precision motion. The design procedure of the AR-CM NCTF controller remains easy and is independent of friction characteristics. The usefulness and advantages of the proposed controller are shown in the experimental studies. Besides, this study also highlights the robustness of the AR-CM NCTF controller by examining its performances in point-to-point and tracking motions in the presence of mass and disturbance force variations. In the robust performance, the AR-CM NCTF controller is compared with two types of proportional derivative control systems with disturbance observers (PDDOs). The comparative experimental results illustrate that the AR-CM NCTF controller shows the higher motion performances the higher robustness to plant parameter variations than the PDDO controllers.

This study investigates the problem of event-based synchronisation of linear discrete-time dynamical networks. Leader-following and leaderless synchronisations are achieved by a distributed event-trigger strategy. It is shown that feedback control updating is unnecessary until an event is triggered. The combinational-state variables and the Riccati equation are used to construct a Liapunov function and to design the event-triggering conditions. Numerical examples are provided to illustrate the theoretical results.

This study addresses the semi-global consensus of linear multi-agent systems with a virtual leader, in which the control input of each agent is subject to periodically intermittent saturating actuator. Depending on multiple Lyapunov stability theorem and applying the algebraic-Riccati-equation-based low-gain feedback technique, the authors can obtain that: when the control width is larger than a fixed value, a connected system with each agent being asymptotically null controllable with bounded controls and marginally stable can guarantee the semi-global consensus of multi-agent systems with a virtual leader. Numerical simulations verify the author's theoretical analysis.

This study studies the protocol of robust synchronisation of second-order multi-agent systems via pinning control. First, it is shown that, for the second-order multi-agent system with disturbances, by pinning one node with small coupling strength, the whole system can reach synchronisation. Then, these results are applied to the cooperative control of multiple 3-degree of freedom helicopters systems with disturbances. Finally, simulations are performed to illustrate the effectiveness of the theoretical results.

In this study, the authors probe the multi-agent consensus problem with general linear dynamics via the distributed reduced-order observer-based protocols under directed switching topology. A new type reduced-order observer is adopted to modify the existed consensus protocols. Based on graph theory, Riccati equation and Lyapunov method, a multi-step algorithm is provided to design the gain matrices involved in the used protocols. The consensus stability problem is investigated by use of the piecewise Lyapunov functions incorporated with an average dwell time approach. It is shown that if the average dwell time is chosen sufficiently large and all directed switching topologies have a directed spanning tree, then the multi-agent system can achieve consensus via the author's modified protocols. Furthermore, as the special cases, the consensus conditions under fixed topology and balanced switching topology are obtained easily. To obtain a desired consensus decay rate, the related gain matrix design approach is provided. Finally, a simulation example is given to illustrate the effectiveness of their obtained results.

Swarm stability is studied for descriptor compartmental networks with linear time-invariant protocol. Compartmental network is a specific type of dynamical multi-agent system. Necessary and sufficient conditions for both consensus and marginal swarm stability are presented, which require a joint matching between the interactive dynamics of nearest neighbouring vertices and the Laplacian spectrum of the overall network topology. Three numerical instances are provided to verify the theoretical results.

This study addresses semi-global practical asymptotic stabilisation and performance recovery of a class of sampled-data non-linear systems using a time-scale separation redesign. In particular, a high-gain filter is designed to estimate uncertainties in continuous-time and a fast variable coming from the filter is used to cancel the effect of the uncertainty, then the controller including the filter is descritised in Euler method. The authors provide conditions relating the sampling time and the filter gain, with which the results for the sampled-data system are the same as those that have been developed for the continuous-time system. As a verification of results, numerical simulations are given.

In this study, a constructive criterion algorithm of the global controllability for a class of planar polynomial systems is obtained. This algorithm is imposed on the coefficients of polynomials only and can be realised easily by computer. The analysis is based on a classical result in real algebraic geometry – Sturm theorem and its modern progress. According to this algorithm, the global controllability of the system can be determined in finite steps arithmetic operations. Finally, the authors give some examples to show the application of the author's results.