In this study, the authors study the optimal guaranteed cost control problem for a class of non-linear uncertain systems based on adaptive dynamic programming (ADP) with concurrent learning. A neural network-based approximate optimal guaranteed cost control design is developed not only to ensure the system stability for all admissible uncertainties but also to achieve a minimal guaranteed cost. First, the optimal guaranteed cost control problem is transformed into an optimal control problem of the nominal system by properly modifying the cost function to account for all possible uncertainties. Then based on ADP, an adaptive optimal learning algorithm is proposed for the nominal system by using a single critic network with concurrent learning to approximate the solution of Hamilton–Jacobi–Bellman equation. To relax the demands of the persistence of excitation condition, the recorded past data are used simultaneously with the current data for the adaptation of the critic network weights. Besides, an additional adjusting term is employed to stabilise the system and relax the requirement for an initial stabilising control. Moreover, uniform ultimate boundedness of the closed-loop system is guaranteed by using the Lyapunov approach. Finally, three simulation examples are provided to demonstrate the effectiveness of the proposed approach.

This study presents an observer-based robust adaptive type-2 (T2) fuzzy tracking control scheme for the longitudinal dynamics of flexible air-breathing hypersonic vehicles. The control scheme is composed of three parts, namely an uncertain dynamics approximator, a reduced-order adaptive state observer, and command filter-based backstepping altitude and velocity controllers. First, the approximator is implemented by utilising interval T2 fuzzy logic systems for approximating unknown vehicle dynamics in the control scheme. Then, the reduced-order adaptive state observer is designed by the combination of the approximator and output state feedback techniques, which guarantee the estimation of unmeasurable states as well as uncertain dynamics identification. By using the linear matrix inequalities technique, a new condition for obtaining the gains of the state observer is presented. Next, on the basis of the designed approximator and state observer, the altitude and velocity tracking controllers are constructed by command-filtered backstepping control approach which avoids the explosion of complexity in conventional backstepping design. Thorough stability analysis of the closed-loop systems is conducted. Nominal and comparison simulation studies considering parametric uncertainty, incomplete state measurement, and measurement noises are carried out, illustrating the effectiveness of the proposed control scheme.

The study is concerned with the filtering problem of discrete time positive switched delay systems under an improved delay-dependent persistent dwell time (PDT) switching, which includes delay-independent PDT switching as a special case. Under delay-dependent PDT switching, a pair of state bounding positive filters is designed such that the output of positive switched delay systems can be estimated at all times, and the effect of delay on PDT switching and the performance is also discussed. Finally, a numerical example is presented to demonstrate the effectiveness of the developed results.

In this study, the robust estimation problem is investigated for discrete-time switched linear systems with unknown persistent excitation. The robust current estimator is proposed to estimate the real state of the switched systems without the stability restriction. The estimator input is constructed based on the current and previous information of a switching signal and output measurement. Owing to the reference system and its estimator, the exponential stability of the estimation error systems is presented under the average dwell time switching and arbitrary switching. The upper bound or the property of attenuation is unnecessary for the unknown input considered here. In addition, neither the conventional decoupling principle nor non-singular transformation is employed. At last, the effectiveness of established results is illustrated by a numerical example and a DC–DC boost converter.

A novel direct identification using the residual model of Kalman filter (KF) is proposed for multiple-input and multiple-output Box–Jenkins model of the system formed of the signal and disturbance models using the residual model relating the input and output of the system without any a priori knowledge of the statistics of the disturbance and measurement noise corrupting the output. To avoid a non-linear optimisation, the auto-regressive and moving average (MA) residual model is approximated by a high-order MA model, so that the unknown parameters of the KF enter the residual model linearly. A key property of the KF is established, namely that the transfer matrix of the signal model is the matrix fraction description (MFD) model relating the residual and the system input and output. A two-stage identification method is developed here. In stage 1, a high-order KF of the system is identified using the robust, and computationally efficient least-squares method to capture completely both the signal and disturbance models. In stage 2, the KF for the signal is derived using the balanced model reduction technique. The signal model is derived using the key MFD property. The performance of the proposed scheme is successfully evaluated on both simulated and physical systems.

This study is concerned with the sliding mode control design subject to actuator saturation. The actuator saturation is formulated with the rate limitation and the standard magnitude limitation. Both the saturated sliding mode control approaches against the known and the unknown bounded uncertainties are discussed. The stability analysis for the resulting overall closed-loop systems is conducted. Moreover, several optimisation conditions are established to estimate the attraction domain of the saturated system under the designed controllers, by determining the invariant set of the system. Finally, simulation examples are shown to illustrate the proposed control design scheme.

This study addresses an attitude tracking problem for a rigid spacecraft with bounded external disturbances. Attitude dynamics of the rigid spacecraft is modelled by a unit quaternion for global representation. Based on this representation, a novel continuous controller is proposed based on the full-order terminal sliding mode method. The finite-time stability of the closed-loop system is assured by Lyapunov and homogeneous finite-time stability theorems. Moreover, the singularity term in the terminal sliding surface is compensated by an identical item in the feedback control law, and this makes the closed-loop system trajectories converge to the equilibrium in finite-time, and hence a high precision is obtained. Finally, simulation results are presented to illustrate the effectiveness of the proposed controller.

In this study, a unified distributed static output-feedback (OPFB) control protocol is presented for multi-agent systems. The proposed approach is unified in the sense that it is applicable to both homogeneous and heterogeneous multi-agent systems. Despite its importance, distributed OPFB control design is not considered for heterogeneous systems in the literature. Moreover, as will be shown, existing static OPFB controllers for homogeneous systems are vulnerable to attacks on sensors and actuators. More precisely, it is shown that a compromised agent can make an intact agent turn away from the leader if there is a directed path of any length from the compromised agent to the intact agent. To overcome these shortcomings, a distributed OPFB controller is presented which is (i) applicable to both homogeneous and heterogeneous systems, and (ii) is resilient against attacks on sensors and actuators. The proposed framework prevents attacks on sensors and actuators from propagating across the network and, thus, guarantees synchronisation of intact agents to the leader. To further improve the resiliency and guarantee synchronisation of even compromised agents, a disturbance compensator is designed. A significant advantage of this approach is that no assumption on topological connectivity and the number of agents under attack is required.

In this study, the problem of adaptive multi-dimensional Taylor network (MTN) control for single-input single-output (SISO) uncertain stochastic non-linear systems is investigated. How to minimise the influence of randomness and uncertain non-linearity for less complex computation, and how to improve the real-time performance of the controller are of great significance. To this end, a control approach based on MTN is proposed for tracking control of stochastic non-linear systems. MTNs are used to approximate the non-linearities, and the backstepping technique is employed to construct the MTN controller (MTNC). MTNC involves only addition and multiplication, featuring desirable simplicity and real-time performance. Stability of the system is guaranteed via Lyapunov approach, and it is proved that the proposed controller can guarantee that all signals of the closed-loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighbourhood around the origin. Finally, a numerical example is given to illustrate the effectiveness of the proposed design approach, and simulation results demonstrate that the method presented in this study has good real-time performance and control quality.

This study designed a suboptimal output control strategy to characterise an attractive and invariant set for the state trajectories of perturbed linear systems with noisy measurements and state constraints. The state constraints were defined by a given polytope formed of by n-dimensional vectors. An adaptive linear controller enforced the existence of an attractive and invariant set (centred at the origin) for the trajectories of the perturbed system. A barrier Lyapunov function (BLF) and the attractive ellipsoid method (AEM) derived the adjustment law of the adaptive gain. The controller design used the linear matrix inequality technique to solve two optimisation problems. The first solution provided a maximal set where the initial conditions must belong without violating the state constraints. The second optimisation solution characterised the invariant minimal attractive set for the system trajectories. An academic example verified how the proposed adaptive control generated the system trajectories that converged to the minimal attractive ellipsoid while keeping them inside the polytope defining the state constraints. The simulation script showed the advantages of the adaptive BLF controller (ABLC) against classical AEM controller. A second numerical example considered a direct current motor showing the advantages of the ABLC against the sliding mode technique.

This study deals with the stabilisation of discrete-time linear systems subject to static finite-level quantisation on the control inputs. Two kinds of quantisers are considered: uniform and logarithmic. The modelling of the finite-level quantisation is obtained by the application of deadzone and saturation maps to an infinite-level quantiser. From this model, conditions for the synthesis of state feedback control laws guaranteeing the convergence of the trajectories to an attractor around the origin provided that the initial state belongs to a certain admissible set are proposed. These conditions can thus be incorporated in linear matrix inequality-based optimisation schemes to compute the stabilising gain while minimising the size of the attractor.

Due to the complexity of practical systems, the used models generally mismatch the practical ones. For the Kalman filtering with a single mismatched measurement noise covariance, the ranking of the ideal MSE (IMSE), the filter calculated MSE (FMSE), and the true MSE (TMSE) has been established. This study considers the ranking of the relative closenesses from the FMSE and TMSE to the IMSE when multiple mismatched measurement noise covariances are used. It is found that for the case with two deviations of the same signs, the larger the absolute deviation is, the farther away the FMSE or TMSE is from the IMSE. It is also found that for the case with two deviations of different signs, if the positive deviations are less than the absolute value of the negative deviation, then the FMSE or TMSE with positive deviation is relatively closer to the IMSE. Otherwise the ranking of the two correspondingrelative closenesses depends on the parallel sum of two deviations with a non-zero threshold. Then the pair-wised ranking of the relative closenesses corresponding to two arbitrary deviations is further extended to the case with more than two deviations. Numerical examples are provided to validate the results.

This study concerns the problems of stability and control for a class of discrete-time switched systems by introducing a one-step ahead Lyapunov function (LF) approach. The one-step ahead LF is a function of future states. The design objectives are to reduce the conservatism of the stability criterion developed for arbitrarily switched systems and further get a better disturbance attenuation capability. The distinguishing feature is that the one-step ahead LF has no structural constraint, such as, diagonal structure, and the resulting analysis and synthesis criteria can cover the non-monotonic method considering two samples variation, i.e. or as a special case. The obtained results can be easily extended to the multi-step ahead case. Numerical examples are included to demonstrate the effectiveness of the developed method.

The fault detection filter design for Markov jump linear system (MJLS) in finite-frequency domain based on derandomisation is proposed in this study. By means of generalised Kalman–Yakubovich–Popov (GKYP) lemma, the finite-frequency fault detection problem for deterministic systems can be easily solved. However, MJLS is a multi-mode system jumping among different modes stochastically. Consequently, its performance in finite-frequency domain cannot be directly achieved by GKYP lemma. Therefore, the derandomisation technique is introduced to transform stochastic multi-mode systems to deterministic single-mode systems. Then based on the transformed deterministic system, a fault detection filter for MJLS with both fault and noise in specific frequency ranges is designed. To demonstrate the superiority of the authors' theoretical results, a numerical example and a real application with engineering background are presented.

In this work, the exponential weighted square-of-error functions are exploited for controller design. It is reported that the exponential weight in square-of-error objective function is related to the maximum sensitivity of the process. Therefore, it is possible to control the maximum sensitivity of the process without measuring the frequency response. Moreover, the existing integral-square-error- and integral-time-square-error-based proportional-integral-derivative (PID) tuning rule is modified with the proposed exponential weighted square-of-error functions that allow the user to further tune the maximum sensitivity of the process. The proposed theory is corroborated with the help of a gain optimisation example by the traditional minimisation approach and a PID controller design example by the proposed tuning rule (for the stable/unstable process) and stochastic optimisation approach.