In this study, three general formulations are presented for trajectory optimisation in patrolling problems. In the traditional patrolling problem, some basic assumptions are made (often implicitly). For example, it is known how many robots and how many starting depots exist. Furthermore, the starting depots are assumed to be pre-specified. Each of the three formulations provided here relaxes some (or all) of these assumptions, hence generalising the patrolling problem. A group of robots are supposed to travel through a number of nodes (viewpoints) in such an order so that the total travel distance is minimised. This problem is, in fact, a variant of the Travelling Salesman Problem and is called Multidepot multiple Travelling Salesman Problem. The effectiveness of the approach is demonstrated by comparing the results with those in the literature.

This study is concerned with observer-based fault estimation (FE) and fault-tolerant controller design for a class of discrete-time Takagi–Sugeno (T–S) fuzzy systems. There exist multiple time-varying state delays, sensor and actuator faults, local non-linear dynamics and exogenous disturbances in the systems. In comparison with the existing results, the approach suggested in this study is more flexible and feasible. By means of the n-step induction FE, a novel fuzzy adaptive descriptor observer is developed to obtain the n-step error functions. Then, an active dynamic output feedback fault-tolerant controller is designed to stabilise the closed-loop fuzzy system. Furthermore, a set of delay-dependent sufficient conditions are provided by the fuzzy Lyapunov function which utilises the form of linear matrix inequalities. The stability results from the observer and the controller in this study have less conservatism compared with the ones from the existence of observers and fault-tolerant controllers. At last, a simulation example is presented to demonstrate the advantages and effectiveness of the approach proposed in the study.

In this study, hybrid extended-cubature Kalman filters (HECKFs) for non-linear continuous-time fractional-order systems with uncorrelated and correlated noises are investigated. A non-linear continuous-time fractional-order system using the fractional-order average derivative is discretised to gain a difference equation. The fractional-order average derivative method can achieve more accurate state estimation compared with the Grünwald–Letnikov difference method and the non-linear functions in the system description are dealt with the extended Kalman filter (EKF) and cubature Kalman filter (CKF). The first-order Taylor expansion used in the EKF method is implemented for a non-linear function at the current time. Meanwhile, by using the third-degree spherical-radical rule, the functions in the state equation and output equation are performed by the cubature points. Based on these cubature points, the CKFs for uncorrelated and correlated noises are presented to achieve the effective state estimation. Besides, the simulation results are offered to validate the effectiveness of the HECKF proposed in this study.

The authors consider the stabilising problem for switched linear systems subject to denial-of-service (DoS) attacks that block communications on the network. Using the periodic sampled-data control, the authors first research the switched systems where no DoS attacks occur, and a class of switching signals satisfying the average dwell time is presented to stabilise the switched systems in which the authors take asynchronous switching into consideration. Then, using the presented switching signals, a sufficient condition with respect to DoS attack duration and frequency is given to keep switched systems stable under DoS attacks. The condition reflects the relation between attack rate and system stability. The authors also analyse the qualitative relation between average dwell time and system robustness against attacks. Compared with non-switched systems, the analysis of switched systems under DoS attacks is more challenging. They finally give a numerical example to show the validity of the result.

Having no internal states, static corrective controllers are advantageous over dynamic ones in terms of resource usage, albeit requiring stricter existence conditions. This study presents a novel static corrective control strategy that solves the model matching problem of input/state asynchronous sequential machines. Compared with the previous result, the proposed scheme provides a relaxed existence condition by utilising the model matching indicator that specifies the desirable state at hand. It is shown that the proposed static controller can be designed as long as a corresponding dynamic one exists. The improvement of resource usage in controller synthesis is validated by applying the proposed scheme to the payload data manager in the mass memory unit of satellite systems.