A novel estimator for the identification of continuous-time linear time-varying systems is presented in this paper. The estimator uses kernel-based regression to identify the time-varying coefficients of a linear ordinary differential equation, based on noisy samples of the input and output signals. The estimator adopts a mixed time- and frequency-domain formulation, which allows it to be formulated as the solution of a set of algebraic equations, without relying on finite differences to approximate the time derivatives. Since a kernel-based approach is used, the model complexity selection of the time-varying parameters is formulated as an optimisation problem with continuous variables. Variance and bias expressions of the estimate are derived and validated on a simulation example. Also, it is shown that, in highly noisy environments, the proposed kernel-based estimator provides more reliable results than an ‘Oracle’-based estimator which is deprived of regularisation.

In this study, the authors apply iterative learning control (ILC) theory to address the urban traffic signal control problem in a macroscopic level traffic environment. The original urban traffic signal control problem is first formulated into an output regulating and disturbance rejection problem, and the ILC approach is applied to deal with this class of control problem using the repeatability feature of traffic flow. Then, the ILC strategy is further integrated with the traffic-responsive urban control framework to cope with the random disturbances of traffic conditions in iteration cycle. Theoretical analysis shows that the proposed ILC-based traffic signal control methods can guarantee the asymptotic convergence of the link occupancies to the desired ones. The main advantage of the proposed approaches is that they require less prior modelling knowledge in the control system design. The effectiveness of the proposed methods is further verified by extensive simulations.

For the identification of a class of nonlinear multi-input multi-output (MIMO) Hammerstein systems with different types of coefficients: a matrix coefficient and scalar coefficients, it is difficult to parameterise such Hammerstein systems into an identification model to which the standard identification method can be easily applied to implement parameter estimation. By the matrix transformation and the over-parametrisation idea, this study transforms an MIMO Hammerstein system with different types of coefficients into an over-parametrisation regression identification model, and points out the aroused large computation problem. To overcome the large computational load of the over-parametrisation method, by the matrix transformation and the hierarchical identification principle, this study recasts the MIMO Hammerstein system into two models, each of which is expressed as a regression form in the parameters of the nonlinear part or in the parameters of the linear part. Then a hierarchical extended stochastic gradient algorithm is presented to alternatively estimate the parameters of the nonlinear part and the parameters of the linear part. The simulation results indicate that the proposed algorithm can effectively identify the nonlinear MIMO Hammerstein system.

A distributed robust consensus of multiple autonomous underactuated surface vessels (AUSV) is studied in the presence of unknown environmental disturbances. The vehicles have 3 degrees of freedom and two actuators. Since the actuated and unactuated states of the vehicles are strongly coupled, first their kinematics and dynamics are transformed to a cascade non-linear system. Then, based on the properties of non-linear cascade systems, a state-based switching controller is proposed which guarantees the robust consensus of AUSVs. To illustrate the performance of the proposed consensus approach, simulation results are provided.

Predictor control for a class of multi-input non-linear systems with time- and state-dependent input delays is considered. First, a delay-free control law is given for the original system in the absence of delays based on the control Lyapunov function. Second, sufficient conditions are obtained and a predictor control for the original system is presented. Stability analysis is done by a Lyapunov functional. Due to the delay dependent on time and state, a region of attraction is estimated. Further, the stabilisation formula is optimal with respect to a meaningful cost functional. The proposed design is illustrated by a mobile robot with input delay.

This study introduces a general framework for the formation tracking control of all types of wheeled mobile robots (WMRs). On the basis of a coordinate transformation, a second-order input–output model is developed for the general type (m, s) WMR with the mobility m and the steerability s. Then, a saturated feedback linearising controller in conjunction with a non-linear velocity observer is proposed in order to leave out the velocity sensors in all agents. In addition, a radial basis function neural network and an adaptive robust compensator are incorporated in the formation controller design to improve the tracking performance in the presence of uncertain non-linearities and unknown parameters. Semi-global stability of the closed-loop formation system is proved using direct Lyapunov method. Moreover, a generalisation of the proposed controller is introduced for the cooperative control of mobile manipulators. Finally, simulation examples are given to illustrate the effectiveness of the proposed formation control system for two types of WMRs.

This study addresses the problem of designing state feedback controllers for Markov jump systems subject to input quantisation mismatch, and general transition rates allowed to be uncertain and unknown. First, a non-linear control law is constructed for eliminating the effect of input quantisation in the presence of mismatch between quantisation parameters. Then, a new method based on vertex separator algorithm is proposed for designing the controller. A sufficient condition is derived such that the stochastic stability and also the disturbance attenuation performance of the resulting closed-loop system can be ensured. Moreover, it is proved that the obtained result is theoretically less conservative than previous results. Finally, numerical examples are presented to show the effectiveness and advantages of the proposed method.

This studies an adaptive control problem of pure-feedback non-linear systems with full state constraints. The mean value theorem is employed to deal with unknown non-linearities. A novel backstepping design is constructed via barrier Lyapunov function (BLF) combined with dynamic surface control (DSC). The BLF guarantees the full state constraints are not violated and all the closed-loop signals remain bounded. DSC solves the problems of restrictions on high order differentiability of stabilising functions and avoiding the complexity that arises due to the explosion of terms in backstepping design. It is shown that all the signals in the closed-loop system are ultimately bounded and the tracking error converges to an adjustable neighbourhood of the origin while the full state constraints remain unchanged. The performance of the BLF-based DSC is illustrated with two simulation examples.

With the goal of monitoring physical processes, a wireless sensor network (WSN) is often deployed along with a fusion center to estimate the state of general linear stochastic systems. As WSNs comprise a large number of low-cost, battery-driven sensor nodes with limited transmission bandwidth, conservation of transmission resources (power and bandwidth) is of paramount importance. In this context, the present study considers power scheduling for Kalman filtering (KF) using scalar messages exchanged over wireless sensor links, where random measurement packet drops are possible. Each sensor node sequentially decides whether a high or low transmission power is needed to communicate its scalar observations based on a rule that promotes power scheduling with minimal impact on the state estimator's mean-squared error. Assuming approximately Gaussian state predictors, the minimum mean-squared error optimal power schedule is developed for KF that also accounts for dropped data packets. Leveraging statistical convergence characteristics of the estimation error covariance matrix, both sufficient and necessary conditions are established that guarantee the stability of the resultant KF estimator.

This study deals with mathematical modelling and motion control of a pendulum-driven spherical robot (PDSR) moving on an inclined plane. Firstly, the model of a PDSR on an inclined plane is developed using a Lagrangian formulation. Afterwards, a PID controller is tuned to stabilise the robot on the inclined plane. A heuristic fuzzy controller and a PID controller are also designed to move the robot upward or downward the inclined plane and approach the target point. A switched control, i.e. a combination of the designed controllers, is finally suggested to control the motion of the robot on the inclined plane. Simulations are conducted to investigate and compare the performance of the proposed controllers. Experiments are also conducted for different cases to validate the simulations and also evaluate the control strategies via image processing.

The finite-time robust fault-tolerant control problem is addressed for a class of perturbed linear systems with actuator faults and input amplitude saturations. A compensation control strategy is proposed to eliminate the effects of actuator faults and non-linear disturbance-like inputs within a finite-time, as well as to ensure the control inputs be limited within a desired constraint. Based on Lyapunov stability theory, it is shown that system states can converge to a small region in the cases of actuator faults and saturations by choosing suitable control parameters. Some relationships among convergence bounds, actuator faults and amplitude limits, as well as the control parameters are studied deeply and illustrated explicitly with formulas. Simulations of a linearised F-18 longitudinal dynamical control model are given to verify the effectiveness of the proposed method.

This study develops stochastic model predictive control that guarantees the recursive feasibility of the closed-loop performance. Multi-step sets with scaling parameters are proposed to contain the uncertain system trajectory. Meanwhile, by extending the probabilistic invariance to disturbed stochastic systems, we formulate probabilistic constraints as linear matrix inequalities. We show that the introduced scaling parameters enhance the feasibility of predictive control and reduce the conservatism of the constraint satisfaction. The designed control algorithm is recursively feasible and stabilises the system in the mean-square sense. A simplified algorithm further reduces much computational burden and makes the proposed approach more practical.

This study proposes an adaptive neural network controller for a 3-DOF robotic manipulator that is subject to backlash-like hysteresis and friction. Two neural networks are used to approximate the dynamics and the hysteresis non-linearity. A neural network, which utilises a radial basis function approximates the robot's dynamics. The other neural network, which employs a hyperbolic tangent activation function, is used to approximate the unknown backlash-like hysteresis. The authors also consider two cases: full state and output feedback control. For output feedback, where system states are unknown, a high gain observer is employed to estimate the states. The proposed controllers ensure the boundedness of the control signals. Simulations are also performed to show the effectiveness of the controllers.

This study addresses the specified-time containment control problem of multi-agent systems over directed topologies. By using motion-planning approaches, a new framework is constructed to solve the containment control problem of multi-agent systems. In this framework, a class of sampled-data-based protocols are proposed to solve the specified-time containment control problem for single-integrator multi-agent systems. These protocols only require relative information measurements at the sampling instants, without requiring information exchange over the sampling interval. Furthermore, the containment protocols are also developed for the multi-agent system with double-integrator dynamics, such that their states converge to the convex hulls formed by those of the target points in a specified settling time over directed topologies. Compared with the existing results, the proposed sampled-data-based protocols have a couple of advantages: first the settling time can be pre-specified, which is very meaningful and consistent with practical needs. Second, the sampling periods, communication topologies and control gains are all decoupled and can be separately designed. This relaxes many restrictions in controllers design. Numerical simulations are provided to demonstrate the effectiveness of the proposed protocols.

This study addresses the autopilot design problem for a bank-to-turn missile to improve the manoeuvrability. A modified dynamic model is introduced by adding new reaction jet inputs to provide extra manouvrability. The H_ index, which is defined as the minimum singular value of the transfer function, is utilised to assess the manoeuvrability and the autopilot design problem is then transformed to a problem of H_ index controller design. An iterative linear matrix inequality algorithm is presented to obtain the control law. Simulation results illustrate the effectiveness of the proposed approach.

This study focuses on a discrete-time Hammerstein system to investigate the identification with quantised inputs and quantised output observations. After the discussion of the system identifiability and by parameterising the static non-linear function, a three-step algorithm is proposed to estimate the unknown parameters for the identifiable system. The strong convergence and the mean-square convergence rate of the algorithm are established. It is shown that the asymptotic efficiency can be achieved in terms of the Cramér–Rao lower bound by selecting a suitable transformation matrix. A numerical simulation is given to demonstrate the effectiveness of the algorithm.