A differential flatness theory-based control and state estimation method has been developed for electric power units that consist of synchronous generators connected to gas turbines. The dynamic model of the power unit satisfies the properties of differential flatness and this allows for its transformation into an input–output linearized form. Moreover, it is shown that the state-space description of the power system can be written in the canonical (Brunvsky) form. Using this, a solution for the power unit's control and state estimation problem is given. First, a stabilizing feedback controller is designed. Moreover, with the use of differential flatness theory-based implementation of the Kalman Filter it becomes possible to solve the state and disturbances estimation problem of the gas-turbine power unit. The considered filtering method, under the name of Derivative-free nonlinear Kalman Filter, consists of application of the Kalman Filter's recursion on the linearized equivalent model of the power system, and of an inverse transformation that allows for computing estimates for the state variables of the initial nonlinear system. By redesigning the aforementioned Kalman Filter as a disturbance observer one can also identify and annihilate in real time exogenous perturbations.

This study investigates delay-dependent stability of a class of highly non-linear stochastic functional differential equations with Markovian switching. Some novel boundedness and stability criteria are first established, including stability in , asymptotic stability in and almost surely asymptotic stability, based on Lyapunov functions and generalised Itô formula. Concretely, the authors generalise and improve the existing results to the hybrid stochastic functional differential equations case. An example is presented to illustrate the effectiveness of the obtained results.

Designing discrete time variable structure control with sliding mode (SM) schemes implies finding an asymptotically stable sliding surface with a control policy which assures the existence of a SM. Based on a recently innovative approach, where the authors developed a flexible design of sliding surfaces applied to discrete time linear multi-input multi-output (MIMO) systems, a novelty controller design strategy is proposed, where a switching surface parameter is used for the adjustment of the control signal limitations and for the improvement of the controlled system dynamics against model uncertainties. It is the first time that these drawbacks are solved modifying the switching surface values because it has been always resolved via control law adjustment. Moreover, a new chattering elimination method using adjustable sigmoid functions is also implemented in the controller. The main advantages of the proposed methodology are: firstly, it can be easily applied to high-order linear MIMO systems; secondly, system dynamics coordinates representation transformations are not needed and thirdly, the non-ideal SM dynamics is considered in the design procedure. Both the sliding surface and the control law specification are included in the proposed methodology. An illustrative example is included.

In this work, an enhanced model-free adaptive control algorithm considering the time delay (EMFAC-TD) is proposed for a class of multi-input and multi-output systems and is further applied to the path tracking control problem of a self-driving wheel excavator. First, a preview-deviation-yaw-based method is first proposed for the simplification of excavator dynamics. Then, based on the simplified dynamics, the EMFAC-TD controller is designed via a novel dynamical linearisation technique with a time-varying parameter termed pseudo Jacobian matrix, which contains the coupling information of the excavator driving dynamics. Moreover, for the time delay of the excavator, EMFAC-TD method also handles it by introducing the Smith estimating method. The main feature of the proposed EMFAC-TD is that the controller is designed only based on the input and output data of the excavator. Further, the stability of the proposed EMFAC-TD is proved via rigorous mathematical analysis. The experimental results implemented on a real self-driving excavator show that the maximum tracking error of the excavator controlled via EMFAC-TD method can be limited as 0.3–0.7 m for different driving tasks, satisfying the practical requirement. The experimental results verify that EMFAC-TD method can improve the tracking performance and complete the required task successfully.

This study employs a novel fuzzy co-positive Lyapunov function to investigate the stability of discrete-time polynomial-fuzzy-model-based control systems under positivity constraint. The fuzzy co-positive Lyapunov function consists of a number of local sub-Lyapunov function candidates which includes the positivity property of a non-linear system and the contribution of each sub-Lyapunov function candidates depends on the corresponding membership functions. Imperfect premise matching design concept is used for the design of a closed-loop polynomial fuzzy controller based on the constructed polynomial fuzzy model. The bounded control signal conditions (upper and lower boundary demands on control signal) are included in the Lyapunov stability and positivity conditions, in which all are formulated in the form of sum-of-squares conditions. A numerical example is given to validate the proposed approach.

An observer-based finite-time asynchronous control law is designed for a class of hidden Markov jumping systems with non-linearities and external disturbances. The non-linearities satisfy the conic-type constraint condition that lies in a known hypersphere with an uncertain centre. The non-synchronisation phenomenon between the system modes and observer/controller modes is modelled by a hidden Markov model. By means of the proper stochastic Lyapunov–Krasovskii functional method, a sufficient condition is obtained to guarantee the stochastic finite-time boundedness of the corresponding argument error dynamic systems with a satisfied disturbance rejection level. Finally, the feasibility and validity of the main results is illustrated through a pratical example related to the DC motor.

In this study, the authors propose a distributed discrete-time algorithm for unconstrained optimisation with event-triggered communication over weight-balanced directed networks. They consider a multi-agent system where each agent has a state and an auxiliary variable for the estimates of the optimal solution and the average gradient of the entire cost function. Agents send the states and auxiliary variables to their neighbours when their trigger errors exceed thresholds. They derive a convergence rate of the proposed algorithm which shows faster convergence to the optimal solution compared to the subgradient-based method.

This study focuses on the recursive parameter estimation problems for the non-linear exponential autoregressive model with moving average noise (the ExpARMA model for short). By means of the gradient search, an extended stochastic gradient (ESG) algorithm is derived. Considering the difficulty of determining the step-size in the ESG algorithm, a numerical approach is proposed to obtain the optimal step-size. In order to improve the parameter estimation accuracy, the authors employ the multi-innovation identification theory to develop a multi-innovation ESG (MI-ESG) algorithm for the ExpARMA model. Introducing a forgetting factor into the MI-ESG algorithm, the parameter estimation accuracy can be further improved. With an appropriate innovation length and forgetting factor, the variant of the MI-ESG algorithm is effective to identify all the unknown parameters of the ExpARMA model. A simulation example is provided to test the proposed algorithms.

This study considers the time-varying anti-disturbance formation control problem for a class of high-order uncertain non-linear multi-agent systems with switching directed topologies. A distributed extended state observer (ESO) is constructed to estimate the unknown non-linear dynamics and external disturbances for each agent during the time-varying formation process. Based on the ESO, a novel ESO-based formation protocol is proposed and an algorithm to specify the protocol is derived. The feasibility conditions for the realisation of the anti-disturbance formation under the protocol are also demonstrated. It is rigorously proved that if the feasibility conditions are satisfied and the protocol is designed in the proposed form, the time-varying anti-disturbance formation can be achieved by the high-order uncertain non-linear multi-agent systems with switching directed topologies. The effectiveness and innovations of theoretical results are finally illustrated by some numerical simulations.

In this study, the authors propose a simple adaptive trajectory tracking control scheme for underactuated autonomous underwater vehicles (AUVs) subject to unknown dynamic parameters and disturbances under asymmetric time-varying line-of-sight (LOS) range and angle constraints. A simple error mapping function is constructed to transform the LOS range and angle constraint problems of AUVs trajectory tracking into the problem of the boundedness of transform variable, such that any constraint boundaries of LOS range and angle can be handled. The compounded uncertain item caused by the unknown dynamic parameters and disturbances is transformed into a linear parametric form with only three unknown parameters called virtual parameters. Based on the above, a simple adaptive trajectory tracking control law is developed using dynamic surface control technique, where the adaptive laws online provide the estimations of virtual parameters. As a result, the proposed trajectory tracking control scheme is simple to compute and easy to implement in engineering applications. Strict stability analysis indicates that the designed control law makes AUVs track the desired trajectory within the LOS range and angle constraints and guarantees the boundedness of all signals of the closed-loop control system. Simulation results and comparison verify the effectiveness of the designed control scheme.

Consensus problems for both leaderless and leader-follower disturbed higher-order multi-agent systems are investigated in this study. Based on the combination of integral sliding-mode control and disturbance observer techniques, composite sliding-mode consensus protocols are proposed for leaderless and leader-follower disturbed multi-agent systems, respectively. First, for the leaderless case, composite sliding-mode consensus protocols are designed to make the agents achieve asymptotic consensus. Second, for the leader-follower case, finite-time composite sliding-mode consensus protocols are presented to make the followers achieve consensus with the leader in finite time. Then based on the consensus algorithms proposed in this study, a consensus control strategy is given to realise the velocity and altitude finite-time consensus for a class of leader-follower multi-hypersonic vehicle systems. Finally, the numerical simulations are conducted to validate the efficiency of the proposed consensus algorithms.

Most identification algorithms do not consider the prescribed error bound on the parameter estimation error information, which may result in the poor transient performance of parameter estimation during the identification process. In this study, a novel identification scheme is presented for the extended Wiener–Hammerstein systems with backlash non-linearity, which is implemented by using prescribed performance function and error transformation technique. To improve the transient performance of parameter estimation, the prescribed performance function is designed to prescribe estimation error bound. Then, the error transformation technique is applied to transform the prescribed estimation error problem into an equivalent generalised error problem, which can simplify the design of identification algorithm. By developing the parameter updating law, the convergence of generalised error problem can be guaranteed, and the parameter estimation of considered system can be achieved. The numerical example and experiment results validate that the proposed scheme can provide more accurate parameter estimation and better transient performance than the available identification approaches.

In this study, the authors consider how to use discrete-time state feedback to stabilise hybrid stochastic differential delay equations. The coefficients of these stochastic differential delay equations do not satisfy the conventional linear growth conditions, but are highly non-linear. Using the Lyapunov functional method, they show that a discrete feedback controller, which depends on the states of the discrete-time observations, can be designed to make the solutions of such controlled hybrid stochastic differential delay equations asymptotically stable and exponentially stable. The upper bound of the discrete observation interval is also given in this study. Finally, a numerical example is given to illustrate the proposed theory.

In this study, output feedback control is utilised to stabilise descriptor fractional order systems (FOS) with the fractional order belonging to and , respectively. Firstly, by the restricted equivalent transformations, a new necessary and sufficient condition of admissibility for descriptor FOS with is presented. Then, based on the methods of singular value decomposition, static and dynamic output feedback stabilisers of descriptor FOS with and are obtained, respectively. Finally, four numerical examples are provided to verify the effectiveness of the proposed approaches.

Two multi-parametric iterative algorithms are developed to solve the forward discrete periodic Lyapunov matrix equation associated with discrete-time linear periodic systems. An important feature of one of the proposed algorithms is that the information in the current and the last steps is used to update the iterative sequence. Necessary and sufficient conditions for these two algorithms to be convergent are provided in terms of the roots of a set of polynomial equations. Based on these conditions, a two-dimensional section method is established to search suboptimal tuning parameters for these two algorithms. In addition, convergence properties are also analysed for some special cases of the obtained algorithms. Finally, numerical examples are provided to illustrate the effectiveness of the proposed algorithms. It can be found that the presented algorithms have better convergence performance than some existing iterative algorithms by choosing proper tuning parameters.

Move blocking (MB) is a widely used strategy to reduce the degrees of freedom (DoFs) of the optimal control problem (OCP) arising in receding horizon control. The size of the OCP is reduced by forcing the input variables to be constant over multiple discretisation steps. In this study, the authors focus on developing computationally efficient MB schemes for multiple shooting-based non-linear model predictive control (NMPC). The DoFs of the OCP is reduced by introducing MB in the shooting step, resulting in a smaller but sparse OCP. Therefore, the discretisation accuracy and level of sparsity are maintained. A condensing algorithm that exploits the sparsity structure of the OCP is proposed, that allows to reduce the computation complexity of condensing from quadratic to linear in the number of discretisation nodes. As a result, active-set methods with warm-start strategy can be efficiently employed, thus allowing the use of a longer prediction horizon. A detailed comparison between the proposed scheme and the non-uniform grid NMPC is given. Effectiveness of the algorithm in reducing computational burden while maintaining optimisation accuracy and constraints fulfilment is shown by means of simulations with two different problems.

The positive edge consensus problem of linear systems on undirected as well as directed nodal networks is studied here. The authors first present a distributed observer-based positive edge consensus algorithm to address the problem. The proposed observer-based protocol has more design freedom and a general form which includes the classical Luenberger observer-based protocol as a special case. Moreover, with the help of line graph theory, they map the edge topology to the line topology such that the state of each edge in the connected networks can reach consensus. Sufficient conditions in terms of solving the Sylvester matrix equation, and the linear matrix inequalities are provided to design the proposed algorithm. Finally, a simulation example is given to verify the effectiveness of the proposed positive edge consensus protocol.

In subspace identification, prior information can be used to constrain the eigenvalues of the estimated state-space model by defining corresponding linear matrix inequality (LMI) regions. In this study, first the authors argue on what kind of practical information can be extracted from historical data or step-response experiments to possibly improve the dynamical properties of the corresponding model and, also, on how to mitigate the effect of the uncertainty on such information. For instance, prior knowledge regarding the overshoot, the period between damped oscillations and settling time may be useful to constrain the possible locations of the eigenvalues of the discrete-time model. Then, they show how to map the prior information onto LMI regions and, when the obtaining regions are non-convex, to obtain convex approximations.