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This paper presents a novel application of the metaheuristic Slime Mould Algorithm (SMA) to the optimal tuning of interval type-2 fuzzy controllers. Inserting the information feedback model F1 in SMA leads to a new version of the metaheuristic algorithm, further referred to as SMAF1. The paper discusses implementation details specific to interval type-2 fuzzy controllers for the position control of processes modelled by nonlinear servo systems with an integral component and dead zone plus saturation nonlinearity. The linear PI controllers are tuned on the basis of the Extended Symmetrical Optimum method using only one tuning parameter and next fuzzified to result in interval type-2 fuzzy controllers. The optimisation requires the minimisation of a discrete-time objective function expressed as the sum of time multiplied by squared control errors, and the vector variable is the parameter vector of the Mamdani PI fuzzy controller. Experimental results conclusively illustrate the superiority of SMAF1 and SMA in comparison with other metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

This paper discusses the problem of estimating a stochastic signal from nonlinear uncertain observations with time-correlated additive noise described by a first-order Markov process. Random deception attacks are assumed to be launched by an adversary, and both this phenomenon and the uncertainty in the observations are modelled by two sets of Bernoulli random variables. Under the assumption that the evolution model generating the signal to be estimated is unknown and only the mean and covariance functions of the processes involved in the observation equation are available, recursive algorithms based on linear approximations of the real observations are proposed for the least-squares filtering and fixed-point smoothing problems. Finally, the feasibility and effectiveness of the developed estimation algorithms are verified by a numerical simulation example, where the impact of uncertain observation and deception attack probabilities on estimation accuracy is evaluated. [ABSTRACT FROM AUTHOR]

This paper aims to solve the sliding mode control issue for the discrete nonlinear two-dimensional (2D) Fornasini–Marchesini second (FMII) model under the influence of quantisation error and stochastic packet loss. Firstly, an innovative stochastic 2D FMII sliding mode control model is constructed by considering quantisation error and Bernoulli packet loss process. And then we study the stability issue and formulate the corresponding stability criterion by virtue of the 2D sliding mode surface and a 2D sliding mode control law with data compensation. Subsequently, the reachability for the 2D sliding surface is verified by a innovative and executable 2D sliding mode control law. Besides, the article also formulates the adaptive intelligent iterative algorithms for the sliding mode surface gain and 2D sliding mode control algorithm, respectively. To conclude the paper, an example is provided to analyse its SMC problem under quantisation and stochastic packet loss. This example also shows the effectiveness of the theorems and algorithms proposed in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with the state feedback control for linear systems in the presence of state delay using a direct numerical design methodology. The design algorithm iteratively searches the solution space of controller parameters to find a proper controller gain that guarantees the delay-independent stability of the closed-loop system. The algorithm divides the solution space to some simplexes, selects one simplex and evaluates two checking methods on this simplex. The first method checks the stabilisability of the corner points (to establish the feasible point) and the other detects the total infeasibility (total de-stabilisability) of the simplex (to omit the undesired parts). One interesting property of the method is its capability in detecting total de-stabilisability of a simplex through its corner points. If none of these methods is successful, the simplex is divided into two smaller ones which will be checked in the next algorithm's iterations. According to the direct search nature, the algorithm is non-conservative and assuredly reaches a stabilizable point in the feasible space of the design space. The proposed algorithm and previous methods are evaluated on a set of random generated systems to compare the feasibility of the methods. Simulation results reveal the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Nonlinear dynamics is frequently encountered in practical applications. Adaptive dynamic programming (ADP), which is implemented via actor/critic neural networks with excellent approximation capabilities, is appropriate to be used in finding the solution for the control problem in the presence of known/unknown nonlinear dynamics. The objective of this paper is to introduce state-of-the-art ADP-based algorithms and survey the recent advances in the ADP-based control strategies for nonlinear systems with various engineering-oriented complexities. Firstly, the main motivation of the ADP-based algorithms is thoroughly discussed, and the way of implementing the ADP-based algorithms is highlighted. Then, the latest research results concerning ADP-based control policy design for nonlinear systems are reviewed in detail, Finally, we conclude the survey by outlining the challenges and possible research topics in the future. [ABSTRACT FROM AUTHOR]

The fraction model has been widely used to represent a range of engineering systems. To accurately identify the fraction model is however challenging, and this paper presents a regularised fast recursive algorithm (RFRA) to identify both the true fraction model structure and the associated unknown model parameters. This is achieved first by transforming the fraction form to a linear combination of nonlinear model terms. Then the terms in the denominator are used to form a regularisation term in the cost function to offset the bias induced by the linear transformation. According to the structural risk minimisation principle based on the new cost function, the model terms are selected based on their contributions to the cost function and the coefficients are then identified recursively without explicitly solving the inverse matrix. The proposed method is proved to have low computational complexity. Simulation results confirm the efficacy of the method in fast identification of the true fraction models for the targeted nonlinear systems. [ABSTRACT FROM AUTHOR]

This paper is concerned with the parameter estimation problem for the multivariate system disturbed by coloured noises. Since coloured noises will reduce the estimation accuracy, the model transformation technique is employed to whiten the original system without changing the input-output relationship. In order to alleviate the heavy computational burden caused by high-dimensional variables and different types of parameters, the transformed model is divided into several sub-models according to the numbers of outputs. However, after the decomposition, all the sub-models contain a same parameter vector, resulting in many redundant estimates. A model transformation based distributed stochastic gradient (MT-DSG) algorithm is derived to cut down the redundant estimates and exchange the information among the sub-models. Compared with the centralised multivariate generalised stochastic gradient algorithm, the MT-DSG algorithm has more accurate estimates and less computational complexity. Finally, an illustrative example is employed to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The impulse response function (IRF) identification of linear mechanical systems is important in many engineering applications. This paper proposes a novel IRF identification method of linear systems based on Kautz basis expansion with multiple poles. In order to reduce the parameters to be identified, the IRF is expanded in terms of orthogonal Kautz functions with multiple poles, and the poles in Kautz functions should be optimised. This allows the identification of IRF for linear mechanical systems operated under more than one mode, such as systems under the white noise excitation or the swept frequency excitation with a wide range of frequency, and can improve the identification accuracy. Furthermore, based on the backpropagation through-time technique and the expectation maximisation algorithm, a pole optimisation algorithm is presented in this paper. The simulation studies verify the effectiveness of the proposed IRF identification method. [ABSTRACT FROM AUTHOR]

In this paper, we study an adaptive method to select online the pole value for a Laguerre scheme in Model Predictive Control (MPC) that yields high performance. It has been observed that, while still using a small numbers of decision variables, the location of the pole affects the closed-loop behaviour significantly. In the present paper, an adaptive algorithm is developed to systematically improve the closed-loop performance of the system as well as the volume of the feasible region and robust feasible region in the case of using a small numbers of decision variables. In order to do this, a method to select a pole value that yields high performance for the initial condition of the system is proposed. The method generates a lookup table of the high-performance pole value obtained through off-line computations. Then, the table is used to assign the pole in the online process. Closed-loop stability for the scheme is established using sub-optimality arguments. Simulations illustrate the suggested method's effectiveness to achieve a balance between performance, optimality, and computational load. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the optimal output feedback control problem for networked control systems (NCSs) involving multiplicative noises, packet dropouts, input delays and measurement delays. The main contributions of this paper can be concluded as follows. Firstly, different from the previous results, this paper overcomes the barrier of the packet dropouts and measurement delays. Based on the measurement data, the optimal estimator is given. Secondly, by using maximum principle, a sufficient and necessary condition for the optimal control problem is presented. Moreover, the explicit output feedback controller is derived with feedback gain based on the coupled Riccati difference equations. Numerical example is illustrated to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Solving the optimal mean-field control problem usually requires complete system information. In this paper, a Q-learning algorithm is discussed to solve the optimal control problem of the unknown mean-field discrete-time stochastic system. First, through the corresponding transformation, we turn the stochastic mean-field control problem into a deterministic problem. Second, the H matrix is obtained through Q-function, and the control strategy relies only on the H matrix. Therefore, solving H matrix is equivalent to solving the mean-field optimal control. The proposed Q-learning method iteratively solves H matrix and gain matrix according to input system state information, without the need for system parameter knowledge. Next, it is proved that the control matrix sequence obtained by Q-learning converge to the optimal control, which shows theoretical feasibility of the Q-learning. Finally, two simulation cases verify the effectiveness of Q-learning algorithm. [ABSTRACT FROM AUTHOR]

In this paper, a novel cooperative constrained distributed model predictive control algorithm is proposed to control the nonlinear interconnected constrained large-scale systems. In this algorithm, a novel reduced-order cooperative optimisation approach is proposed which is its main contribution that reconstructs and improves the global cost function of any local controller. In proposed algorithm, each local controller computes its optimal control by minimising the corresponding global cost function which is a combination of its own and its neighbouring subsystems' cost functions. The sufficient conditions are derived to guarantee the recursive feasibility and closed-loop stability specifications to ensure the convergence of the overall states into the positive region which is the neighbourhood of origin. The performance of the proposed algorithm is illustrated via simulation results of a nonlinear large-scale cart-spring-damper system. [ABSTRACT FROM AUTHOR]

In this paper, the problem of fixed-time consensus tracking control is investigated for multi-agent networks with input uncertain dynamics under the undirected graph. First, a nonsingular terminal sliding mode manifold is proposed, with which the convergence time is globally bounded irrelevant to initial states. Then, with the aid of the observer method and sliding mode technique, the distributed nonsingular controller is designed for the underlying system to ensure that the consensus tracking errors go into sliding mode manifold and converge to origin within a desired time. Finally, examples are presented to verify the validity of the new control strategy. [ABSTRACT FROM AUTHOR]

This paper investigates the data-driven consensus tracking problem for heterogeneous multi-agent systems. All of the heterogeneous dynamics, disturbances and measurement noises are considered for the output tracking consensus of nonlinear multi-agent network under a data-driven scheme. A dynamic linearisation method is introduced to deal with the nonlinear nonaffine structures of the agents and a heterogeneous linear data model for the agent is obtained due to the heterogeneous dynamics of the agent itself. On this basis, a distributed model-free adaptive predictive control (DMFAPC) algorithm is constructed by the use of consensus errors and the robustness analysis is conducted in the presence of disturbances. Further, the results are modified by using measured outputs to replace the system outputs, and thus a measured output-based DMFAPC is presented to deal with the omnipresent measurement noises in practical applications. The two proposed DMFAPC methods are data driven since no mechanistic model information is required wherein. And thus, no unmodelled dynamics affects the consensus performance. Instead, they can improve the control performance by utilising additional predictive information. The two proposed DMFAPC methods are verified using numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the optimal tracking problem for discrete-time linear systems with multiple delays is studied without system dynamics. It is known that the total state of a system without specific dynamic characteristics is hard to be measured, unless such a system is equipped with massive sensors, which, however, may lead to an increase in cost and complexity for analysing. To deal with this problem and avoid adverse effects caused by using system state information, a new data-driven value iteration (DDVI) algorithm is proposed by considering three factors: past control inputs, system outputs, and external reference trajectories. Before the algorithm is proposed, a transformation is made to the original system according to the characteristics of the time-delay system, so that the time-delay number can be reduced or become a delay-free system. A novel data-driven state equation is derived from the historical data of the three factors, and then, it is adopted to solve the optimal control of multi-delay systems. Further results show that the proposed DDVI algorithm is convergent and the tracking error is asymptotically stable. Finally, simulations are provided to show the effectiveness of the controller. [ABSTRACT FROM AUTHOR]

This paper discusses a convex optimisation problem with a common set of constraints in the framework of multi-agent systems. Each agent only exchanges information with its neighbours and collaboratively searches for the optimal solution of the global function. To this addressed problem, a distributed multi-step subgradient projection algorithm is developed, where an adaptive event-triggering protocol is designed to govern the information exchange. It is disclosed that the state of each agent representing the estimate of the optimal solution asymptotically converges to one of the optimal solutions under suitably chosen stepsizes and momentum parameters. Simulation results verify that the proposed algorithm has better convergence performance than the standard event-triggered subgradient projection algorithm. In addition, the communication frequency between agents can be effectively reduced to save communication resource consumption. [ABSTRACT FROM AUTHOR]

In this paper, we study distributed multiagent optimisation over undirected graphs. The optimisation problem is to minimise a global objective function, which is composed of the sum of a set of local objective functions. Recent researches on this problem have made significant progress by using primal-dual methods. However, the inner link among different algorithms is unclear. This paper shows that some state-of-the-art algorithms differ in that they incorporate the slightly different last dual gradient terms based on the augmented Lagrangian analysis. Then, we propose a distributed Nesterov accelerated optimisation algorithm, where a doubly stochastic matrix is allowed to use, and nonidentical local step-sizes are employed. We analyse the convergence of the proposed algorithm by using the generalised small gain theorem under the assumption that each local objective function is strongly convex and has Lipschitz continuous gradient. We prove that the sequence generated by the proposed algorithm linearly converge to an optimal solution if the largest step-size is positive and less than an explicitly estimated upper bound, and the largest momentum parameter is nonnegative and less than an upper bound determined by the largest step-size. Simulation results further illustrate the efficacy of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper concentrates on Bayesian state estimation approach in the presence of slow-rate integrated measurements. In chemical process, some quality variables, in the sense of measuring, often have an important characteristic resulting from the time taken for samples collection. These kinds of measurements are obtained based on sample of materials that are collected in a period of time. So, the measurement indicates the average property of the measurand in the period of samples collection, which is called Slow-Rate inTegrated Measurement (SRTM). In this paper, our goal is to estimate the fast-rate instantaneous states using available SRTM. Bayesian estimation approach is reformulated to acquire this goal. First, new Bayesian formulation is provided which ends to some complex integral formula. Then, with using the idea of Monte Carlo sampling method a numerical solution is presented for this problem. The advantage of the proposed algorithm is that it can deal with integrated measurement problem in a broader range of models with nonlinearity and non-Gaussian noise. The effectiveness of the proposed methodology is verified and demonstrated through simulation and empirical experiment on a level-flow laboratory-scale plant. [ABSTRACT FROM AUTHOR]

This paper aims to tackle the problem of multiobjective search for swarms of UAVs in unknown complex environments and proposes a multiobjective coordinated search algorithm based on a 3D-simplified virtual forced model (MOCS-3D-SVFM). First, it decomposes the search behaviour into the roaming search state and coordinated search state based on the detection of target signals by a swarm of UAVs. Second, a nearest neighbour exclusion diffusion (NNED) algorithm is introduced for the UAV of the wander search state, and a 3D adaptive inertia weight extended particle swarm algorithm (IAEPSO) is proposed by combining the motion characteristics of UAV with a 3D particle swarm algorithm aiming at the UAV with coordinated search state. Finally, the 3D-simplified virtual force model proposed based on the concept of the 2D-simplified virtual force model by the rotation matrix is introduced to solve the model parameters and the control strategy under the UAV of wander search state and coordinated search state is established, which effectively solves the real-time obstacle avoidance problem. Moreover, this paper sets the comparison mode of the three search methods; compared to Mode1, the search time T and energy consumption S can be significantly reduced, and the numerical simulations verify its effectiveness. [ABSTRACT FROM AUTHOR]

This paper investigates finite-horizon optimal control problem of continuous-time uncertain nonlinear systems. The uncertainty here refers to partially unknown system dynamics. Unlike the infinite-horizon, the difficulty of finite-horizon optimal control problem is that the Hamilton–Jacobi–Bellman (HJB) equation is time-varying and must meet certain terminal boundary constraints, which brings greater challenges. At the same time, the partially unknown system dynamics have also caused additional difficulties. The main innovation of this paper is the proposed cyclic fixed-finite-horizon-based reinforcement learning algorithm to approximately solve the time-varying HJB equation. The proposed algorithm mainly consists of two phases: the data collection phase over a fixed-finite-horizon and the parameters update phase. A least-squares method is used to correlate the two phases to obtain the optimal parameters by cyclic. Finally, simulation results are given to verify the effectiveness of the proposed cyclic fixed-finite-horizon-based reinforcement learning algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes the use of interval observers and viability theory in fault detection and isolation (FDI). Viability theory develops mathematical and algorithmic methods for investigating the viability constraints characterisation of dynamic evolutions of complex systems under uncertainty. These methods can be used for checking the consistency between observed and predicted behaviour by using simple sets that approximate the exact set of possible behaviour (in the parameter or state space). In this paper, FDI is based on checking for an inconsistency between the measured and predicted behaviours using viability theory concepts and sets. Finally, an example is provided in order to show the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, the iterative learning control problem for a class of nonlinear singular impulsive systems is discussed. Then, a D-type (derivative-type) iterative learning control algorithm is presented such that the output tracks the desired output trajectory as accurate as possible. Furthermore, the sufficient condition for the convergence of the proposed algorithm is established in detail. Finally, a numerical example is included to corroborate the theoretical analyses. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed optimisation problem over a multi-agent network, where the objective function is described by a sum of all the local objectives of agents. The target of agents is to collectively reach an optimal solution while minimising the global objective function. Under the assumption that the information exchange among agents is depicted by a sequence of time-varying undirected graphs, a distributed optimisation algorithm with uncoordinated time-varying step-sizes is presented, which signifies that the step-sizes of agents are not always uniform per iteration. In light of some reasonable assumptions, this paper fully conducts an explicit analysis for the convergence rate of the optimisation method. A striking feature is that the algorithm has a geometric convergence rate even if the step-sizes are time-varying and uncoordinated. Simulation results on two numerical experiments in power systems show effectiveness and performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates distributed connectivity-preserving consensus problems of networked multi-agent systems with limited communication ranges. Compared with existing literature, a main contribution of this paper is to present a new nonlinear transformation approach of consensus errors for preserving the initial interaction patterns of multi-agent systems. Both the consensus and the connectivity preservation can be achieved by using one transformed error function. Based on the proposed nonlinear error transformation, we derive distributed connectivity-preserving consensus algorithms for single-integrator dynamics, double-integrator dynamics and second-order nonlinear systems. The asymptotic stability of consensus errors and the connectivity preservation among agents are established through Lyapunov stability analysis. [ABSTRACT FROM PUBLISHER]

In this paper, the classical optimal control problem in air transportation system is studied. The optimisation model is based on the principle of 'first come first serve' and the arrival traffic flow only occurs in the first queue which is assumed to be infinite. In addition, it is assumed that all processing times and arrival intervals are predefined. This paper aims to propose a new optimal control problem of series air traffic system and an effective solution. The exact algorithm of each sub-segment is given, and the required results are obtained. Numerical experiments show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, two iterative algorithms are constructed to obtain the positive definite solutions of the discrete periodic algebraic Riccati matrix equations. In these two algorithms, the estimation of the unknown matrices are updated by using the available estimation information at the current iteration step. The convergence properties of the proposed algorithms are also given. Finally, numerical examples are employed to illustrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Model structure selection for nonlinear system identification has been widely studied over the last 30 years due to its great importance. There are many methods in the literature to deal with structure selection, although these methods have their specific benefits, they face some difficulties in selecting the structure for a parsimonious model. In this paper, two methods based on the Randomised Model Structure Selection (RaMSS) approach are introduced in order to deal with the structure selection problem. The first one is the Randomised Model Structure Selection with Error Reduction Ratio (RaMSS-ERR) that uses the error reduction ratio as a filter for the terms analysis, improving the convergence, and the second one is the Randomised Model Structure Selection with Genetic Inheritance (RaMSS-EGI) that uses a genetic inheritance in order to get a faster convergence. The methods were applied to benchmark models and the results are encouraging. Applications to systems with a large candidate regressor set and to a continuous stirred-tank reactor are also carried out. The results show that the proposed method may be used to identify both linear and nonlinear model structures with a reduced number of iterations, computational time, and number of explored models. [ABSTRACT FROM AUTHOR]

This paper investigates the off-line fault detectability of logical control networks (LCNs) by the method of semi-tensor product. Firstly, two concepts of off-line fault detectability, that is, weak off-line fault detectability and strong off-line detectability, are presented. Secondly, based on a recursive algorithm, the verification matrix for off-line fault detection is proposed to verify the off-line detectability of LCNs. Thirdly, necessary and sufficient conditions are presented to analyse the off-line fault detectability of LCNs. Finally, two illustrative examples show the effectiveness of the obtained new results. [ABSTRACT FROM AUTHOR]

This paper develops a correlation-based method into the Youla parameterisation structure for a fault-tolerant controller design strategy. By tuning the Youla parameters with the proposed correlation-based algorithm, a number of conditional faults described by the dual Youla parameters are attenuated. The traditional fault-tolerant control (FTC) schemes under the Youla parameterisation often require the gradient information of the defined cost function for minimisation, which is either tedious or even unfeasible with unknown fault model. However, the proposed correlation-based FTC algorithm in this paper can compensate the faults via system data without the explicit fault model or the cost function gradient information. It is also proved that the algorithm convergence can be achieved without identifying the unknown fault model. For illustration, a simulation example with corresponding comparisons are presented to show the effectiveness of the proposed method in the end. [ABSTRACT FROM AUTHOR]

This article focuses on the problem of the diffusion event-triggered sequential asynchronous state estimation for the stochastic multiplicative noise systems. In this paper, we propose a diffusion sequential asynchronous state estimation algorithm for each node to obtain the final estimate. In order to ease the communication burden of the system, we propose a two-stage event-triggered mechanism to avoid the unnecessary information transmissions, and the corresponding state estimation algorithm is derived. The sufficient conditions to guarantee the boundedness of the estimation error of the proposed algorithm are established. The effectiveness of the proposed algorithm is verified through its application to a target tracking system. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive generalised function projective synchronisation scheme of fractional-order chaotic systems with different dimensions and orders and fully unknown parameters is presented. On the basis of the Lyapunov method of fractional-order systems, a stability theorem of the fractional-order system with non-identical orders is proven. Using the fractional-order controller and adaptive control theory, sufficient conditions for synchronisation and unknown parameters update rules are obtained. Theoretical analysis and numerical simulations are provided to verify the validity of the proposed scheme. Moreover, synchronisation results are applied to secure communication via modified chaotic masking (MCM) method. The unpredictability of the scaling function matrix and the use of fractional-order systems with different orders can increase the security of the cryptosystem. The security analysis shows that the introduced algorithm has large key space, high sensitivity to encryption keys, higher security and the acceptable encryption speed. [ABSTRACT FROM AUTHOR]

In the presence of probabilistic communication networks between agents, the convergence analysis of max-consensus algorithm (MCA) is addressed in this paper. It is considered that at each iteration of MCA, all agents share their measurements with adjacent agents via local communication networks which is applicable in many multi-agent systems (MASs). It is assumed that the communication networks have Bernoulli dropouts, i.e. the information exchanged between agents may be lost with Bernoulli distribution. In the proposed method, the information topology of MAS is modelled as a dynamic graph with the Bernoulli adjacency matrix. It is proved that in the presence of Bernoulli dropouts and under non-restrictive assumptions concerning the MAS features and communication topology, the MCA converges with a probability one in the finite time. Furthermore, the upper bounds are provided by means of deterministic and probabilistic expressions for the expectation and dispersion of convergence time, respectively. It is shown that the proposed upper bounds are asymptotic, i.e. there are specific conditions of MAS in which the convergence time of MCA tends to the proposed upper bounds. The convergence accuracy of MCA is discussed in terms of probabilistic equations. The validity of the proposed theorems is illustrated by means of simulation results. [ABSTRACT FROM AUTHOR]

This paper is concerned with convergence characterisation of an iterative algorithm for a class of reverse discrete periodic Lyapunov matrix equation associated with discrete-time linear periodic systems. Firstly, a simple necessary condition is given for this algorithm to be convergent. Then, a necessary and sufficient condition is presented for the convergence of the algorithm in terms of the roots of polynomial equations. In addition, with the aid of the necessary condition explicit expressions of the optimal parameter such that the algorithm has the fastest convergence rate are provided for two special cases. The advantage of the proposed approaches is illustrated by numerical examples. [ABSTRACT FROM AUTHOR]

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two sub-algorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance. [ABSTRACT FROM AUTHOR]

This paper proposes an exact order reduction approach for the multidimensional (n-D) Fornasini-Marchesini (F-M) model by making use of the common eigenvector. Specifically, by introducing the concept of common eigenvectors, sufficient conditions of exact order reductions are developed for an n-D F-M model, which are able to simultaneously deal with n eigenvalues of the system matrices of the n-D F-M model. The obtained results reveal, for the first time, the internal connection between the multiple eigenvalues of the system matrices and the reducibility of the considered n-D F-M model. Then, a corresponding algorithm is proposed to exactly reduce the order of an n-D F-M model as much as possible. Examples are given to illustrate the details as well as the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we review some of the main discrete and finite time average consensus implementations in the literature, discussing their strengths and shortcomings from a theoretical and empirical point of view. In particular, we compare the computational characteristics of the different algorithms, their behaviour considering different underlying network topologies, their ability to withstand packet losses and their robustness to attacks where a malicious node aims to steer the result of the algorithm towards a desired value, without letting the other nodes detect the attack. Specifically, we will discuss synchronous approaches, where the nodes broadcast their messages, and asynchronous approaches, where the nodes need to be able to address their neighbours individually on a point-to-point basis (i.e. by direct communication between a specific sender and a specific receiver). With the aim to overcome some critical aspects of the considered methodologies, in this paper we present an asynchronous consensus algorithm based on a broadcast-only approach. The algorithm is characterised by a good trade-off between the robustness of synchronous approaches and to low computational demands of asynchronous methods. [ABSTRACT FROM AUTHOR]

The domain of attraction of a given non-linear system constitutes a zone of safe operation that can avoid unnecessary operational restrictions. In this paper, an alternative approach to the estimation of the domain of attraction of a saturated linear system is presented. Given a system with m saturated control inputs, we show how to choose a linear difference inclusion (LDI) in such a way that the conservativeness in the estimation is reduced. For that purpose, an LMI problem with 2 m   +   m constraints must be solved. In this paper, an algorithm that estimates the domain of attraction of the non-linear system is provided. Moreover, sufficient conditions to guarantee that the proposed algorithm obtains the greatest domain of attraction for the linear difference inclusion are given. Some illustrative examples are presented. [ABSTRACT FROM AUTHOR]

Nowadays, the Inertial Navigation System/Global Navigation Satellite System (INS/GNSS) integrated navigation system is widely used in many applications. The extended Kalman Filter (EKF) is a popular data fusion method for the INS/GNSS integrated navigation system. However, the process and measurement noise covariance matrices of the EKF cannot be modelled accurately due to varied scenes and complicated GNSS signal errors in urban environments, which undermines or deteriorates the EKF's performance. To mitigate noise covariance uncertainties' influence, this paper proposes an adaptive EKF algorithm named SARSA EKF, which enables the State-Action-Reward-State-Action (SARSA) method in EKF to realise the autonomous selection of the noise covariance matrices based on the Q-value. Meanwhile, a pruning algorithm is designed to remove inappropriate selections of noise covariance matrices and enhance the performance. The simulation and field test results indicate that the positioning accuracy of the SARSA EKF is better than the traditional EKF and the Q-learning EKF (QLEKF). The positioning accuracy's mean error of the SARSA EKF decreases by 34.32% and 25.95% compared with the traditional EKF and the QLEKF, respectively. And the positioning accuracy's standard deviation of the SARSA EKF decreases by 41.74% and 32.99% compared with the traditional EKF and the QLEKF, respectively. [ABSTRACT FROM AUTHOR]

This paper establishes a framework within which interaction control is designed for the aerial slung load system composed of an underactuated aerial vehicle, a cable and a load. Instead of developing a new control law for the system, we propose the interaction control scheme by the controllers for under-actuated aerial systems. By selecting the deferentially flat output as the configuration, the equations of motion of the two systems are described in an identical form. The flight control task of the under-actuated aerial vehicle is thus converted into the control of the aerial slung load system. With the help of an admittance filter, the compliant trajectory is generated for the load subject to external interaction force. Moreover, the convergence of the whole system is proved by using the boundedness of the tracking error of vehicle attitude tracking as well as the estimation error of external force. Based on the developed theoretical results, an example is provided to illustrate the design algorithm of interaction controller for the aerial slung load via an existing flight controller directly. The correctness and applicability of the obtained results are demonstrated via the illustrative numerical example. [ABSTRACT FROM AUTHOR]

This paper focuses on the recursive parameter estimation problem of the exponential autoregressive (ExpAR) model. Applying the Newton search and multi-innovation theory, a multi-innovation Newton recursive algorithm is presented for identifying the ExpAR model. In order to improve the computational efficiency, the hierarchical identification principle is employed to decompose an ExpAR model into two sub-models, and to derive a hierarchical multi-innovation Newton recursive algorithm. A simulation example is provided to demonstrate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper is devoted to the design of an optimal infinite-dimensional Luenberger observer combined with a linear-quadratic state feedback controller for a system of hyperbolic PDEs. The design is based on the duality fact between the control design and the observer design. Both the original linear-quadratic and dual control problems have been solved by using the associated Riccati equations. A general algorithm that combines the designed observer together with the (estimated) state-feedback controller has been developed. The theoretical development has been applied to a fixed-bed reactor to validate the performances of the designed observer-controller via numerical simulation. Estimation and control of the temperature and the reactant concentration in a fixed-bed reactor is investigated by using the developed algorithm, which lead to express the jacket temperature (manipulated variable) as a feedback of the estimated temperature and concentration in the reactor. [ABSTRACT FROM AUTHOR]

To develop an effective control and monitoring scheme for automotive engines, a precise knowledge of the parameters and unmeasurable states of the nonlinear model capturing the overall dynamics of engines is of utmost importance. For a new vehicle out of the assembly line, the nonlinear model has constant parameters. However, in the long run, due to regular wear-and-tear, and for other unpredictable disturbances, they may change. The main challenges are how to obtain the information of parameters and states under the influence of process noise and measurement noise. To address these challenges, we present a new integrated state and parameter estimation algorithm in this paper for spark ignition (SI) engines based on the constrained unscented Kalman filter and the improved recursive least square technique. The system under consideration is a highly nonlinear mean value SI engine model consisting of the throttle, intake manifold, engine speed dynamics, and fuel system. The performance of the proposed algorithm in terms of root-mean-square-error and robustness with regards to initial conditions and random noises is analysed through exhaustive simulation scenarios considering constant, and time-varying parameters. In addition, the performance of other state-of-the-art estimation algorithms is also compared with that of the developed integrated algorithm. [ABSTRACT FROM AUTHOR]

Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of the characteristic equation and the argument principle, an algorithm is generated, which is shown to outperform the Lyapunov-Krasovskii (LK) approaches with respect to conservatism in the presented examples. Despite the conventional manual use of the Nyquist criterion, the proposed algorithm is fully algebraic, cheaper and easily implemented in computer programs. The kernel matrix function in this method is not limited to the exponential type and can include any bounded real function as its elements. [ABSTRACT FROM AUTHOR]

In this paper, we for the first time explore the model order reduction (MOR) of parametric systems based on the tensor techniques and a parallel tensor compression algorithm. For the parametric system characterising multidimensional parameter space and nonlinear parametric dependence, we first approximate the system matrices by tensor functions of the parameters, whose first-order coefficients are third-order tensors. In order to effectively reduce the computational cost and the storage burden, we propose a parallel tensor compression algorithm based on Tensor-SVD to deal with the tensors in the tensor functions. Then, we obtain the low-rank approximation in Kruskal form of third-order tensors. After that, by computing the first several expansion coefficients of the state variable with the selected parameter vectors, the projection matrix is constructed to obtain the reduced parametric system. Theoretical analysis shows that the reduced parametric system can match the first several expansion coefficients of the output variable of the original system at the selected parameter vectors. Moreover, the stability of the proposed MOR method is discussed. Finally, the efficiency of the proposed method is illustrated by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents a novel training algorithm for adaptive neuro-fuzzy inference systems. The algorithm combines the error back-propagation algorithm with the variable structure systems approach. Expressing the parameter update rule as a dynamic system in continuous time and applying sliding mode control (SMC) methodology to the dynamic model of the gradient based training procedure results in the parameter stabilizing part of training algorithm. The proposed combination therefore exhibits a degree of robustness to the unmodelled multivariable internal dynamics of the gradient-based training algorithm. With conventional training procedures, the excitation of this dynamics during a training cycle can lead to instability, which may be difficult to alleviate owing to the multidimensionality of the solution space and the ambiguities concerning the environmental conditions. This paper shows that a neuro-fuzzy model can be trained such that the adjustable parameter values are forced to settle down (parameter stabilization) while minimizing an appropriate cost function (cost optimization), which is based on state tracking performance. In the application example, trajectory control of a two degrees of freedom direct drive robotic manipulator is considered. As the controller, an adaptive neuro-fuzzy inference mechanism is used and, in the parameter tuning, the proposed algorithm is utilized. [ABSTRACT FROM AUTHOR]

This paper addresses a fault accommodation issue for flexible hypersonic vehicles by the static output feedback. Firstly, a longitudinal dynamics for hypersonic vehicles is established in the ODE-beam cascade form and the distributed fault model is built. Next, a novel fault accommodation scheme is developed to achieve fault accommodation and vibration suppression. Such a control strategy is based on the control separation formulation: one component is for accommodating the distributed fault, another one is for the closed-loop stability. The input-to-state stability of the closed-loop system is analysed by using the direct Lyapunov method and bilinear matrix inequalities technique. Then, a new algorithm is provided to obtain the control gain matrices of the fault-tolerant control law. Finally, the simulation results are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, a method for fault estimation with a multiplicative model in a nonlinear system by the unscented Kalman filter is introduced. The faults appear in the form of component, sensor, and actuator in the system equations. By using the augmented method, a fault signal will be as state variable of the system, the system dynamic equations are rewritten to represent a fault as a state variable. The existence of nonlinear equations in the presence of system noises results in an identical non-Gaussian noise, which leads to the difficulty in solving the problem of fault estimation with the unscented Kalman filter. Therefore, a filter combining a Gaussian mixture model (GMM) and the augmented ensemble unscented Kalman filter (AEnUKF) is designed to estimate the fault in this class of nonlinear systems. Suitable conditions and assumptions are appointed to guarantee the convergence of the estimation error. Next, the performance of the proposed method is evaluated by simulating a bioreactor system. The results of the simulation for the multiplicative fault estimation demonstrated performance by the AEnUKF-GMM algorithm better than the AUKF in the presence of non-Gaussian noise. [ABSTRACT FROM AUTHOR]

In this paper, a dimension reduction method via general orthogonal polynomials and multiorder Arnoldi algorithm is proposed, which focuses on the topic of structure-preserving for k-power bilinear systems. The main procedure is using a series of expansion coefficient vectors of each state variables in the space spanned by general orthogonal polynomials that satisfy a recurrence formula to generate a projection based on multiorder Arnoldi algorithm. The resulting reduced-order model not only matches a desired number of expansion coefficients of the original output but also retains the topology structure. Meanwhile, the stability is well preserved under some certain conditions and the error bound is also given. Finally, two numerical simulations are provided to illustrate the effectiveness of our proposed algorithm in the views of accuracy and computational cost. [ABSTRACT FROM AUTHOR]

In the time- and frequency-limited model order reduction, a reduced-order approximation of the original high-order model is sought to ensure superior accuracy in some desired time and frequency intervals. We first consider the time-limited H 2 -optimal model order reduction problem for bilinear control systems and derive first-order optimality conditions that a local optimum reduced-order model should satisfy. We then propose a heuristic algorithm that generates a reduced-order model, which tends to achieve these optimality conditions. The frequency-limited and the time-limited H 2 -pseudo-optimal model reduction problems are also considered wherein we restrict our focus on constructing a reduced-order model that satisfies a subset of the respective optimality conditions for the local optimum. Two new algorithms have been proposed that enforce two out of four optimality conditions on the reduced-order model upon convergence. The algorithms are tested on three numerical examples to validate the theoretical results presented in the paper. The numerical results confirm the efficacy of the proposed algorithms. [ABSTRACT FROM AUTHOR]