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To solve the control problem of time-varying state-scale nonlinear systems whose initial state is not affected by settling time, fixed-time convergence algorithms are proposed for first-order systems and higher-order systems in this paper. First, a scalar model is used to illustrate how the time-varying feedback parameter can guarantee that the system achieves asymptotic stability while achieving finite-time convergence, and it is proved that the settling time obtained in this paper is only related to the prescribed boundary. This allows us to design the settling time with an appropriate parameter based on the prescribed boundary. To exhibit the effectiveness and extensibility of the proposed algorithm for first-order scalar systems, the results are subsequently extended to general higher-order systems based on the backstepping method. By introducing numerical simulation results, this paper verifies that the proposed algorithm will make the system achieve asymptotic stability and its output can converge to a given boundary, regardless of the system's initial states. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of transforming a single-input single-output discrete-time system into the extended observer form which comprises a linear observable component and a nonlinear injection term depending on the input, output and their forward shifts up to a finite order. The necessary and sufficient conditions for the existence of the extended observer form are provided in terms of vector fields. The algorithm is presented to find a parametrised state transformation necessary to transform the system into the extended observer form. The obtained results are applicable also in case of non-reversible systems. [ABSTRACT FROM AUTHOR]

One of the main difficulties for application of sliding mode control is the presence of chattering. It is a well known fact that the amplitude of chattering is proportional to the magnitude of discontinuous control. The problem can be alleviated by making the magnitude as small as possible while still ensuring the existence of the sliding mode. In this paper, a novel predefined-time single layer adaptive scheme based on equivalent concept with a relaxed assumption about unknown dynamics is proposed for dynamically tuning the gain associated with the control magnitude, and applying this scheme in sliding mode control algorithms enables decreasing the control action magnitude to the minimum possible value remaining the characteristic of finite-time convergence. Simulation results are shown to verify the effectiveness of the designed scheme. [ABSTRACT FROM AUTHOR]

Designing a full-state observer for nonlinear systems has always been accompanied by challenges and restrictive constraints. Mainly, applying a state observer in nonlinear systems with non-minimum phase characteristics is more challenging when the limiting constraints are not satisfied due to diverging internal dynamics. In this paper, a robust sliding-mode observer approach has been successfully employed to estimate the states of nonlinear systems with unbounded and diverging dynamics. The design principles of this observer are based on applying a classifying algorithm in single-input single-output and multiple-input multiple-output nonlinear systems. It is noteworthy that this observer is highly robust against disturbance, uncertainty and measurement noise, and its conditions are less conservative compared to previous nonlinear sliding-mode observers. One novel feature of the proposed observer is that while the system's state gets unbounded and diverged in fault-occurring scenarios or critical circumstances, this observer retains accuracy. The efficiency of the proposed observer is verified in the simulation results for two nonlinear industrial systems, including a hydro-turbine power generation plant and a continuous stirred tank reactor. [ABSTRACT FROM AUTHOR]

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]

In this paper, we are concerned with the investigation problem of finding a common element of the set of fixed points of a total uniformly L-Lipschitzian mapping and the set of solutions of a system of generalized nonlinear variational-like inequalities. For this end, based on P-η-proximal mapping, an iterative algorithm is constructed and under some suitable conditions, the strong convergence and stability of the sequence generated by our proposed iterative algorithm to a common element of the above two sets are proved. [ABSTRACT FROM AUTHOR]

For a class of discrete-time nonlinear systems, this paper proposes a discrete-time sliding mode control algorithm with an exponential term that acts as a variable gain to improve the convergence to a bounded region around the origin for the state variable. To compensate for unknown, but bounded disturbances, it has been employed a discontinuous function through a discrete-time integral action. A discrete-time neural network has also been employed to identify such nonlinear system with a block controllable structure. Finally, the proposed controller and the neural network algorithms are applied to a discretised direct current (DC) motor to follow a desired admissible trajectory. Numerical simulations show the effectiveness of the proposed control law. [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 distributed filtering problem for a class of delayed nonlinear systems with random sensor saturation (RSS) under a dynamic event-triggered mechanism. The nonlinear function is assumed to satisfy the Lipschitz condition. A dynamic event-triggered mechanism is employed to further reduce the innovation transmission frequencies among the adjacent nodes. Both the Bernoulli distributed random variables and saturation function are employed to model the phenomenon of RSS. The aim of this paper is to design a sub-optimal filter such that the covariance of the filtering error has an upper bound, which is minimized by appropriately computing the filter gain. Furthermore, the error boundedness is analysed and a sufficient criterion is presented to ensure that the filtering error is mean-square bounded. Finally, a numerical example is provided to verify the effectiveness of the proposed filtering algorithm. [ABSTRACT FROM AUTHOR]

Direct model predictive control applications for nonlinear systems can result in non-convex minimisation problems, which is additionally complicated if systems are non-minimum phase. In this paper, the Particle Swarm Optimisation (PSO) is applied for these global minimisation problems and tested on two selected nonlinear systems. Obtained results show that, in comparison to the sequential quadratic programming method, PSO is less vulnerable to local minima, and, with appropriate parameters, provides superior quality in nonlinear predictive control. The main results concerning PSO application show that the higher number of particles, comparing to the number of iterations, provides improved accuracy with limited computational burden; this way up to 5 % reduction of a proposed quality index is obtained preserving unchanged time of calculations. The performance is also boosted when after several iterations of the algorithm greater emphasis is put on the local search, which is achieved by appropriate learning factors and inertia weight. [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 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 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]

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 an improved Gaussian particle filter integratingthe Artificial Fish School Algorithm to optimise the measured values to improve the overall estimation accuracy of the system. Meanwhile, it also solves the problems of susceptibility to interference and insufficient estimation accuracy in nonlinear systems. Furthermore, since the calculation time of the fusion algorithm increases, in order to ensure the speed of state estimation, the linear transformation of standard particle swarm is used to replace the particle sampling link of Gaussian particle filter. Simulation results show that the calculation speed of a fast Gaussian Particle Filter based on the Artificial Fish School Algorithm is 21.7% faster than the Particle Filter based on the Artificial Fish School Algorithm. Compared with Particle Filter, Gaussian particle filter, and the Artificial Fish School Algorithm, the proposed algorithm has a higher accuracy. [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]

Numerical simulation of a two-phase compressible displacement problem is considered in this paper, modelled by a nonlinear system of PDEs. Considering the characters of mathematical model, we present an efficient combination algorithm of the method of characteristics (MOC) and mixed finite volume element (MFVE). The MFVE is used for computing the pressure, Darcy velocity and the saturation. Furthermore, the saturation equation is convection-dominated. MOC eliminates numerical dispersion and nonphysical oscillation, and computes the values at the sharp fronts well. An MFVE-MOC is formed for the saturation. An optimal error estimates in l2 norm is concluded. Finally, numerical examples are given to show the effectiveness and practicability. The composite scheme possibly solves this actual problem well. [ABSTRACT FROM AUTHOR]

The paper investigates the global adaptive output regulation problem (ORP) for nonlinear systems with full-state constraints (FSCs). First, in order to avoid the disadvantages of barrier Lyapunov functions (BLFs) method and logarithmic constraint functions, radical constraint functions method is proposed to solve the FSCs problem of nonlinear systems. Second, a new internal model is designed based on the regulator equations. Third, the ORP of nonlinear systems is transformed into a stabilization problem. Then, according to the changing supply functions method and the Lyapunov analysis method, a non-backstepping control algorithm is proposed to ensure that all signals of the closed-loop system are globally asymptotically bounded, the tracking error is asymptotically stable, and all states of the system can be constrained. Finally, two simulation examples show the effectiveness of the control algorithm. [ABSTRACT FROM AUTHOR]

The diversity of power generation provides an important guarantee for the electric reliability of human society. The forecasting of power generation is an important topic in the electrical industry. However, most of recent work are focus on some special type power generation, overall electric load forecasting is lacking attention. In order to improve practical applications, this paper proposes a power generation predication method based on one of popular machine learning algorithm that is support vector machine, so as to predict both overall power generation and some special types of power generation. The nonlinear relation of electric net power generation is explored by historical monthly recorded data, this relation can help the predication of net electric generation for the next month. Experimental results show that our proposed electric generation forecasting method based on support vector machine can get suitable predication model and achieve high predicted precision, which is in accordance with the real data in the record. [ABSTRACT FROM AUTHOR]

This paper presents sliding mode tracking control for a class of uncertain nonlinear systems with unknown parameters and system states. The sliding mode tracking controller with the differential evolution (DE) algorithm using integral-chain differentiator (ICD) is designed for the trajectory tracking in uncertain nonlinear systems. The ICD added into the sliding mode tracking systems provides the estimation of unknown states. The DE optimisation algorithm on the basis of ICD realises the unknown parametric identification in the limitation of unknown system states. The simulation is implemented to illustrate that the combined control scheme achieves high precision tracking performances. [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]

This paper presents a new hybrid PPSOGSA algorithm based on the phasor particle swarm optimization (PPSO) and gravitational search algorithm (GSA) for solving the Volt/VAr/THDv control optimization problem in radial distribution systems with non-linear loads. The PPSOGSA's performance is analyzed and evaluated using the standard IEEE 30-bus radial distribution test system. The optimal solutions are obtained based on the following three optimization criteria: minimization of total active power losses, minimization of the voltage deviation, and a simultaneous minimization of total active power losses and voltage deviation. The voltage total harmonic distortion levels (THDv) are estimated using the decoupled harmonic power flow (DHPF) algorithm. Simulation results, obtained using the proposed PPSOGSA-based approach, are compared with those obtained using the other optimization algorithms such as PSO, PPSO, GSA, and PSOGSA. It is shown that the PPSOGSA-based approach has better performance in comparison to the other optimization techniques. [ABSTRACT FROM AUTHOR]

This paper studies one identification problem for a piecewise affine system which is a special nonlinear system. As the difficulty in identifying the piecewise affine system is to determine each separated region and each unknown parameter vector simultaneously, here we propose a multi-class classification process to determine each separated region. This multi-class classification process is similar to the classical data clustering process, and the merit of our strategy is that the first-order algorithm of convex optimization can be applied to achieve this classification process. Furthermore, to relax the strict probabilistic description on external noise and identify each unknown parameter vector, a zonotope parameter identification algorithm is proposed to compute a set that contains the parameter vector, consistent with the measured output and the given bound of the noise. To guarantee our derived zonotope not growing unbounded with iterations, a sufficient condition for this requirement to hold may be formulated as one linear matrix inequality. Finally, a numerical example confirms our theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a new method to design an adaptive controller for generating stable limit cycles in a class of nonlinear systems subject to unknown dead-zone nonlinearity and unknown parameters. In this regard, the set stabilisation-based approach is utilised and the proper Lyapunov function is taken concerning the geometric shape of the desired limit cycle. Firstly, the state feedback control is designed to create the desired limit cycle in the second-order subsystem and then, extended to the arbitrary n order system through the adaptive backstepping technique. Besides, the explosion of a complex problem, which happens during the backstepping implementation in high-order systems, is handled. In the final stage, the boundedness of all the closed-loop signals is guaranteed via Lyapunov analysis. The effectiveness of the proposed control algorithm is demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper addresses decentralised optimal control problems for large-scale nonlinear systems subject to mismatched interconnections with unknown time-delay by adaptive dynamic programming. To eliminate the effects of mismatched interconnections with unknown time-delay, a novel local value function is constructed to transform the decentralised control problem into an optimal control problem. A local robust observer is established to identify the bound of the unknown interconnections. Then, based on the observer-critic architecture, the decentralised optimal control policy is achieved by solving local Hamiltonian–Jacobi–Bellman equation via local policy iteration algorithm. The stability of the closed-loop large-scale nonlinear system is guaranteed to be uniformly ultimately bounded by implementing a set of decentralised control policies. Simulation examples demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, the adaptive fuzzy iterative learning control scheme is proposed for coordination problems ofMth order (M≥ 2) distributed multi-agent systems. Every follower agent has a higher order integrator with unknown nonlinear dynamics and input disturbance. The dynamics of the leader are a higher order nonlinear systems and only available to a portion of the follower agents. With distributed initial state learning, the unified distributed protocols combined time-domain and iteration-domain adaptive laws guarantee that the follower agents track the leader uniformly on [0,T]. Then, the proposed algorithm extends to achieve the formation control. A numerical example and a multiple robotic system are provided to demonstrate the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

This work is motivated by a recent work on an extended linearproximal point algorithm(PPA) [B.S. He, X.L. Fu, and Z.K. Jiang,Proximal-point algorithm using a linear proximal term, J. Optim. Theory Appl. 141 (2009), pp. 299–319], which aims at relaxing the requirement of thelinearproximal term of classical PPA. In this paper, we make further contributions along the line. First, we generalize the linear PPA-based contraction method by using a nonlinear proximal term instead of the linear one. A notable superiority over traditional PPA-like methods is that the nonlinear proximal term of the proposed method may not necessarily be a gradient of any functions. In addition, thenonlinearityof the proximal term makes the new method more flexible. To avoid solving a variational inequality subproblem exactly, we then propose aninexactversion of the developed method, which may be more computationally attractive in terms of requiring lower computational cost. Finally, we gainfully employ our new methods to solve linearly constrained convex minimization and variational inequality problems. [ABSTRACT FROM PUBLISHER]

The goal of the paper is to identify the Hammerstein-type systems excited and disturbed by correlated random processes. The problem is semi-parametric in the sense that the nonlinear static characteristic is recovered without prior knowledge about the linear dynamic block, i.e. when its order is unknown. The method is based on the instrumental variables technique, with the instruments generated by input inverse filtering. It is proved that, in contrast to the least-squares-based approach, the proposed algorithm leads to an asymptotically unbiased, strongly consistent estimate. Constructive procedures of instrumental variables generation are given for some popular cases. [ABSTRACT FROM PUBLISHER]

This paper presents an output-feedback control strategy based on the variable gain super-twisting algorithm. The proposal achieves robust global/semi-global exact tracking results for plants with arbitrary relative degree. This is ensured in spite of parametric uncertainties and disturbances that may be state-dependent and time-varying. The construction of such controller is based on a (non)homogeneous higher order sliding-mode differentiator with dynamic gains. The gain adaptation schemes for the controller and differentiator are based on norm observers to overcome the lack of state measurement. The continuous nature of the obtained control signal alleviates the chattering phenomenon. The stability properties of the proposed controller are demonstrated by means of a Lyapunov function-based analysis. The theoretical results are verified through a simulation example, and experimentally tested on a seesaw module. [ABSTRACT FROM AUTHOR]

This article discusses the issue of robust adaptive neural network (NN) consensus tracking control for nonlinear strict-feedback multi-agent systems with quantised input. By combining the neural network approach with robust techniques, a novel switching function is introduced to guarantee the tracking performance of this system. To estimate the unmeasured state, an NN-based adaptive state observer is developed. Based on backstepping dynamic surface control algorithms, a robust output feedback controller is constructed to guarantee that all signals in the closed-loop system remain globally uniformly ultimately bounded. Finally, numerical simulations are carried out to demonstrate the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]

In this article, two adaptive iterative learning control (ILC) algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced. [ABSTRACT FROM AUTHOR]

Throughout this paper, we present a method for designing feedback-laws which stabilise nonlinear discrete Volterra systems. Our method is based on a factorisation algorithm which decomposes the original system as a composition of a δ-polynomial and a linear series. [ABSTRACT FROM AUTHOR]

In this paper, we propose an adaptive control scheme that can be applied to nonlinear systems with unknown parameters. The considered class of nonlinear systems is described by the block-oriented models, specifically, the Wiener models. These models consist of dynamic linear blocks in series with static nonlinear blocks. The proposed adaptive control method is based on the inverse of the nonlinear function block and on the discrete-time sliding-mode controller. The parameters adaptation are performed using a new recursive parametric estimation algorithm. This algorithm is developed using the adjustable model method and the least squares technique. A recursive least squares (RLS) algorithm is used to estimate the inverse nonlinear function. A time-varying gain is proposed, in the discrete-time sliding mode controller, to reduce the chattering problem. The stability of the closed-loop nonlinear system, with the proposed adaptive control scheme, has been proved. An application to a pH neutralisation process has been carried out and the simulation results clearly show the effectiveness of the proposed adaptive control scheme. [ABSTRACT FROM AUTHOR]

This paper presents a new robust predictive controller for a special class of continuous-time non-linear systems with uncertainty. These systems have bounded disturbances with unknown upper bound as well as constraints on input states. The controller is designed in the form of an optimization problem of the 'worst-case' objective function over an infinite moving horizon. Through this objective function, constraints and uncertainties can be applied explicitly on the controller design, which guarantees the system stability. Next, LMI tool is used to improve the calculation time and complexity. To do this, in order to find the optimum gain for state-feedback, the optimization problem is solved using LMI method in each time step. Finally, to show the efficiency and effectiveness of the proposed algorithm, a surge phenomenon avoidance problem in centrifugal compressors is solved. [ABSTRACT FROM AUTHOR]

In a series of two papers, we analyze the numerical performances of the preconditioned conjugate gradient algorithms (BICGSTAB and GMRES) and multigrid method in solving two-dimensional multicomponent mass transfer equations. The present test problems are steady-state, linear and nonlinear diffusion-reaction equations. The nonlinear algorithm used in connection with the preconditioned conjugate gradient methods is the modified Picard iteration. Theoretical results about the preconditioning are presented. The multigrid algorithm used is the Full Approximation Storage algorithm. The finite difference method was used to discretize the mathematical model equations. The numerical results obtained show good numerical performances. [ABSTRACT FROM PUBLISHER]

One typical approach to implement model predictive control in relatively fast sample rate applications utilises linearised plant models to simplify the online optimisation problem in the presence of limited computation budget. A number of linearisation points may be used to account for the variation in the non-linear plant over the entire operating domain, leading to potential switched linear time-invariant (LTI) or linear time-variant (LTV) implementations. The choice of these linearisation points, and the regions over which they are considered valid, can have a significant impact on the closed loop performance of the overall controller. In this work, in the presence of a high-fidelity digital twin of a non-linear plant, a numerical algorithm for the selection of linearisation points is proposed. The approach makes use of the concept of disturbance sets to determine both the linearisation points and the domain to which each linearisation point applies. The use of disturbance sets provides an implicit connection to closed-loop controller performance if robust model predictive control algorithms are implemented. The proposed approach is implemented for the challenging problem of diesel air-path control, with simulation results on a high-fidelity mean value engine model used to demonstrate the efficacy of the approach. [ABSTRACT FROM AUTHOR]

In this paper, nonlinear model predictive control (NMPC) has been used to control an induction motor (IM). The IM model that is used in the control is third or fifth order model that is based in the vector analysis of the IM. In the third order model, the rotor speed and fluxes are considered as system states where the source frequency and the stator currents are control variables. In the fifth order, the state variables involve stator currents, rotor speed and fluxes where the control variables are stator voltages and source frequency. The formulated nonlinear optimal control problems that are used in the NMPC frameworks are not based on the field ordination technique, however, the input frequency is computed by the MPC optimizer. Moreover, the convergence or stability of the motor speed is guaranteed using stability auxiliary constraint. Simulation studies show the performance of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

This paper was aimed at using an adaptive control to develop a backstepping method for a special class of nonlinear systems, which requires no information on the upper bound of parametric uncertainty or disturbance. In this research, a novel control approach, including a developed backstepping method and an adaptive controlling method, is introduced as an adaptive generalized backstepping method (AGBM). Compared to the standard backstepping method, AGBM is far more efficient because the standard method is applicable in strictly feedback systems, but AGBM expands this class of systems. Another advantage of AGBM is that it can be applied to a special class of nonlinear systems with unmatched uncertainty as well as unknown upper bound disturbance. In this method, an adaptive controlling method is used to compensate uncertainty and parametric uncertainty besides stabilizing the controller against disturbances applied to the system. Finally, numerical simulation results demonstrate the advantages and feasibility of the presented algorithm, showing that the AGBM controller guarantees robustness and system stability in the presence of disturbance and uncertainty. [ABSTRACT FROM AUTHOR]

Cardiac or heart sound ca.rries important diagnosis information for several cardiovascular diseases, such as natural or prosthetic valve dysfunction and heart failure. Hence, algorithms are required for the analysis of cardiac sound for computer-based automatic diagnosis. In the cardiac sound-based analysis, one of the tasks is to classify abnormal cardiac sounds, i.e. murmurs, caused by various cardiac anomalies. We introduce a new feature named system response which is chosen to be estimated using wavelet bispectrum over Fourier bispectrum because of non-stationary and non-Gaussian nature of cardiac sounds. System response essentially characterizes the cardiac structure responsible for the production of cardiac sounds which is later employed to automatically classify different types of cardiac murmurs. In cases of various types of cardiac murmurs, such as aortic regurgitation and mitral stenosis, system response of the cardiac structures is studied in this paper. Later, an artificial neural network-based classifier is constructed using the system response as a set of features to automatically classify murmur types. Performance of the classifier is obtained with the sensitivity of 93.57% and specificity of 94.24% which is comparable with the sate of the art. Furthermore, system response computed from wavelet bispectrum shows 4% higher accurate classification than Fourier bispectrum. [ABSTRACT FROM AUTHOR]

Two algorithms named Recursive Least Square algorithm for Ill-Conditioned situations (RLS-IC) and Multi Innovation Stochastic Gradient algorithm for Ill-Conditioned situations (MISG-IC) are proposed based on multi-innovation identification theory, least squares, stochastic gradient and singular value decomposition to identify Hammerstein systems in ill-conditioned situations. In ill-conditioned situations, identification algorithms based on classic least-squares and stochastic gradient lead to uncertain estimates and may be ineffective. Simulation examples show that the proposed algorithms are suitable for parameter estimation in Hammerstein nonlinear systems with ill-conditioned situations. [ABSTRACT FROM AUTHOR]

For the fractional-order Hammerstein system with white noise, the difficulty of identification is that the parameters of the linear and the nonlinear blocks and the fractional order are unknown and the intermediate variable and the states are unmeasurable. To overcome this difficulty, we transform the system from an input nonlinear pseudo-state-space system to an input–output representation and we develop an algorithm based on the Recursive Least Squares, the Levenberg–Marquardt and the Auxiliary Model Principle. The convergence of the identified parameters is studied. The performance of the proposed algorithm are tested by two numerical examples. [ABSTRACT FROM AUTHOR]

An optimal feedback input design method for active parameter identification of dynamic nonlinear systems is presented. The problem is formulated in a receding horizon framework where extended Kalman filter is used for system identification and the optimal input is designed in a nonlinear model predictive control framework. Towards this end, a suitable optimality criterion related to the unknown parameters is proposed and motivated as an information measure. The aim of the optimal input design is to yield maximal information from the unknown system by minimising the cost related to the unknown parameters while maintaining some process performance and satisfying the possible constraints. Simulations are performed to show the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

A distributed adaptive containment control scheme is developed for a class of discrete-time multi-agent systems (MASs) under directed graphs. Each agent's model is described by nonlinear dynamics with unknown parameters that are nonlinearly coupled with the states. To deal with the uncertainties, a criterion function with weighted factor is adopted. By minimising the criterion function, a projection algorithm for each agent is designed to estimate the unknown parameters. Using the estimated parameters, an adaptive controller with only local information is designed for each agent to achieve containment control of MASs. Under the proposed distributed adaptive containment control scheme, it is guaranteed that all the leaders can finally track their reference signals and all the states of followers asymptotically converge to the convex hull formed by leaders (i.e. the convex hull formed by the reference signals). Finally, two simulation examples are given to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Numerical solutions of nonlinear system of two-dimensional integral equations have been rarely investigated in the literature. In this study, we suggest a numerically practical algorithm to approximate the solutions of nonlinear system of two-dimensional Volterra–Fredholm and Volterra integral equations. This scheme is based on two-dimensional Legendre wavelet to reduce these nonlinear systems of integral equations to a system of nonlinear algebraic equations. The main characteristic of this approach is high accuracy and computational efficiency of performing which are the consequences of Legendre wavelet properties. The main benefit of this basic function is their ability to detect singularities and their efficiency in dealing with non-sufficiently smooth function in comparison with Legendre polynomials and they minimize the error. The convergence analysis and error bound of the proposed Legendre wavelet method is investigated. Numerical examples confirm that the Legendre wavelet collocation method is accurate, reliable for solving nonlinear system of two-dimensional integral equations. [ABSTRACT FROM AUTHOR]

A sufficiently convenient algorithm for constructing differentiable control functions that guarantee the translation of a wide class of nonlinear non-stationary systems of ordinary differential equations from the initial state to a given point in the phase space, with account of the control constraint and the non-stationary perturbation. Constructive sufficient conditions are imposed on the right part of the controlled system, under which the indicated translation is possible. The problem of motion control by a robot manipulator when moving a body of variable mass to a given point is considered and its numerical simulation is carried out. [ABSTRACT FROM AUTHOR]

A computationally efficient one-parameter family of explicit (i.e., non iterative for nonlinear systems) direct integration algorithms featuring second-order accuracy, unconditional stability for linear systems, and controllable numerical dissipation is developed for solving inertial problems. Unconditional stability is attained within an explicit formulation using the concept of model-based algorithms in which the algorithmic parameters are functions of the model matrices. The proposed method improves the overshoot and nonlinear stability characteristics of the KR- method, an existing explicit-model-based algorithm. Numerical characteristics of the proposed method are compared with those of the KR- method and further demonstrated through representative numerical examples. [ABSTRACT FROM AUTHOR]

Increasing convergence rates of observers and differentiators for a class of nonlinear systems in the output canonical form (under presence of bounded matched disturbances, Lipschitz uncertainties and measurement noises) is investigated. A supervisory algorithm is designed that switches among different values of observer gains to accelerate the estimation. In the noise-free case, the presented switched-gain observer ensures global uniform time of convergence of the estimation error to the origin. In the presence of noise, the goals of overshoot reducing for the initial phase, acceleration of convergence and improvement of asymptotic precision of estimation are achieved. Efficiency of the proposed switching-gain observer is demonstrated by numerical comparison with a sliding mode and linear high-gain observers. [ABSTRACT FROM AUTHOR]

An algorithm for adaptation of the gains of higher-order sliding mode-based exact differentiators is developed for the case where the upper bound for the ρth derivative of the tracking error signal exists but it is unknown. Unlikely other publications in the literature, the developed adaptive algorithm based on monitoring functions guarantees global and exact tracking when used in closed-loop output feedback. In the closed-loop scenario, a global-exact and finite-time estimate for the variables is applied to construct the sliding surface of the proposed sliding mode controller. The class of uncertain systems of arbitrary relative degree (ρ ≥ 1) takes into account time-varying perturbations with unknown bounds and state-dependent nonlinearities satisfying a linear growth condition with any unknown rate. The norm of the unmeasured state is majorised by using a hybrid state-norm estimator. Numerical examples and an engineering application to wing rock control are presented in order to illustrate the properties and advantages of the novel adaptation approach for sliding mode control design. [ABSTRACT FROM AUTHOR]