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In this paper, an extension of an algorithm for the implicit discretization of a super‐twisting sliding mode observer is presented. Implicit and explicit discretization algorithms for homogeneous differentiators, where no physical model information is considered, are investigated in literature. This article studies the behavior when considering models of a rather general class of nonlinear systems. The discrete equations of the super‐twisting observer are reformulated as generalized equation and an algorithm for the step‐by‐step solution is given. The uniqueness of the derived algorithm is investigated with an equivalent variational inequality formulation which is derived for a class of nonlinear systems. Furthermore, a semi‐implicit predictor‐corrector discretization is presented which is an approximation method for the presented algorithms and allows an explicit implementation in practical applications. Accuracy properties under noise and sampling are given. The algorithm is applied on two mechanical example systems taken from practice. [ABSTRACT FROM AUTHOR]

This paper proposes a novel nonlinearly parameterized advanced single‐hidden layer neural extreme learning machine (ASHLN‐ELM) model in which the hidden and output weighting values are simultaneously updated using adaptively robust rules that are implemented based on Lyapunov stability principle. The proposed scheme guarantees the fast convergence speed of the state‐estimation residual errors bounded to null regarding to the influence of time‐varied disturbances. Additionally, proposed method needs no any knowledge related to desired weighting values or required approximating error. Typical uncertain hyper‐chaotic benchmark systems are used as to verify the new ASHLN‐ELM approach and to demonstrate the efficiency and the robustness of proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the optimal event‐triggered control for constrained‐input discrete‐time switched nonlinear systems. Firstly, the optimal time‐triggered control problem is analyzed based on the necessary optimality condition. Secondly, the optimal event‐triggered control problem is presented, and the optimal results are presented based on the periodic time‐triggered ones, and an event‐triggered integer‐mixed adaptive dynamic programming algorithm is put forward to obtain the optimal results. The proposed algorithm is only executed at trigger instants, which decreases the execution times compared with the periodic time‐triggered algorithm, and the neural networks are applied to approximate the control input and costate vector functions of each subsystem based on the triggered states. Thirdly, an event‐triggered condition is designed to make the closed‐loop switched system asymptotically stable. Fourthly, it is shown that during the iteration process, the value function sequence corresponding to the costate vector converges to the optimal value function. Finally, the simulation results demonstrate the effectiveness of the presented algorithm. [ABSTRACT FROM AUTHOR]

This paper presents a novel practical fixed‐time parameter identification algorithm and a composite learning based practical fixed‐time adaptive dynamic surface control (DSC) scheme for nonlinear strict‐feedback systems subject to linear‐in‐parameters uncertainties. The convergence of conventional parameter estimation algorithms often requires a restrictive prerequisite termed persistent excitation (PE) condition. By contrast, a new fixed‐time parameter identification algorithm configured with two layer transformation technique is firstly proposed under relaxed sufficient excitation condition rather than strict PE condition. The key point of avoiding PE condition is by introducing a smooth switching function to adjust the forgetting factor in the filtered regressor dynamics. Instead of using the fractional power of the tracking errors to construct the control laws, a smooth hyperbolic tangent function based adaptive DSC scheme is designed such that the potential singular problem caused by time derivations of virtual control laws in back‐stepping algorithm is avoided. Integrating the parameter identification algorithm into the adaptive DSC scheme, a composite learning based control is formed to guarantee the practical fixed‐time convergence of parameter estimation errors and tracking errors. Comparative simulation results are given to illustrate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Summary: This paper concerns the analysis of an iterative scheme delivering approximate control laws for the tracking regulation problems for nonlinear systems. The procedure can be applied to finite‐ and infinite‐dimensional systems, and the underlying methodology derives from the geometric methods, which have been developed for both linear and nonlinear systems. In the nonlinear case, the main tool is the center manifold theorem. Indeed, in the geometric methodology, under the assumption that the signals to be tracked are generated by a finite‐dimensional exo‐system, the desired control is obtained by solving a pair of operator equations called the regulator equations. In this paper, we extend the concept of regulator equations to what we refer to as the dynamic regulator equations. Just as it is generally quite difficult to solve the regulator equations, it can be equally difficult to solve the dynamic regulator equations. As the authors have already shown in the linear case, a straightforward attempt to solve the dynamic regulator equations leads to a singular system, which can be regularized to obtain an iterative scheme that provides approximate control laws that provide accurate tracking with very a small tracking error after only a couple of iterations. In this paper, we generalize the iterative scheme to nonlinear systems and provide error estimates for the first 3 iterations. Both finite‐ and infinite‐dimensional examples are given to validate the estimates. We comment that the method has also been applied to a wide range of nonlinear distributed parameter examples described in the references. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the periodic event‐triggered control problem for distributed networked multiagent systems with interconnected nonlinear dynamics subject to asynchronous communication. A method of state trajectory estimation for the interconnected neighboring agents over each prediction horizon with guaranteed error bounds is addressed to handle the asynchronous communication. Based on it, a distributed robust model predictive control (MPC) is proposed with a distributed periodic event‐triggered scheme for each agent. According to this algorithm, each subsystem generates presumed state trajectories for all its upstream neighbors and computes its own control locally. By checking the designed triggering condition periodically, the optimization problem of MPC will be implemented and solved when the local error of the subsystem exceeds a specified threshold. Then, the optimized control input will be determined and applied until the next time instant when the triggering condition is invoked. Moreover, sufficient condition for ensuring feasibility of the designed algorithm is conducted, along with the analysis of asymptotic stabilization of the closed‐loop system. The illustrative example for a set of coupled Van der Pol oscillators is reported to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we study a distributed optimization problem for a class of high‐order multiagent systems with unknown dynamics. In comparison with existing results for integrators or linear agents, we need to overcome the difficulties brought by the unknown nonlinearities and the optimization requirement. For this purpose, we employ an embedded control‐based design and first convert this problem into an output stabilization problem. Then, two kinds of adaptive controllers are given for these agents to drive their outputs to the global optimal solution under some mild conditions. Finally, we show that the estimated parameter vector converges to the true parameter vector under some well‐known persistence of excitation condition. The efficacy of these algorithms was verified by a simulation example. [ABSTRACT FROM AUTHOR]

Summary: Domain of attraction plays an important role in stability analysis and safety verification of nonlinear control systems. In this paper, based on the concept of multiple Lyapunov‐like functions, we propose iteration algorithms for computing inner estimates of domains of attraction for a class of switched hybrid systems, where the state space is composed of several regions and each region is described by polyhedral sets. Starting with an initial inner estimate of domain of attraction, we firstly present a theoretical framework for obtaining a larger inner estimate by iteratively computing multiple Lyapunov‐like functions. Successively, the theoretical framework is underapproximatively realized by using S‐procedure and sums of squares programming, associated with the coordinatewise iteration method. Afterwards, for obtaining a required initial inner estimate of domain of attraction, we propose an alternative higher‐order truncation and linear semidefinite programming based method for computing a common Lyapunov function. Especially, a bisection method based improvement is proposed for obtaining better estimates in each iteration step. Finally, we implement proposed algorithms and test them on numerical examples with comparisons. These computation and comparison results show that the advantages of our multiple Lyapunov‐like functions based algorithm. Especially, we provide alternative underapproximations for avoiding the possible numerical problem. [ABSTRACT FROM AUTHOR]

This paper is concerned with application of expectation maximization (EM) algorithm for deriving an adaptive version of divided difference filter for joint state estimation and multiplicative parameter identification of nonlinear system with the colored measurement noise. Owing to the fact that there exist a mutual coupling and interaction of state and parameter on each other, it requires a joint or simultaneous estimation of both state and parameter by a mutual iteration, and justly, EM iterates Expectation (E-)step and Maximization (M-)step to meet such requirement. Firstly, E-step involves state filtering and smoothing issues under knowing the previous parameter identification results, which is well solved by resorting to the Gaussian approximation with a trade-off between accuracy and complexity. Further, such Gaussian approximation estimators are applied for evaluating the condition expectation of complete-data likelihood function, nonlinearly characterized by the multiplicative parameter needed to be optimized. Secondly, M-step deals with the maximization of the condition expectation by directly making its derivative as zero to obtain the current general parameter identification equation as the nonlinear integral. Thirdly, by iteratively operating E-step and M-step, an adaptive divided difference filter is proposed for joint state estimation and parameter identification by using the second-order Stirling interpolation to compute the associated nonlinear integral. Finally, the robust performance of the EM-based adaptive version of divided difference filter to the unknown or time-varying multiplicative parameter, as compared with the standard augmentation method, is demonstrated by a maneuvering target tracking example. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed model predictive control algorithm for the consensus of nonlinear second-order multi-agent systems. At each update time, all the agents are permitted to optimize. A positively invariant terminal region and a corresponding auxiliary controller are developed for each agent. Furthermore, time-varying compatibility constraint is presented to denote a degree of consistency between the assumed trajectories and the actual trajectories of each agent. Given the designed terminal ingredients (terminal region, auxiliary controller, and terminal cost) and compatibility constraints, the recursive feasibility and closed-loop stability of the whole system are guaranteed. The simulation results are given to illustrate the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes a new robust adaptive control method for Wiener nonlinear systems with uncertain parameters. The considered Wiener systems are different from the previous ones in the sense that we consider nonlinear block approximation error, process noise, and measurement noise. The parameterization model is obtained based on the inverse of the nonlinear function block. The adaptive control method is derived from a modified criterion function that can overcome non-minimum phase property of the linear subsystem. The parameter adaptation is performed by using a robust recursive least squares algorithm with a deadzone weighted factor. The control law compensates the model error by incorporating the unmodeled dynamics estimation. Theoretical analysis indicates that the closed-loop system stability can be guaranteed under mild conditions. Numerical examples including an industrial problem are studied to validate the results. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]