Infinite horizon linear quadratic Pareto game of the stochastic singular systems

This paper is concerned with the linear quadratic (LQ) Pareto game of the stochastic singular systems in infinite horizon. Firstly, the optimal control problem of the weighted sum cost functional is discussed. Utilizing the equivalent transformation method, the weighted sum LQ optimal control problem is transformed into a stochastic LQ optimization problem. Based on the classical stochastic LQ optimal control theory, the necessary and sufficient condition for the solvability of the indefinite weighted sum LQ optimal control is put forward. Then, the LQ Pareto game of the stochastic singular systems is studied. By the discussion of the convexity of the cost functionals, a sufficient condition for the existence of the Pareto solutions is obtained via the solvability of the corresponding generalized algebraic Riccati equation (GARE). Moreover, we derive all Pareto solutions based on the solution of a Lyapunov equation. Finally, an example is given to show the effectiveness of the proposed results.     

A hybrid fuzzy-molecular controller enhanced with evolutionary algorithms: A case study in a one-leg mechanism

Intelligent control systems are able to work well in uncertain nonlinear systems, mainly for: changes in the operating point, presence of environmental noise and disturbances, uncertainty in sensor measurements, miscalibration, uncertain model plant, and others. For instance, fuzzy controllers have been widely studied and applied. Recently, artificial organic controllers (AOC) have been proposed as an ensemble of fuzzy logic and artificial hydrocarbon networks. However, a weakness in AOC is the lack of training methods for tuning parameters for desired output responses in control. In this regard, this paper aims to introduce an evolutionary optimization method, i.e. particle swarm optimization, for tuning artificial organic controllers. Three objectives are proposed for automatic tuning of AOC: overall error, steady-state error and settling time of output response. The proposed methodology is implemented in the well-known cart-pole system. Also, the proposed method is applied on a one-leg unstable mechanism as case study. Results validate that automatic tuning of AOC over simulation systems can achieve suitable output responses with minimal overall error, steady-state error and settling time.     

Twin SVM with a reject option through ROC curve

This paper proposes a new method which embeds a reject option in twin support vector machine (RO-TWSVM) through the Receiver Operating Characteristic (ROC) curve for binary classification. The proposed RO-TWSVM enhances the classification robustness through inclusion of an effective rejection rule for potentially misclassified samples. The method is formulated based on a cost-sensitive framework which follows the principle of minimization of the expected cost of classification. Extensive experiments are conducted on synthetic and real-world data sets to compare the proposed RO-TWSVM with the original TWSVM without a reject option (TWSVM-without-RO) and the existing SVM with a reject option (RO-SVM). The experimental results demonstrate that our RO-TWSVM significantly outperforms TWSVM-without-RO, and in general, performs better than RO-SVM.     

Flatness-based adaptive sliding mode tracking control for a quadrotor with disturbances

In this paper, a flatness-based adaptive sliding mode control strategy is presented to solve the trajectory tracking problem of a quadrotor. According to the differential flatness theory, the typical under-actuated quadrotor dynamics is transformed into a fully-actuated one. Based on this model, backstepping sliding mode controllers are designed to solve the trajectory tracking problem. To improve the robustness to disturbances, extended state observers are applied as a feedforward compensation of disturbances. Moreover, considering the high-order dynamics and possible instability caused by large observer gains, the adaptive method is applied to compensate for the estimation error. The effectiveness of the proposed control scheme is verified in simulations.     

Turing patterns in a diffusive epidemic model with saturated infection force

In this paper, we investigate the complex dynamics of a reaction–diffusion epidemic model with a saturated infection force analytically and numerically. We give the stability of the constant positive steady–states and the nonexistence/existence of nonconstant positive steady–states of the model which shows that, if the diffusion coefficients are properly chosen, the model exhibits stationary Turing pattern as a result of diffusion. Via numerical simulations, we present the evolutionary processes that involve organism distribution and the interaction of spatially distributed infection with local diffusion, and find that the model dynamics exhibits a diffusion-controlled formation growth of holes, stripes and spots pattern replication. In the viewpoint of epidemiology, we must regulate and control the parameters in the special range to control the disease.     

Disturbance-observer-based control design for a class of uncertain systems with intermittent measurement

The robust control problem of a class of uncertain systems subject to intermittent measurement as well as external disturbances is considered. The disturbances are supposed to be generated by an exogenous system, while the state information is assumed to be available only on some nonoverlapping time intervals. A composite design consisting of an intermittent state feedback controller augmented by a disturbance compensation term derived from a disturbance observer is formulated. Unlike the conventional disturbance observers, the proposed disturbance observer is modelled by a switched impulsive system, which makes use of the intermittent state data to estimate the disturbances. Stability analysis of the resulting closed-loop system is performed by applying a piecewise time-dependent Lyapunov function. Then a sufficient condition for the existence of the proposed composite controllers is derived in terms of linear matrix inequalities (LMIs). The controller and observer gains can be achieved by solving a set of LMIs. Further, a procedure to limit the norms of the controller and observer gains is given. Finally, an illustrative example is presented to demonstrate the validity of the results.     

Impulsive observer design for a class of switched nonlinear systems with unknown inputs

This paper investigates hybrid observer design of a class of unknown input switched nonlinear systems. The distinguishing feature of the proposed method is that the stability of all subsystems of the error switched systems is not necessarily required. First, an output derivative-based method and time-varying coordinate transformation are considered to eliminate the unknown input. Then in order to maintain a satisfactory estimation performance, an impulsive full-order and switched reduced-order observer are developed with a pair of upper and lower dwell time bounds and constructing time-varying Lyapunov functions combined with convex combination technique. In addition, the time-varying Lyapunov functions method is also used to analyze the stability of a class of error switched nonlinear systems with stable subsystems. Finally, two examples are presented to demonstrate the effectiveness of the proposed method.     

Stability and bifurcation control of a delayed fractional-order eco-epidemiological model with incommensurate orders

In this paper, a delayed fractional eco-epidemiological model with incommensurate orders is proposed, and a control strategy of this model is discussed. Firstly, for the system with no controller, the stability and Hopf bifurcation with respect to time delay are investigated. Secondly, under the influence of the controller, the stability and Hopf bifurcation of the system is discussed, and it is indicated that the stability of the system can be changed by increasing the feedback control delay. In particular, a separate study is carried out on the bifurcation with respect to the extended feedback delay, and the bifurcation point is calculated. At last, to support the theoretical results, some numerical simulations are depicted.     

Exponential synchronization of stochastic complex networks with multi-weights: A graph-theoretic approach

This paper concerns the exponential synchronization problem of stochastic complex networks with multiple weights (SCNMW). By the method of network split, SCNMW can be modelled as stochastic coupled systems driven by Brownian motion. By combining graph theory, Lyapunov stability theory and state feedback control technique, drive-response synchronization criteria of SCNMW have been obtained. Two kinds of exponential synchronization criteria are obtained, one is given with Lyapunov functions of vertex systems, and the other is shown with the coefficients of SCNMW. The obtained synchronization principles are closely related to the coupling strength of multiple sub-networks and the intensity of noise perturbation. Finally, a numerical example with some simulations is presented to illustrate the theoretical results.     

Safe-circumnavigation of one single agent around a group of targets with only bearing information

This paper investigates the safe-circumnavigation problem of a single agent along a group of static targets. We assume in this paper that the distance information cannot be measured directly and only bearing measurements are available. In order to localize the targets, we design the positional estimator where the bearing measurements of the targets are used to construct the system matrix of the state equation of the estimator. To guarantee that the bearing angles are meaningful and with enough precision, we build the condition keeping safe distance between the agent and the targets. Furthermore, a gradual relaxed method is provided to reduce the limitations brought by the mutual restraint between the accuracy of the initial estimation and the desired encircling radius, so as to make the proposed method easy to apply. The performance of the proposed algorithms is verified through an experiment based on a wheeled robot platform.     

Robust sliding mode control of a DC/DC Boost converter with switching frequency regulation

This paper presents the design of a hysteresis band controller to regulate the switching frequency in a sliding mode controlled nonlinear Boost power converter. The proposed architecture relies on a piecewise linear modeling of the switching function behavior within the hysteresis band, and consists of a continuous-time integral-type controller that modifies the amplitude of the hysteresis band of the comparator in accordance with the error between the desired and the actually measured switching period. The study provides the dynamical models of the converter operating in sliding mode and the switching frequency control loop. Moreover, the design of the parameters of both the sliding mode control and the switching frequency controller guarantee the fulfilment of the desired output voltage regulation of the Boost converter and the steady state setting of the switching frequency with a known, taylored dynamics. A Boost power converter prototype has been built to validate the proposal. Experimental results confirm the predicted good performance of the controllers, as well as the robustness with respect to changes in the switching frequency reference and the system parameters.     

Adaptive quantized tracking control for a class of uncertain nonlinear systems with guaranteed transient performance

In this paper, an adaptive quantized control method with guaranteed transient performance is presented for a class of uncertain nonlinear systems. By introducing the Nussbaum function technique, the difficulty caused by quantization is handled and a novel adaptive control scheme is designed. In comparing with the existing adaptive control scheme, the key advantages of the proposed control scheme are that the controller needs no information about the parameters of the quantizer and the stability of the closed-loop system and the transient performance are independent of the coarseness of the quantizer. Based on Lyapunov stability theory and Barbalat’s Lemma, it is proven that all the signals in the resulting closed-loop system are bounded and the tracking error converges to zero asymptotically with the prescribed performance bound at all times. Simulation results are presented to verify the effectiveness of the proposed control method.     

Global sampled-data output feedback stabilization for a class of stochastic nonlinear systems with time-varying delay

This paper studies the global sampled-data output feedback stabilization problem for a class of stochastic nonlinear systems. The considered system is in non-strict feedback form with unknown time-varying delay. A state observer is introduced to estimate the unmeasured states. With the help of the backstepping method, a linear sampled-data output feedback controller is constructed. By choosing an appropriate Lyapunov–Krasoviskii functional and an allowable sampling period, it is shown that the stochastic system can be globally asymptotically stabilized in the mean square sense under the developed control scheme. Finally, two examples are presented to verify the effectiveness of the designed control scheme.     

Dynamics for an SIRS epidemic model with infection age and relapse on a scale-free network

A new SIRS epidemic model with infection age and relapse on a scale-free network is introduced. The basic reproduction number R₀ is defined. Asymptotic smoothness of solution and uniform persistence of system are proved. It is shown that the disease-free equilibrium is globally asymptotically stable by using Fluctuation Lemma if R₀ < 1 and the endemic equilibrium is globally asymptotically stable by constructing suitable Lyapunov functional if R₀ > 1. Effects of two immunization schemes are studied. Numerical simulations and sensitivity analysis are performed. Results manifest that infection age and degree of node play a significant role in controlling the emergence and spread of the epidemic disease.     

Passive controller realization of a bicubic admittance containing a pole at s=0 with no more than five elements for inerter-based mechanical control

This paper is concerned with a passive network synthesis problem about the damper-spring-inerter realization of a bicubic admittance containing a pole at $s=0$ with at most five elements, where the least number of elements for the possible realizations is four. The admittances of many passive mechanisms (controllers) in inerter-based control systems are in this form. A specific four-element realizability that is a parallel connection of a spring and a three-element subnetwork is first solved. By utilizing the realizability constraints based on graph theory, it is proved that only one configuration can cover all the other four-element cases through the discussions of other possible network graphs. By deriving its realizability condition, a necessary and sufficient condition for the four-element realizations can be combined. More generally, the five-element realizability can be investigated. The specific five-element realizability that is the parallel connection of a spring and a four-element subnetwork is solved. By making use of realizability constraints described by network graphs and eliminating impossible configurations, a set of four configurations is found out to cover all the other five-element cases. By investigating their realizability conditions, a necessary and sufficient condition for the five-element realizations can be combined. The results of this paper can reduce the realizability redundancy compared with classical synthesis approaches like Bott–Duffin procedure, which provide a first critical step towards solving the minimal realization problem of such admittances. The results can be applied to the design and optimization of mechanical control systems based on inerters, and in the long term can also contribute to the development of other areas of circuits and systems.     

Parameter identification of time-delayed nonlinear systems: An integrated method with adaptive noise correction

This paper proposes a novel method called the adaptive-noise-correction integrated parameter identification (ANCPI) for time-delayed nonlinear systems. Compared with the existing de-noising techniques, the significance of the proposed method is the use of the system itself to correct the noise-polluted components so that the accuracy of parameter identification is enhanced. To achieve the goal of adaptive noise correction, this study starts from the case of periodic response and then parameterizes the noise correction as the coefficient correction of harmonic basis. In this way, the parameter identification integrated with noise correction can be performed as the parameter optimization of the error function. For the convenience of application, a user-friendly program package is further provided and a detailed tutorial is presented in the supplementary material.     

Neural networks-based adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances

This paper focuses on the problem of adaptive output feedback control for a class of uncertain nonlinear systems with input delay and disturbances. Radial basis function neural networks (NNs) are employed to approximate the unknown functions and an NN observer is constructed to estimate the unmeasurable system states. Moreover, an auxiliary system is introduced to compensate for the effect of input delay. With the aid of the backstepping technique and Lyapunov stability theorem, an adaptive NN output feedback controller is designed which can guarantee the boundedness of all the signals in the closed-loop systems. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.     

Memory-based controller design for neutral time-delay systems with input saturations: A novel delay-dependent polytopic approach

In this paper, a new memory-based control problem is addressed for neutral systems with time-varying delay, input saturations and energy bounded disturbances. Attention is focused on the design of a memory-based state feedback controller such that the closed-loop system achieves the desirable performance indices including the boundedness of the state trajectories, the H_∞ disturbance rejection/attenuation level as well as the asymptotic stability. By using the combination of a novel delay-dependent polytopic approach, augmented Lyapunov–Krasovskii functionals and some integral inequalities, delay-dependent sufficient conditions are first proposed in terms of linear matrix inequalities. Then, three convex optimization problems are formulated whose aims are to, respectively, maximize the disturbance tolerance level, minimize the disturbance attenuation level and maximize the initial condition set. Finally, simulation examples demonstrate the effectiveness and benefits of the obtained results.     

Hierarchical recursive generalized extended least squares estimation algorithms for a class of nonlinear stochastic systems with colored noise

This paper considers the parameter identification problem of a bilinear state space system with colored noise based on its input-output representation. An input-output representation of a bilinear state-space system is derived for the parameter identification by eliminating the state variables in the model, and a recursive generalized extended least squares algorithm is presented for estimating the parameters of the obtained model. Furthermore, a three-stage recursive generalized extended least squares algorithm is proposed for reducing the computational cost. The validity of the proposed method is evaluated through a numerical example.     

Discrete-time stochastic impulsive BAM neural networks with leakage and mixed time delays: An exponential stability problem

In this paper, the stability analysis of impulsive discrete-time stochastic BAM neural networks with leakage and mixed time delays is investigated via some novel Lyapunov–Krasoviskii functional terms and effective techniques. For the target model, stochastic disturbances are described by Brownian motion. Then the result is further extended to address the problem of robust stability of uncertain discrete-time BAM neural networks. The conditions obtained here are expressed in terms of Linear Matrix Inequalities (LMIs), which can be easily checked by MATLAB LMI control toolbox. Finally, few numerical examples are presented to substantiate the effectiveness of the derived LMI-based stability conditions.