Time-varying Perturbations Research Articles

Maiden application of SSA‐optimised CC‐TID controller for load frequency control of power systems

This study describes a maiden application of salp swarm algorithm (SSA) optimised cascade tilt-integral-derivative controller (CC-TID) for frequency and tie-line power control of interconnected power systems (IPSs). The proposed controller includes both the merit of the cascade control algorithm and fractional-order calculus. In the proposed CC-TID controller, TID controller is used as a slave controller and a proportional-integral (PI) controller served the role of master controller. To elucidate the effectiveness, the designed controller has employed to, initially, two-area IPS followed by four-area IPS. SSA is used to pursue the optimum settings of the CC-TID controller via the minimisation of area control error. Performances of CC-TID controller is obtained and compared with I-, PI-, PI-derivative-, cascade PI-PD, and TID controllers. Simulation results, apparently, show that SSA: CC-TID controller exhibits superior performance compared with other controllers described above. Moreover, the performance of SSA is evaluated and compared with differential evolution and flower pollination algorithm in terms of convergence profile, power density, and statistical results. Finally, time-varying step load perturbation and random load perturbation are applied to confirm the robust behaviour of SSA: CC-TID controller.

Globally adaptive control for stochastic nonlinear time-delay systems with perturbations and its application

This paper addresses the globally adaptive state-feedback control problem for a more general class of stochastic nonlinear systems with an unknown time-varying delay and perturbations. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller is skillfully designed by using adaptive backstepping control technique. Then, based on Lyapunov–Razumikhin lemma and stochastic stability theory, it is proven that the constructed controller can guarantee the closed-loop system to be globally asymptotically stable in probability. Finally, a practical example of stochastic chemical reactor system with time delay and perturbations is presented to demonstrate the effectiveness of the proposed control scheme.

Keyed Hash Function Using Hyper Chaotic System With Time-Varying Parameters Perturbation

Secure hash function plays an important role in cryptography. This paper constructs a hash algorithm using the hyperchaotic Lorenz system, which serves as a sponge function to absorb input message via multiple parameters time-varying perturbation. First, the input message is divided into four 1D arrays, to generate four perturbation sequences via parameter updating rule, the perturbed parameters are still within their significant intervals, to make the system remain a hyperchaotic state. Each iteration of the discrete hyperchaotic system uses updated parameters, and the last state variable values are extracted to generate a len-bit hash value by transformation algorithm. The algorithm is so flexible that it can generate 256, 512, 1024 or longer hash value through parameter switcher. The experimental evaluation and comparison demonstrated the hash function's resistance to differential attack and second pre-image attack. The proposed hash function can be applied in the identification, information integrity, and figure signature.

Stabilization of Steady Motions for Systems with Redundant Coordinates

The vector-matrix Shulgin’s equations are used to stabilize the steady motions of mechanical systems with nonlinear geometric constraints in the case of incomplete information on the state. The momenta are introduced only for the cyclic coordinates that are not used to control. Three variants of the measurement vector are used to prove a theorem on the stabilization of control with the help of a part of the cyclic coordinates described by Lagrange variables. The control coefficients and the estimation system coefficients are specified by solving the corresponding Krasovskii linear-quadratic problem for a linear controlled subsystem without the critical variables corresponding to the redundant coordinates and to the introduced momenta. The stability of the complete closed nonlinear system is proved by reducing to a special Lyapunov case and by the application of the Malkin stability theorem in the case of time-varying perturbations.

Novel Criteria for Exponential Stability of Linear Non-Autonomous Functional Differential Equations

General linear non-autonomous functional differential equations are considered. Explicit criteria for exponential stability are given. Furthermore, the authors present an explicit robust stability bound for systems subject to time-varying perturbations. Two examples are given to illustrate the obtained results.

On local asymptotic stabilization of the nonlinear systems with time-varying perturbations by state-feedback control

ABSTRACTIn this paper, we are interested in the relation between the solutions of the control system and the solutions of its (potentially unknown) perturbation Under the assumption that the linear part of the unperturbed system at the point is controllable and that disturbance is asymptotically sufficiently small, there exists a state-feedback controller of the form u=−Kx such that the perturbed system preserves the local asymptotic stability of the zero solution of unperturbed system. The main result of this paper gives the sufficient conditions, more specifically, the relations between the important parameters of the system, to ensure this property and at the same time provides the method for calculating the lower bound of region of attraction. Moreover, we obtain a nontrivial extension of the classical result of H. K. Khalil regarding the behavior of the (uncontrolled) perturbed systems whose nominal part is exponentially asymptotically stable at the origin x=0.

Delay-Dependent Robust H∞ Performance for Uncertain Neutral Systems with Mixed Time-Varying Delays and Nonlinear Perturbations

This paper deals with the problems of delay-dependent stability and H∞ performance for uncertain neutral systems with time-varying delays, and nonlinear perturbations. The time-varying delays are neutral, discrete, and distributed time-varying delays that the upper bounds for the delays are available. The restrictions on the derivatives of the discrete and distributed time-varying delays are removed, which mean that a fast discrete time-varying delay is allowed. The uncertainties under consideration are nonlinear time-varying parameter perturbations and norm-bounded uncertainties, respectively. Firstly, by applying a novel Lyapunov-Krasovskii functional approach, Wirtinger-based integral inequality, Peng-Park’s integral inequality, decomposition technique of constant matrix, descriptor model transformation, Leibniz Newton formula and utilization of zero equation, and improved delay-dependent bounded real lemmas (BRL) for systems are established in terms of linear matrix inequalities (LMIs). Then, based on the obtained BRL, some less conservative delay-dependent stability criteria of uncertain neutral systems with mixed time-varying delays and nonlinear perturbations are obtained and improved H∞ performance criterion with the framework of LMIs is introduced. Finally, some numerical examples are given to illustrate that the presented method is effective.

Optimal tuning of 3 degree-of-freedom proportional-integral-derivative controller for hybrid distributed power system using dragonfly algorithm

The objective of this paper is to study the dynamic stability of a hybrid energy distributed power system (HEDPS) subject to load and wind power variations. A three degree-of-freedom (3-DOF) proportional-integral-derivative (PID) controller is designed and implemented in the HEDPS to stabilize frequency and power fluctuations after the perturbation. For enhancing system dynamics, the parameters of the 3-DOF PID controller are optimized by using dragonfly algorithm (DA). The results are compared with the results obtained by Zeigler–Nichols tuning and some other well-known meta-heuristic algorithms. The efficacy of proposed DA over different reported algorithms is established in terms of convergence rate, minimum fitness value and dynamic performance of the system. The robustness of the 3-DOF PID-controller is ascertained with time-varying step load perturbation, random wind power perturbation, and under system parameter variation. The robust performance of proposed DA has also been established by performing statistical analysis.

Design of a K-Winners-Take-All Model With a Binary Spike Train.

A continuous-time K -winners-take-all (KWTA) neural model that can identify the largest K of N inputs, where command signal is described. The model is given by a differential equation where the spike train is a sum of delta functions. A functional block-diagram of the model includes N feed-forward hard-limiting neurons and one feedback neuron, used to handle input dynamics. The existence and uniqueness of the model steady states are analyzed, the convergence analysis of the state variable trajectories to the KWTA operation is proven, the convergence time and number of spikes required are derived, as well as the processing of time-varying inputs and perturbations of the model nonlinearities are analyzed. The main advantage of the model is that it is not subject to the intrinsic convergence of speed limitations of comparable designs. The model also has an arbitrary finite resolution determined by a given parameter, low complexity, and initial condition independence. Applications of the model for parallel sorting and parallel rank-order filtering are presented. Theoretical results are derived and illustrated with computer-simulated examples that demonstrate the model's performance.

Temporal Variability in Thermally Driven Cross-Shore Exchange: The Role of Semidiurnal Tides

AbstractWe examine temporal variability of thermally driven baroclinic cross-shore exchange in the context of a tropical fringing reef system focusing on the role of tidally driven alongshore flow. Ensemble diurnal phase averaging of cross-shore flow at the Kilo Nalu Observatory (KNO) in Oahu, Hawaii, shows a robust diurnal signal associated with an unsteady buoyancy/diffusive dynamic balance, although significant variability is observed at subdiurnal time scales. In particular, persistent fortnightly variability in the cross-shore diurnal flow pattern is consistent with modulation by the semidiurnal alongshore tidal flow. The alongshore flow plays a direct role in the cross-shore exchange momentum balance via Coriolis acceleration but also affects the cross-shore circulation indirectly via its influence on vertical turbulent diffusion. An idealized linear theoretical model for thermally driven cross-shore flow is formulated using the long-term time-averaged diurnal dynamic balance at KNO as a baseline. The model is driven at leading order by the surface heat flux, with contributions from the alongshore flow and cross-shore wind appearing as linear perturbations. Superposition of the idealized solutions for Coriolis and time-varying eddy viscosity perturbations are able to reproduce key aspects of the fortnightly variability. Modifying the model to consider a more realistic alongshore flow and considering effects of nightly convection lead to further improvements in comparisons with KNO observations. The ability of the theoretical approach to reproduce the fortnightly patterns indicates that semidiurnal variations in the alongshore flow are effective in modulating the cross-shore flow via Coriolis and vertical turbulent transport mechanisms.

Rigid body stabilization under time-varying perturbations with zero mean values

The problem of monoaxial attitude control of a rigid body subjected to nonstationary perturbations is investigated. The control torque consists of a dissipative component and a restoring one. The cases of linear and nonlinear restoring and perturbing torques are analyzed. Two theorems on asymptotic stability of the programmed orientation are proved. The results of a numerical simulation are presented to confirm the conclusions obtained analytically.

Connected cruise control of a car platoon: A time-domain stability analysis

A compact representation of a vehicle platoon following model considering the headway, velocity, and vehicle-to-vehicle communication delay is presented. Then, a connectivity structure is selected, which includes vehicles equipped with connected cruise control and a conventional vehicle as the leader. The platoon exponential stability and its robust stability with respect to time-varying matrix perturbations are studied. The analysis is carried out in the time domain, via Lyapunov–Krasovskii functionals depending on the delay Lyapunov matrix. The stability results are illustrated by stability charts of the plane of control gain parameters. A total of three platoon illustrative vehicle scenarios show the interest of the approach.

Pinning Synchronization of Coupled Memristive Recurrent Neural Networks with Mixed Time-Varying Delays and Perturbations

In this paper, the pinning synchronization of coupled memristive recurrent neural networks (MNNs) with mixed time-varying delays and perturbations is investigated. Precisely, the considered coupled MNNs include the non-delay, discrete time-varying delays, distributed time delays, impulsive perturbations and stochastic perturbations. Comparing with the existing results, the new and simple feedback controller and adaptive feedback controller are designed to achieve exponential synchronization with pinning schemes. Based on the suitable Lyapunov functional and the definition of pinning control, with the aid of inequality techniques and differential inclusions theory, some effective and novel sufficient conditions are obtained to guarantee the synchronization of our proposed model. Finally, numerical examples are given to illustrate the effectiveness and reasonable of our theoretical results.

Attitude Fusion of Inertial and Magnetic Sensor under Different Magnetic Filed Distortions

By virtue of gravity measurement from a handheld inertial measurement unit (IMU) sensor, current indoor attitude estimation algorithms can provide accurate roll/pitch dimension angles. Acquisition of precise heading is limited by the absence of accurate magnetic reference. Consequently, initial stage magnetometer calibration is deployed to alleviate this bottleneck in attitude fusion. However, available algorithms tackle magnetic distortion based on time-invariant surroundings, casting the post-calibration magnetic data into unchanged ellipsoid centered in the calibration place. Consequently, inaccurate fusion results are formulated in a more common case of random walk in time-varying magnetic indoor environment. This article proposes a new fusion algorithm from various kinds of IMU sensors, namely gyroscope, accelerometer, and magnetometer. Compared to state-of-the-art attitude fusion approaches, this article addresses the indoor time-varying magnetic perturbation problem in a geometric view. We propose an extend Kalman filter--based algorithm based on this detailed geometric model to eliminate the position-dependent effect of a compass sensor. Experimental data demonstrate that, under different indoor magnetic distortion environments, our proposed attitude fusion algorithm has the maximum angle error of 2.02°, outperforming 7.17° of a gradient-declining-based algorithm. Additionally, this attitude fusion result is constructed in a low-cost handheld arduino core--based IMU device, which can be widely applied to embedded systems.

Interval Observer Design for Nonlinear Systems: Stability Radii Approach

This paper presents a new approach to design preserving order and interval observers for a family of nonlinear systems in absence and in presence of parametric uncertainties and exogenous disturbances. A preserving order observer provides an upper/lower estimation that is always above/below the state trajectory, depending on the partial ordering of the initial conditions, and asymptotically converges to its true values in the nominal case. An interval observer is then constituted by means of an upper and a lower preserving order observer. In the uncertain/disturbed case, the estimations preserve the partial ordering with respect to the state trajectory, and practically converge to the true values, despite of the uncertainties/perturbations. The design approach relies on the cooperativity property and the stability radii mathematical tools, both applied to the estimation error systems. The objective is to exploit the stability radii analysis for the family of linear positive systems under the time-varying nonlinear perturbations in order to guarantee the exponential convergence property of the observers, while the cooperativity condition determines the partial ordering between the trajectories of the state and the estimations. The proposed approach, defined for Lipschitz nonlinearities, depends only on two observer matrix gains. The design is reduced to the solution of linear matrix inequalities, which are given by the cooperative condition and convergence constraints. An illustrative example is presented to show the effectiveness of the theoretical results.

Synchronization of a Class of Memristive Stochastic Bidirectional Associative Memory Neural Networks with Mixed Time-Varying Delays via Sampled-Data Control

The paper addresses the issue of synchronization of memristive bidirectional associative memory neural networks (MBAMNNs) with mixed time-varying delays and stochastic perturbation via a sampled-data controller. First, we propose a new model of MBAMNNs with mixed time-varying delays. In the proposed approach, the mixed delays include time-varying distributed delays and discrete delays. Second, we design a new method of sampled-data control for the stochastic MBAMNNs. Traditional control methods lack the capability of reflecting variable synaptic weights. In this paper, the methods are carefully designed to confirm the synchronization processes are suitable for the feather of the memristor. Third, sufficient criteria guaranteeing the synchronization of the systems are derived based on the derive-response concept. Finally, the effectiveness of the proposed mechanism is validated with numerical experiments.

Global adaptive HOSM differentiators via monitoring functions and hybrid state-norm observers for output feedback

ABSTRACTAn 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.

Exponential stability of impulsive systems with random delays under sampled‐data control

In this study, the exponential stability problem of impulsive system is investigated via sampled-data control in the presence of random time-varying delays and non-linear perturbations. In particular, the time delays are considered to be randomly time varying and they obey the Bernoulli distributions. The authors' main attention is focused on the design of a sampled-data controller to ensure an exponential stability for the closed-loop system. By extending the first- and second-order reciprocal convex approach, an efficient method called third-order reciprocal convex technique is used to manipulate the main results. Through the construction of a suitable Lyapunov–Krasovskii functional combined with input delay approach and Briat lemma, several delay-dependent sufficient conditions for the concerned system are derived in the form of linear matrix inequalities which can be readily solved by utilising the valid software packages. Some numerical examples are given to illustrate the effectiveness of the developed control technique.

Stability of nonlinear Volterra equations

AbstractUsing a novel approach, we present some new explicit criteria for global exponential stability of the zero solution of general nonlinear time-varying Volterra difference equations. Furthermore, an explicit stability bound for equations subject to nonlinear time-varying perturbations is given. Finally, the obtained results are used to study uniform attraction of equilibrium of discrete-time bidirectional associative memory (BAM) neural networks. Some illustrative examples are given.

Stochastic mean square exponential synchronisation of time-varying complex dynamical networks via pinning control

ABSTRACTThis paper investigates the problem of stochastic mean square exponential synchronisation of complex dynamical networks with time-varying delay via pinning control. By applying the Lyapunov method and stochastic analysis, criteria on mean square exponential synchronisation are established under linear feedback pinning control and adaptive feedback pinning control, which depend on the time-varying delay and stochastic perturbation. These results complement and improve the previously known results. Two numerical examples are given to illustrate the effectiveness and correctness of the derived theoretical results.