Switching Surface Research Articles

Finite-time stochastic boundedness for Markovian jumping systems via the sliding mode control

The finite-time stochastic boundedness (FTSB) via the sliding mode control (SMC) approach is analyzed for Markovian jumping systems (MJSs) with time-delays. First, an integral switching surface is constructed. And to make sure the reachability of the sliding mode surface in a finite-time, an SMC law is designed. In addition, the delay-dependent criteria for FTSB are obtained over the reaching phase and the sliding motion phase. Furthermore, in line with linear matrix inequalities (LMIs), sufficient conditions are provided to guarantee the FTSB of systems over the whole finite-time interval. Lastly, an example is given to indicate the validity of the proposed approach.

Barrier Function-Based Nonsingular Finite-Time Tracker for Quadrotor UAVs Subject to Uncertainties and Input Constraints

This study proposes an adaptive barrier functions-based non-singular terminal sliding mode control approach for the trajectory tracking of a quadrotor unmanned aerial vehicle subject to bounded uncertainties and input constraints. First, the state-space equations of the six degrees-of-freedom quadrotor system is introduced in the presence of bounded uncertainty and constrained input. Then, a compensation system is designed with the aim of removing the constrained input and leading to high performance. Afterwards, a linear switching surface is defined using the tracking error and virtual control input to guarantee the convergence of the tracking error in the presence of parametric uncertainties and input saturation. Later, a non-singular terminal sliding surface is proposed for fast convergence of the linear switching surface. To eliminate the need for approximating the upper bounds of uncertainties and ensure the fast convergence of the non-singular terminal sliding surface to a pre-specified neighborhood of the origin, we considered an adaptive barrier function scheme. The fast convergence rate of the proposed approach is verified via the Lyapunov stability theory. The accuracy and performance of the proposed approach is assessed using MATLAB/Simulink simulations and robustness analysis using the random number noise.

Trajectory sensitivity analysis of hybrid systems with sliding motion

This paper concerns hybrid control systems exhibiting the sliding motion. It is assumed that the system’s motion on the switching surface is described by index-2 differential–algebraic equations (DAEs), which guarantee the accurate tracking of the sliding motion surface. For those systems the sensitivity analysis is performed with the help of solutions to system’s linearized equations. The paper states conditions under which the solutions to the linearized equations for original DAEs and the solutions to linearized equations for underlying ordinary differential equations (ODEs) exhibit similar properties. Due to the presence of sliding motion, we restrict the class of admissible control functions to piecewise differentiable functions. The presented sensitivity analysis might be useful in deriving the weak maximum principle for optimal control problems with hybrid systems exhibiting sliding motion and in establishing the global convergence of algorithms for solving those problems.

Adaptive Nonsingular Terminal Sliding Mode Control for Performance Improvement of Perturbed Nonlinear Systems

In this study, an adaptive nonsingular terminal sliding mode control technique according to the barrier function is designed for the performance improvement and robust stability of nonlinear systems with outdoor disturbances. For this reason, a novel nonlinear sliding surface is presented based on the states of the system. The nonlinear sliding surface forces the states of the system to converge from initial conditions to zero. Subsequently, a non-singular terminal sliding control scheme is advised for the purpose of finite-time stability of the nonlinear switching surface. Finite-time stabilization of the non-singular terminal sliding surface is verified by the Lyapunov theory. For improvement of the system performance against exterior perturbation, the barrier function adaptive technique is employed to estimate the unknown upper bounds of the exterior disturbance. Finally, the advantage and productivity of the recommended control method is investigated based on the simulation results. In the simulation part, the plasma torch jerk chaotic system is considered as a case study, such that the obtained results are given in different scenarios.

Bifurcation dynamics on the sliding vector field of a Filippov ecological system

A Filippov crop-pest-natural enemy ecological system with threshold switching surface related to the pest control is developed, which has been completely analyzed by employing the qualitative techniques of non-smooth dynamical systems. The main results reveal that the proposed switching model can have multiple pseudo-equilibria in the sliding region, which result in rich bifurcations in the sliding region including saddle-node, Hopf, Bogdanov-Takens and Hopf-like boundary equilibrium bifurcations. Moreover, the pseudo-periodic solution (or pseudo-homoclinic loop) can be generated in the sliding region through a Hopf bifurcation (or a homoclinic bifurcation), which can collide with the tangential lines at the cusp singularities and finally disappears as parameter varies. This reveals that although the system can stabilize on the sliding region to achieve the purpose of pest control, there are complex dynamical behaviors and sliding bifurcations within the sliding region. Furthermore, as the threshold level varies, the model exhibits the interesting global sliding bifurcations including grazing bifurcation, buckling bifurcation, crossing bifurcation, homoclinic bifurcation to a pseudo-saddle, period-halving bifurcation and chaotic dynamics. This implies that control outcomes are sensitive to the threshold level, and hence it is crucial to choose the threshold level to initiate control strategy.

Fewest switches surface hopping with Baeck-An couplings.

In the Baeck-An (BA) approximation, first-order nonadiabatic coupling vectors are given in terms of adiabatic energy gaps and the second derivative of the gaps with respect to the coupling coordinate. In this paper, a time-dependent (TD) BA approximation is derived, where the couplings are computed from the energy gaps and their second time-derivatives. TD-BA couplings can be directly used in fewest switches surface hopping, enabling nonadiabatic dynamics with any electronic structure methods able to provide excitation energies and energy gradients. Test results of surface hopping with TD-BA couplings for ethylene and fulvene show that the TD-BA approximation delivers a qualitatively correct picture of the dynamics and a semiquantitative agreement with reference data computed with exact couplings. Nevertheless, TD-BA does not perform well in situations conjugating strong couplings and small velocities. Considered the uncertainties in the method, TD-BA couplings could be a competitive approach for inexpensive, exploratory dynamics with a small trajectories ensemble. We also assessed the potential use of TD-BA couplings for surface hopping dynamics with time-dependent density functional theory (TDDFT), but the results are not encouraging due to singlet instabilities near the crossing seam with the ground state.

Advance learning technique for the electricity market attack detection

The false data injection (FDI) attacks in the AC smart microgrid (SMG) and the solution for detecting attacks on distributed energy sources in the SMG are discussed in the present paper. As the input indices for the deep machine learning (DML) algorithm, wavelet singular amounts are used as an alternative method of detecting FDI attacks (FDIAs). By means of the suggested approach, a specified error is used to adjust the precision factors of the wavelet transform and subsequently, singular value decomposition is used to retrieve features from wavelet coefficients. The wavelet singular values in switching surfaces of current and voltage are used to determine the indexes used for DML and diagnosing FDIA. Detecting FDIA with great precision is the main goal of the suggested detection plan. A simulation study using MATLAB/Simulink is conducted on SMG to demonstrate the performance of the suggested approach.

Sliding mode control for fractional-order time-varying delay systems under external excitation

In this paper, by using Lyapunov–Krasovskii stability theory and linear matrix inequality approach, the control problem for fractional-order systems under seismic waves with time-varying delays is studied. A novel switching surface is proposed. Based on the linear quadratic regulator and sliding mode control, some sufficient conditions are derived to ensure the fractional system under control. Mittag-Leffler stability theorem is adopted to prove that the switching surface could converge to zero. Finally, a numerical simulation example is provided to validate the advantages and effectiveness of the proposed results.

Synchronization of reaction–diffusion Hopfield neural networks with s-delays through sliding mode control

Synchronization of reaction–diffusion Hopfield neural networks with s-delays via sliding mode control (SMC) is investigated in this paper. To begin with, the system is studied in an abstract Hilbert space C([–r; 0];U) rather than usual Euclid space Rn. Then we prove that the state vector of the drive system synchronizes to that of the response system on the switching surface, which relies on equivalent control. Furthermore, we prove that switching surface is the sliding mode area under SMC. Moreover, SMC controller can also force with any initial state to reach the switching surface within finite time, and the approximating time estimate is given explicitly. These criteria are easy to check and have less restrictions, so they can provide solid theoretical guidance for practical design in the future. Three different novel Lyapunov–Krasovskii functionals are used in corresponding proofs. Meanwhile, some inequalities such as Young inequality, Cauchy inequality,Poincaré inequality, Hanalay inequality are applied in these proofs. Finally, an example is given to illustrate the availability of our theoretical result, and the simulation is also carried out based on Runge–Kutta–Chebyshev method through Matlab.

Using optimal control to optimize the extraction rate of a durable non-renewable resource with a monopolistic primary supplier

<p style='text-indent:20px;'>The problem dealt with in this paper is that of optimizing the path of the extraction rate (and, consequently, the price) for the monopolistic owner of the primary sources of a totally or partially durable non-renewable resource (such as precious metals or gemstones) in a continuous-time frame, assuming that there is an upper bound on the extraction rate and with an interest rate equal to zero. The durability of the resource implies that, unlike the case of non-durable resources, at any time there is a stock of already-used amounts of the resource that are still potentially reusable, in addition to the resource available in the ground for extraction. The problem is addressed using the Maximum Principle of Pontryagin in the framework of optimal control theory, which allows identifying the patterns that the optimal policies can adopt. In this framework, the Hamiltonian is linear in the control input, which implies a bang-bang control policy governed by a switching surface. There is an underlying geometry to the problem that determines the solutions. It is characterized by the switching surface, its time derivative, the intersection point (if any) and the bang-bang trajectories through this point.</p>

Survival of Unmanned Aerial Vehicles by Luring Pursuers in Angle Constrained Interception

In this paper, a sliding mode control-based cooperative guidance strategy for a team of two unmanned aerial vehicles (aircraft), which ensures their survival against pursuers, is proposed. The pursuing interceptors are assumed to employ augmented proportional navigation guidance. The cooperating aircraft maneuver in a way to lure their respective pursuers to an impact angle constrained collision. The problem of controlling impact angle is first transformed to that of tracking line-of-sight angle and its rate, and then the same is achieved by enforcing sliding mode on appropriate chosen switching surface. Furthermore, the allocation of aircraft’s lateral accelerations is performed in a way to minimize the instantaneous aerodynamic drag acting on both unmanned aerial vehicles. Numerical simulations are presented to validate the effectiveness of the proposed guidance strategy under different engagement geometries.

Predicting subdifferential switching surface in a steady-state complex heat transfer problem using deep learning

Predicting subdifferential switching surface in a steady-state complex heat transfer problem using deep learning

Switching Control for Euler-Lagrange Dynamics: An Incremental Stability Approach

This paper discuses the stabilization problem in an Euler-Lagrange dynamics in the incremental stability framework. The work proposes the analysis in bimodal switched domain. The switching here is introduced intentionally in terms of control action to enhance robustness. In such setting, we derive sufficient conditions using matrix measure to show incremental stability in each mode and overall switched system. The proposition uses contraction theory approach to establish incremental stability. In this article, the selection of switching surface is as per the desired characteristics to be achieved. The objective is to minimise the stabilization error irrespective of the initial conditions, which is an inherent advantage of using Contraction theory. The adoption of this technique simplifies the analysis compared to the conventional framework. The efficacy of artefact is well supplemented by the simulation results.

Research of controller of Permanent magnet linear synchronous motors via model predictive direct thrust control

How to achieve high-precision control is the core issues of the linear motor research. To solve this problem, this paper proposes a new control algorithm. on the one hand, through the sliding mode control for the unknown torque observations, in the process of observation, select a specific based function to approximate the sign function in order to eliminate the jitter of the vicinity of the switching surface; On the other hand, the use of model predictive control method (Model Predictive Control) to achieve the torque compensator track to achieve the velocity and displacement tracking. The constant sampling time of the model predictive control in the new method can effectively avoid the problems that the number of switching per unit time of the inverter can’t be expected.

Interpretation of adiabatic and diabatic populations from trajectories of branching corrected surface hopping

The branching corrected surface hopping (BCSH) has been demonstrated as a robust approach to improve the performance of the traditional fewest switches surface hopping (FSSH) for nonadiabatic dynamics simulations of standard scattering problems [J. Chem. Phys. 150, 164101 (2019)]. Here, we study how reliable populations of both adiabatic and diabatic states can be interpreted from BCSH trajectories. Using exact quantum solutions and FSSH results as references, we investigate a series of one-dimensional two-level scattering models and illustrate that excellent time-dependent populations can be obtained by BCSH. Especially, we show that different trajectory analysis strategies produce noticeable differences in different representations. Namely, the method based on active states performs better to get populations of adiabatic states, while the method based on wavefunctions produces more reliable results for populations of diabatic states.

A Comparative Study of Nonlinear Control Schemes for Induction Motor Operation Improvement

In the objective of improving the performance of induction motor operation and ensuring a robust control against different uncertainties and external disturbances, especially at low-speed regions, this research highlights the main features of two nonlinear control techniques. First, the control design is based on the backstepping approach (BSA) with integral action, and then the sliding mode control (SMC) theory. The BSA principle is to define successive causal relations in order to construct the control law in a recursive and systematic way. This allows overcoming the obstacle of the higher-order system's dimension. SMC is designed to drive and then constrain the system state to lie within a neighborhood of the switching surface, this provides very strong and inherent robustness to the resulting controllers. The main reason behind developing the nonlinear control techniques is to ensure a decoupled control of the machine. Besides, it guarantees the stability of the overall system by tracking the speed reference with the fewest static error. Moreover, as the sensorless control increases the reliability and decreases the cost of the control system, an extended Kalman filter is implemented to improve speed and flux observation. The simulations of all the discussed results have been obtained by MATLAB/Simulink.

The global sliding mode tracking control for a class of variable order fractional differential systems

In this paper, a novel variable order fractional control approach is proposed for tracking control of both of variable order fractional and constant order fractional order system with uncertain and external disturbance terms. In term of the global sliding mode control theory and terminal sliding mode control method, the system states are guaranteed to stay on the switching surface from the initial time, and then converge to the origin by the designed controllers which are continuous input signals. Such controllers avoid the undesirable chattering and remove the effects of uncertain and external disturbance completely. Finally, the comparison between the variable order fraction controller and the constant order fractional controller is given by numerical simulation, furthermore, numerical results on the effects of the tracking control are provided.

Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics.

Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent in the molecular structure or induced by the (intense) external field. The curse of dimensionality indicates the intractable exponential scaling of calculation effort with system size and restricts the implementation of "numerically exact" approaches for realistic large systems. The phase space formulation of quantum mechanics offers an important theoretical framework for constructing practical approximate trajectory-based methods for quantum dynamics. This Account reviews our recent progress in phase space mapping theory: a unified framework for constructing the mapping Hamiltonian on phase space for coupled F-state systems where the renowned Meyer-Miller Hamiltonian model is a special case, a general phase space formulation of quantum mechanics for nonadiabatic systems where the electronic degrees of freedom are mapped onto constraint space and the nuclear degrees of freedom are mapped onto infinite space, and an isomorphism between the mapping phase space approach for nonadiabatic systems and that for nonequilibrium electron transport processes. While the zero-point-energy parameter is conventionally assumed to be positive, we show that the constraint implied in the conventional Meyer-Miller mapping Hamiltonian requires that such a parameter can be negative as well and lies in (-1/F, +∞) for each electronic degree of freedom. More importantly, the zero-point-energy parameter should be interpreted as a special case of a commutator matrix in the comprehensive phase space mapping Hamiltonian for nonadiabatic systems. From the rigorous formulation of mapping phase space, we propose approximate but practical trajectory-based nonadiabatic dynamics methods. The applications to both gas phase and condensed phase problems include the spin-boson model for condensed phase dissipative two-state systems, the three-state photodissociation models, the seven-site model of the Fenna-Matthews-Olson monomer in photosynthesis of green sulfur bacteria, the strongly coupled molecular/atomic matter-optical cavity systems designed for controlling and manipulating chemical dynamical processes, and the Landauer model for a quantum dot state coupled with two electrodes. In these applications the overall performance of our phase space mapping dynamics approach is superior to two prevailing trajectory-based methods, Ehrenfest dynamics and fewest switches surface hopping.

Robust sliding mode preview control for uncertain discrete-time systems with time-varying delay

This article focuses on the problem of robust sliding mode preview control for a class of non-linear delayed systems. It is assumed that the reference signal is previewed with a fixed length ahead and the norm of uncertainty is bounded. A model transformation is introduced to approximate the time-varying delay such that augmented error systems can be constructed. Conditions of asymptotic stability of sliding motion are established via the small gain theorem. The sliding mode preview controller is designed such that the controlled system state can be attracted to the switching surface and keep on it thereafter. A numerical example is presented to illustrate the effectiveness of the proposed control design.

Design of a global discrete‐time sliding mode control scheme for a class of nonlinear systems with state delays and uncertainties

AbstractThis paper proposes a discrete‐time sliding mode control design for a class of discrete‐time dynamic systems with time delays, parameter uncertainties, and external disturbances. The robust design implements an adaptive discrete‐time reaching law in order to reduce the effect of the chattering phenomena and improve system robustness. It also considers a lumped disturbance function for the unknown parameters and time‐delayed terms in order to estimate both at the same time. Additionally, the proposed sliding function ensures that the states of the control system are put on the switching surface right from the beginning, thus eliminating the reaching phase. The effectiveness of the proposed scheme was assessed using the longitudinal and lateral dynamics of an Osprey plane model. The obtained results indicated that the proposed approach guarantees system stability and ensures excellent tracking performance in the simultaneous presence of time delays, parameter uncertainties, and external disturbances.