Stabilizing Controller Design Method Research Articles

Event-Triggered Adaptive Security Path Following Control for Unmanned Ground Vehicles Under Sensor Attacks

This paper is concerned with the event-triggered adaptive security control (ET-ASC) for the path following of networked unmanned ground vehicles (UGVs) subject to sensor attacks. Firstly, a security model is well established to capture the dynamics of path following control of UGVs under sensor attacks. Then, the ET-ASC with respect to correction signal is proposed to mitigate the effects of such sensor attacks. In what follows, two theorems, which include both input to state stability (ISS) criterion and controller design method, are carefully derived for the path following control of UGVs under the proposed ET-ASC scheme. The advantage of the proposed ET-ASC scheme lies in that it can actively amend the sensor attacks in an adaptive way and exclude Zeno phenomenon naturally. At last, a verification simulation experiment are conducted to show the effectiveness of the proposed ET-ASC method.

The novel impulsive switching conditions for stability of impulsive switched stochastic systems

This paper studies the problems of stability analysis and stabilisation synthesis for a class of impulsive switched stochastic systems. By constructing a novel impulsive switching condition, the sufficient conditions of globally asymptotic stability in probability and stochastic input-to-state stability for the considered systems are presented. Furthermore, the stabilising controller design method can be presented for the corresponding closed-loop systems. Two examples are given to illustrate the effectiveness of the obtained results.

Sun-pointing safe control for atmospheric environment monitoring satellite using magnetic actuation

The design of sun-pointing safe controller is an important part of spacecraft attitude determination and control system. In this work, a new spin stabilization algorithm using only magnetic torquers is proposed. This algorithm has been developed for the atmospheric environment monitoring satellite, which completes the missions of fixed axis rotation and tracking the sun orientation. Firstly, a Lyapunov function, combining the angular momentum error and angular velocity, is formulated and a new sun-pointing attitude control scheme is derived. Then, it is proved that the magnetic control law is asymptotically stable in the absence of disturbance torques. The proposed method is compared with a state-of-the-art fault-tolerant magnetic spin stabilizing controller design method by numerical simulations. Simulation results show that the proposed method has better performance than the state-of-the-art technique. Finally, the applicability and effectiveness of the proposed control method are demonstrated by the hardware-in-the-loop simulation of the satellite.

Stabilizing Controller Design Using the Lower Bound of the Stability Margin Estimated by a Data-driven Method

In this paper, we propose a stabilizing controller design method to use the lower bounds of the stability margins estimated by a data-driven method in a situation where a plant is unknown. To design a stabilizing controller, we derive a theorem which gives a class of a stabilizing controller. By using this theorem, we can design a controller to stabilize the closed-loop system without the mathematical model of a plant. In the numerical example, we estimate the lower bounds of the stability margins and design a stabilizing controller with only this.

Stability and stabilization of delayed fuzzy systems via a novel quadratic polynomial inequality

The stability and stabilization problems of a class of Takagi-Sugeno(T-S) fuzzy systems with time-varying delay are concerned in this paper. By introducing the tunable parameter l, a novel quadratic polynomial inequality is proposed to reduce the estimation gap with previous work. Sequentially, an appropriate Lyapunov-Krasovskii functional(LKF) containing some new s-dependent integral terms is constructed, the delay-dependent stability condition is further improved by combining the generalized free-matrix-based integral inequality (GFMBII) with the proposed inequality. Finally, four typical numerical examples are carried out to demonstrate the validity and feasibility of the stability criterion and controller design method.

Expected power bound and stability of two-dimensional digital filters with multiplicative noise in the FMLSS model

This paper studies the two-dimensional (2-D) expected power bound (EPB) for 2-D digital filters with multiplicative noise in the Fornasini-Marchesini local state-space (FMLSS) model. By virtue of a class of linear matrix inequalities (LMIs), the novel existence criterion of 2-D EPB for 2-D digital filters in the considered model is obtained. The corresponding stabilization controller design method is presented based on the above criterion. Finally, two examples are presented to verify the effectiveness of our results.

이산시간 불확실 특이시스템의 새로운 강인 유한시간 상태궤환 제어

In this paper, we consider the problem of robust finite-time singular stability(RFSS) and state feedback controller design method for discrete–time linear singular systems with norm-bounded parameter uncertainties. First, the FSS sufficient condition is derived by equivalently transformed closed-loop system. Second, a state feedback controller design method satisfying regular, causal, and RFSS is proposed by LMI(linear matrix inequality) technique on the basis of the obtained FSS condition and equivalent properties of the considering system. The presented conditions are strict LMI conditions in terms of finding all variables compared with previous results. Finally, a numerical example is given to illustrate the validity of the proposed method.

Stability Analysis of Discrete-Time Semi-Markov Jump Linear Systems

This article discusses the stability and stabilization problems for the discrete-time semi-Markov jump linear systems (S-MJLSs) with bounded sojourn times. By using the method of multiple-Lyapunov functions and the concept of discrete-time semi-Markov kernel, we provide the sufficient conditions for σ-error mean square stability of S-MJLSs. In such conditions, the transition probability matrix of embedded Markov chain is considered, which is more general than the scenarios in previous works that only consider the sojourn time of each subsystem mode. Based on such conditions, the stabilization controller design method is also proposed for the resulting closed-loop systems. Two examples are given to illustrate the effectiveness of our results.

Stability and stabilization for delayed fuzzy systems via reciprocally convex matrix inequality

This paper focuses on the problems of stability and stabilization for time-delayed fuzzy systems. By establishing a novel Lyapunov-Krasovskii functional (LKF) and using an extended reciprocally convex matrix inequality with auxiliary function integral inequality, an improved stability condition is proposed. To further improve the results, a delay-product-type term is introduced into the LKF. Then, a delay-dependent stabilization condition is developed based on parallel distributed compensation (PDC) scheme by some linearization techniques. Finally, the efficiency and benefits of the stability criterion and controller design method are illustrated by several classical numerical examples.

Stabilization and synchronization of 5-D memristor oscillator using sliding mode control

ABSTRACTThis article presents a control design method for asymptotic stabilization, synchronization, and antisynchronization of a five dimensional chaotic memristor oscillator system. Two cases are considered: (i) with known parameters, (ii) and with unknown parameters. When a system’s parameters are known, then controllers are designed using sliding mode approach and when system’s parameters are unknown then controllers are devised using adaptive integral sliding mode control method. Hurwitz surfaces are constructed in both approaches. To employ the integral sliding mode, firstly, the system is transformed into a special structure containing a nominal part and some unknown terms computed adaptively. Then, the system is stabilized using integral sliding mode control. The stabilizing controller, consisting of the nominal control plus some compensator control, is then designed. The compensator controller and the adapted laws are derived in such a way that the time derivative of a Lyapunov function becomes strictly negative. The effectiveness of the proposed scheme is tested through computer simulation.

Design of PIλDμ controller for global power control of Pressurized Heavy Water Reactor

In this paper, a robust stabilizing controller design method is presented for global power control of a Pressurized Heavy Water Reactor (PHWR) under step-back condition scheme using a Fractional Order Proportional Integral Derivative (PIλDμ) controller resulting into robust performance. The method is applicable to design a controller for One Non Integer Order Plus Time Delay (NIOPTD-I) plant which satisfies design specifications such as phase margin and gain crossover frequency. Stability boundary locus method is used in (Kp, Ki, Kd) parameter space for NIOPTD-I plants to obtain stability region. The robust performance is obtained by satisfying flat phase condition at gain crossover frequency where phase is almost constant for large span of frequencies. The simulation result of the proposed PIλDμ controller shows active step-back control to the insertion of the rod with no undershoot and with the robust performance, hence safe to the plant for gain variations from 500% lower side to 1000% upper side. The PIλDμ controller with a plant shows that 30% and 50% global power drop from initial 100% is achieved in a reasonable time without undershoot.

General robust stability controller design method for a class of hopf bifurcation systems

For the nonlinear Hopf bifurcation system, the change of bifurcation parameter has an important influence on the state of the system. In order to control the Hopf bifurcations of the nonlinear dynamic system, the parameter values of bifurcation points in the system need to be found out before controller designing. However, due to uncertainties of the system structure and parameters in the nonlinear system, or disturbance, it is difficult to determine the bifurcation point precisely. So it is a good way of designing a robust controller near the bifurcation point. Although, lots of works have discussed the robust control of a Hopf bifurcation in a nonlinear dynamic system, the solutions are not satisfactory and there are still many problems. The controller is always designed for some special system. Its structure is usually complex, not general, and the design process is complicated. And before controller design, the value of bifurcation point must be solved accurately.In this paper, a parametric robust stability controller design method is proposed for a class of polynomial form Hopf bifurcation systems. Using this method, it is not necessary to solve the exact values of the bifurcation parameter, it is only needed to determine the bifurcation parameter range. The designed controller includes a system state polynomial; its structure is general, simple and keeps the equilibrium of the original system unchanged. By using the Hurwitz criterion, the system stability constraints for bifurcation parameter boundaries are obtained at equilibrium, and they are described by algebraic inequalities. Cylindrical algebraic decomposition is applied to calculate the stability region of the controller parameters. And then, in the region, parameters of the robust controller can be calculated to make the dynamic system stable. In this paper, the Lorenz system without disturbance is used as an example to show the designing process of the method, and then the controller of the van der Pol oscillator system with disturbance is designed by this method as an engineering application. Simulations of the two systems are given to demonstrate that the proposed controller designing method can be effectively applied to the robust stability control of the Hopf bifurcation systems.

Stabilization and Separation Principle of Networked Control Systems Using the T–S Fuzzy Model Approach

This paper is concerned with the stabilization problem for a class of discrete-time networked control systems (NCSs) with bounded time delays and packet losses. The controlled plant is represented by a Takagi–Sugeno fuzzy model, and both the state feedback control and output feedback control cases are considered. By guaranteeing the decrement of Lyapunov functional at each control signal updating step, a less conservative stability condition for the state feedback NCSs is derived, and the corresponding stabilizing controller design method is also presented. Under an observer-based framework, the output feedback stabilization problem is further studied, where the main contribution is the development of the separation principle for NCSs. Illustrative examples are provided to show the advantage and effectiveness of the developed results.

Control Design for a Class of Affine Nonlinear Descriptor Systems With Actuator Saturation

This technical note studies the control design problem for a class of affine nonlinear descriptor systems with actuator saturation, and presents several new results. A stabilization controller design method is first proposed by state feedback and compensation, and a robust H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller and a robust adaptive H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> controller are respectively designed for the discussed system when external disturbances and/or parametric perturbations are taken into account. Simulation results on a nonlinear descriptor circuit system illustrate the efficiency of the controllers presented in this technical note.

Attitude Control of Chaotic Satellite with Unknown Input and uncertainties based on Sliding Control

attitude control of missiles, spacecraft and satellites is essential; in order to remain them fixed in space to perform their missions accurately. The attitude equation of a satellite is a six- dimensional nonlinear system which includes some types of nonlinear behavior such as periodic trajectory, chaotic dynamics. In this paper, a sliding mode control design method for stabilization of the attitude chaotic satellites with unknown inputs and uncertainties. Using Lyapunov theory, the stability control system is proven. Simulation results show that the proposed controller can be chaotic satellite attitude in the presence of unknown inputs and uncertainties will converge to the unstable equilibrium points. In this section, the satellite system and the chaotic dynamics are studied. In (16) the problem of satellite attitude control with redundant thrusters, and in (17) satellite attitude control with an uneven inertia distribution has been investigated. However, given that the satellite attitude motion under external disturbances becomes chaotic mode, the control satellite system will be very complex. So, be very careful satellite control system is designed. In (13) and (14) satellite attitude control of chaotic behavior has been investigated. The orientation of the satellite at a given point can be locally described in terms of three angles

Stabilizing Controller Design for Quasi-Resonant Converters Described by a Class of Piecewise Linear Models

This paper presents a stabilizing controller design method for quasi resonant (QR) converters described by a class of piecewise linear (PWL) models. The generalized state-space averaging technique (GSSA) is applied for the modeling and analysis of the half-wave zero current switching quasi-resonant (HW-ZCS-QR) buck converter. The nonlinear GSSA model of the converter is reconstructed using a piecewise linearizing technique. Subsequently, the piecewise linear models are combined together, to form a unified model, using a fuzzy modeling approach. The stability of the applied method has been investigated using Lyapunov method. Finally, a linear H∞ controller synthesis method is applied to the converter described by the proposed model. The experimental results on the converter are presented to verify the performance of the applied method for modeling the dynamics of the converter and designing the appropriate controller.

Nonlinear control design based on generalized Takagi–Sugeno fuzzy systems

This paper is concerned with control design for a generalized Takagi–Sugeno fuzzy system. The Takagi–Sugeno fuzzy system generally describes nonlinear systems by employing local linear system representations, while a generalized fuzzy system to be considered in this paper describes even a wider class of nonlinear systems by representing locally nonlinear systems. For such a generalized system, a stabilizing controller design method is proposed by introducing a new class of non-PDC controllers. A non-PDC controller is a generalized controller of PDC one, which is a traditional fuzzy controller. Stabilizing controller design conditions are given in terms of a set of linear matrix inequalities (LMIs), which are easily numerically solvable. A relaxation method is used to reduce the conservatism of design conditions. Finally, numerical examples are given to illustrate our nonlinear control design and to show the effectiveness over other existing results.

Modeling and Output Feedback Control of Networked Control Systems with Both Time Delays; and Packet Dropouts

This paper is concerned with the problem of modeling and output feedback controller design for a class of discrete-time networked control systems (NCSs) with time delays and packet dropouts. A Markovian jumping method is proposed to deal with random time delays and packet dropouts. Different from the previous studies on the issue, the characteristics of networked communication delays and packet dropouts can be truly reflected by the unified model; namely, both sensor-to-controller (S-C) and controller-to-actuator (C-A) time delays, and packet dropouts are modeled and their history behavior is described by multiple Markov chains. The resulting closed-loop system is described by a new Markovian jump linear system (MJLS) with Markov delays model. Based on Lyapunov stability theory and linear matrix inequality (LMI) method, sufficient conditions of the stochastic stability and output feedback controller design method for NCSs with random time delays and packet dropouts are presented. A numerical example is given to illustrate the effectiveness of the proposed method.

Stabilization bound of singularly perturbed systems subject to actuator saturation

This paper considers the stabilization bound problem for singularly perturbed systems (SPSs) subject to actuator saturation. A state feedback stabilization controller design method is proposed and a basin of attraction depending on the singular perturbation parameter is constructed, which facilitates the formulation of the convex optimization problem for maximizing the basin of attraction of SPSs. Finally, examples are given to show the advantages and effectiveness of the obtained results.

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ‘large’ as possible. An example is provided to demonstrate the effectiveness of the new method.