Simultaneous Stabilization Controller Research Articles

Finite‐time robust simultaneous stabilization control for two nonlinear singular time‐delay systems

AbstractIn this paper, the finite‐time simultaneous stabilization problem of two nonlinear singular time‐delay Hamiltonian systems is investigated. Firstly, the two general nonlinear singular time‐delay Hamiltonian systems are transformed into their Hamiltonian differential‐algebraic forms by equivalent transformation, respectively, they are then converted to two strictly dissipative Hamiltonian forms via the state feedback method, and two strictly dissipative Hamiltonian systems are extended into a Hamiltonian one. Based on which, a suitable Hamiltonian function is constructed to analyze the finite‐time simultaneous stability and finite‐time robust simultaneous stabilization problem. Finally, an illustrative example is given to show the effectiveness of the results obtained. It should be pointed out that since there does not exist a finite‐time stability criterion on the nonlinear singular delay system, we adopt a new double compound asymptotic method.

Simultaneous exponential stabilization for stochastic port-controlled Hamiltonian systems with actuator saturations, fading channels and delays

This paper is concerned with the simultaneous exponential stabilization problem for a set of stochastic port-controlled Hamiltonian (PCH) systems. Due to the limited bandwidth of the channels, the phenomena of fading channels and transmission delays which are described by a time-varying stochastic model always occur in the communication channels from the controller to the actuator. Meanwhile, actuator saturation constraint is taken into account. On the basis of dissipative Hamiltonian structural and saturating actuator properties, those stochastic PCH systems are combined to generate an augmented system. By utilizing the stochastic analysis theory, sufficient criterions are given for the simultaneous stabilization controller design ensuring that the closed-loop system is simultaneously exponentially mean-square stable (SEMSS). For the case that there exist external disturbances in the systems, some results on stability analysis and controller design are given. The developed controller design scheme is proved by a three-helicopter model simulation example.

Leader–follower formation stabilization and tracking control for heterogeneous planar underactuated vehicle networks

In this paper, we solve the distributed leader–follower simultaneous formation stabilization and tracking control problem for heterogeneous planar underactuated vehicle networks without global position measurements of the followers. The vehicles in the network are modeled as generic 3-DOF planar rigid bodies with two control inputs, and are allowed to have identical or non-identical dynamics. By incorporating graph theory, passivity-based control, partial stability theory, Matrosov’s theorem and the persistence of excitation concept, a smooth formation control scheme is proposed to simultaneously address the formation stabilization and formation tracking problems without switching. Moreover, the structure of the controller is relatively simple compared to the existing controllers in the literature, and thus, is practical and easy to implement. Simulations on a group of underactuated vehicles including nonholonomic mobile robots and surface vessels are presented to demonstrate the effectiveness of the proposed control scheme.

Robust simultaneous stabilization of multiple n‐degree‐of‐freedom robot systems

AbstractIn this paper, the robust simultaneous stabilization problem of multiple n‐degree‐of‐freedom (n‐DOF) robot systems is studied by using Hamiltonian function method, and the corresponding L2 interference suppression controller is designed. First, we investigate the general simultaneous stabilization of the multiple n‐DOF robot systems without external disturbance. On this basis, we further study the robust simultaneous stabilization control problem for multiple n‐DOF robot systems with external disturbance and design a simultaneous stabilization controller. Finally, the simulation results show that the simultaneous stabilization controller designed for the paper is very effective in stabilizing multiple robot systems at the same time.

Adaptive Fuzzy Output Feedback Simultaneous Posture Stabilization and Tracking Control of Wheeled Mobile Robots With Kinematic and Dynamic Disturbances

This article proposes a simultaneous posture (i.e., position and heading direction angle) stabilization and tracking control for differential-drive wheeled mobile robots (WMRs) using an adaptive fuzzy output feedback tracking control (AFOFTC) method and a fuzzy basis function network (FBFN). Existing studies on simultaneous posture stabilization and tracking control of WMRs do not compensate for the uncertainties and disturbances caused by kinematics and dynamics (i.e., kinematic and dynamic disturbances). To inhibit the performance degradation caused by these disturbances, an FBFN-based adaptive fuzzy output feedback posture stabilization and tracking control of WMRs is proposed considering the unavailable velocities of the WMR. In this approach, i) kinematic error equations are derived in polar coordinates, ii) a nonlinear velocity observer for WMRs containing the kinematic and dynamic uncertainties is designed, iii) a backstepping-like feedback linearization controller is designed based on the kinematics in polar coordinates to generate a reference trajectory, and iv) an AFOFTC law is proposed based on the dynamics to ensure that the WMR follows the generated reference trajectory. The proposed method can maintain satisfactory posture stabilization and tracking control performance despite the kinematic and dynamic disturbances. A stability analysis as well as the simulation and experimental results are provided to validate the proposed scheme.

Output feedback based simultaneous stabilization of two Port-controlled Hamiltonian systems with disturbances

In motor system control design, a single controller is usually employed to simultaneously control two or more motors for saving costs, which also achieves the computational simplification of control. In practical Hamiltonian systems control, more systems also need to be stabilized by a single controller under some working conditions. Thus, this paper studies simultaneous stabilization problem of two nonlinear Port-controlled Hamiltonian (PCH) systems with disturbances by a composite controller. Based on the Hamiltonian structure properties, two PCH systems are combined together to generate an augmented PCH system by utilizing output feedbacks firstly. Then, to estimate disturbances effectively, it is essential to design a nonlinear disturbance observer (NDOB) and the estimate is employed to feedforward compensate the effects of disturbances. Next, combining the output feedback part and the disturbance compensation part together, a simultaneous stabilization controller is developed. Subsequently, it is proved that the closed-loop system under the proposed controller is asymptotically stable. Finally, an example with simulations reveals that the proposed method is effective.

Fractional Calculus with its Applications in Engineering and Technology

This book aims to provide the basic theory of fractional calculus and its applications based on practical schemes and approaches, illustrated with applicable engineering and technical examples, especially focusing on the fractional-order controller design. In the development of this book, the essential theorems and facts in the first two chapters are proven with rigorous mathematical analyses. In addition, the commonly used definitions of Grunwald-Letnikov, Riemann-Liouville, Caputo, and Miller-Ross fractional derivatives are introduced with their properties proved and linked to fractional-order controller design. The last chapter presents several enlightening scenarios of fractional-order control designs, for example, the suppression of machining chatter, the nonlinear motion control of a multilink robot, the simultaneous tracking and stabilization control of a rotary inverted pendulum, and the idle speed control of an internal combustion engine (ICE).

Multiple Urban Domestic Water Systems: Method for Simultaneously Stabilized Robust Control Decision

The distribution of water resources and the degree of economic development in different cities will result in different parameters for the supply and demand of domestic water in each city. In this paper, a simultaneous stabilization and robust control method is proposed for decision-making regarding multiple urban domestic water systems. The urban water demand is expressed as the product of the urban domestic water consumption population and per capita domestic water consumption. The fixed capital investment and labor input of the urban domestic water supply industry are used as control variables. Based on the Lyapunov stability theory and the linear matrix inequality method, multiple urban domestic water supply and demand systems can accomplish asymptotical stability through the coordinated input of investment and labor. For an empirical analysis, we take six cities—Nanjing, Wuxi, Nantong, Yangzhou, Xuzhou, and Lianyungang—in Jiangsu Province, China, to study the simultaneously stabilized coordinated control scheme. The simulation results show that the same control scheme simultaneously achieves the asymptotic stability of these urban domestic water supply and demand systems, and is robust when it comes to the variation of system parameters. This method is particularly suitable for a water resources administrative agency to make a unified decision-making arrangement for water supply input in different areas. It will help synchronize multiple urban domestic water managements and reduce the difficulty of control.

Adaptive Parallel Simultaneous Stabilization of a Class of Nonlinear Descriptor Systems via Dissipative Matrix Method

This paper investigates the adaptive parallel simultaneous stabilization and robust adaptive parallel simultaneous stabilization problems of a class of nonlinear descriptor systems via dissipative matrix method. Firstly, under an output feedback law, two nonlinear descriptor systems are transformed into two nonlinear differential-algebraic systems by nonsingular transformations, and a sufficient condition of impulse-free is given for two resulting closed-loop systems. Then, the two systems are combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique. Based on the dissipative system, an adaptive parallel simultaneous stabilization controller and a robust adaptive parallel simultaneous stabilization controller are designed for the two systems. Furthermore, the case of more than two nonlinear descriptor systems is investigated. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the adaptive parallel simultaneous stabilization controllers obtained in this paper work very well.

Adaptive robust simultaneous stabilization controller with tuning parameters design for two dissipative Hamiltonian systems

AbstractThis paper investigates the problem of adaptive robust simultaneous stabilization (ARSS) of two dissipative Hamiltonian systems (DHSs), and proposes a number of results on the controller parameterization design. Firstly, an adaptiveH∞control design approach is presented by using the dissipative Hamiltonian structural for the case that there are both external disturbances and parametric uncertainties in two DHSs. Secondly, an algorithm for solving tuning parameters of the controller is proposed using symbolic computation. The proposed controller parameterization method avoids solving Hamilton-Jacobi-Issacs (HJI) equations and the obtained controller is easier as compared to some existing ones. Finally, an illustrative example is presented to show that the ARSS controller obtained in this paper works very well.

A Family of Robust Simultaneous Controllers With Tuning Parameters Design for a Set of Port‐Controlled Hamiltonian Systems

AbstractThis paper investigates the robust simultaneous stabilization (RSS) and robust adaptive simultaneous stabilization (RASS) problem for a set of port‐controlled Hamiltonian (PCH) systems. Some results for designing a family of robust simultaneous controllers with tuning parameters for such systems are proposed. Firstly, using the dissipative Hamiltonian structural properties, these systems are combined to generate an augmented PCH system, and two simultaneous stabilization controllers with parameters are designed for the systems: one is a robust controller and the other is adaptive. Secondly, an algorithm for solving the tuning parameters’ ranges of controller is proposed with symbolic computation. Finally, a numerical example is studied by applying the method obtained in this paper to a set of PCH systems with external disturbance. The effectiveness of the proposed control method is verified by simulations. Compared with conventional simultaneous stabilization control, the controller obtained in this paper not only has strong robustness for a set of systems, but also can optimize the robustness for the systems by adjusting the parameters’ values.

Simultaneous stabilization of Port-Hamiltonian systems subject to actuation saturation and input delay

This paper investigates the simultaneous stabilization of Port-Hamiltonian (PH) systems subject to actuation saturation (AS) and input delay. Firstly, two parallel connecting PH systems subject to the AS and input delay are proposed. Secondly, a simultaneous stabilization control law is designed by a difference between the two feedback control laws containing the input delay. Thirdly, computing a Lyapunov-Krasovskii function assures the simultaneous stabilization of the above systems. Finally, simulation is given to show the correctness of the proposed contents.

Robust Simultaneous Stabilization Control Method for Two Port-Controlled Hamiltonian Systems: Controller Parameterization

This paper investigates robust simultaneous stabilization (RSS) control method for two port-controlled Hamiltonian (PCH) systems and proposes results on the design of simultaneous stabilization controller with parameters for such systems. Firstly, two PCH systems are studied. Using the dissipative Hamiltonian structural properties, the systems are combined to generate an augmented PCH system. When there are external disturbances in the systems, a robust controller with parameters is designed for the systems. Secondly, an algorithm for solving parameters of the controller is proposed with symbolic computation. Finally, an illustrative example is presented to show that the RSS controller obtained in this paper works very well.

Simultaneous Stabilization Control for Multiple City Domestic Water System

Established multiple city domestic water system control model. Used new water population and fixed capital investment flow as control variables. The example result got the negative feedback control scheme, can realize the multiple city domestic water system simultaneous stabilization control.

Simultaneous stabilization of a class of nonlinear descriptor systems via Hamiltonian function method

This paper studies simultaneous stabilization of a class of nonlinear descriptor systems via the Hamiltonian function method. Firstly, based on the Hamiltonian realization of the nonlinear descriptor systems and a suitable output feedback, two nonlinear descriptor systems are equivalently transformed into two nonlinear Hamiltonian differential-algebraic systems by a nonsingular transformation, and a sufficient condition for two closed-loop systems to be impulse-free is given. The two systems are then combined to generate an augmented dissipative Hamiltonian differential-algebraic system by using the system-augmentation technique, based on which a simultaneous stabilization controller and a robust simultaneous stabilization controller are designed for the two systems. Secondly, the case of more than two nonlinear descriptor systems is investigated, and two new results are proposed for the simultaneous stabilization and robust simultaneous stabilization, respectively. Finally, an illustrative example is studied by using the results proposed in this paper, and simulations show that the simultaneous stabilization controllers obtained in this paper work very well.

Simultaneous Stabilization and Robust Control of Polynomial Nonlinear Systems Using SOS Techniques

This technical note is concerned with the simultaneous stabilization and robust performance control for a class of polynomial nonlinear systems. Building on the tenets of state-dependent polynomial Lyapunov functions, we present sufficient conditions for simultaneous stabilization with and without Hinfin performance. These conditions can be verified by the recently developed sum of squares technique which essentially solves a linear matrix inequality feasibility problem.

Parallel simultaneous stabilization of two systems governed by partial differential equations subject to actuator saturation

A parallel simultaneous stabilization of two systems governed by partial differential equation (PDE), with conservation law subject to actuator saturation, is considered, and a method on the control design is proposed. Based on the orthogonal decomposition for a Port-Controlled Hamiltonian system, an abstract approach to the parallel simultaneous stabilization of two systems governed by partial differential equation, with conservation law subject to actuator saturation, is established. The study shows that the parallel simultaneous stabilization controller obtained in this paper is valid in the case of the systems governed by the PDEs.

Simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian systems

This paper investigates simultaneous stabilization of a set of nonlinear port-controlled Hamiltonian (PCH) systems and proposes a number of results on the design of simultaneous stabilization controllers for the PCH systems. Firstly, the case of two PCH systems is studied. Using the dissipative Hamiltonian structural properties, the two systems are combined to generate an augmented PCH system, with which some results on the control design are then obtained. For the case that there exist parametric uncertainties in the two systems’ Hamiltonian structures, an adaptive simultaneous stabilization controller is proposed. When there are external disturbances and parametric uncertainties in the two systems, two simultaneous stabilization controllers are designed for the systems: one is a robust controller and the other is a robust adaptive one. Secondly, the case of more than two PCH systems is investigated, and a new result is proposed for the simultaneous stabilization of the systems. Finally, two illustrative examples are studied by using the results proposed in this paper. Simulations show that the simultaneous stabilization controllers obtained in this paper work very well.

Decentralized simultaneous stabilization and reliable control using periodic feedback

In this note we consider the simultaneous decentralized stabilization problem for linear, periodically time-varying, discrete time systems. We show that a finite number of periodically time-varying systems can be simultaneously stabilized by a periodically time-varying decentralized compensator if and only if each system admits a decentralized stabilizing compensator. The result is applicable in the design of reliable decentralized stabilizing compensators for interconnected systems.