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1.
The main idea of the original parallel distributed compensation (PDC) method is to partition the dynamics of a nonlinear system into a number of linear subsystems, design a number of state feedback gains for each linear subsystem, and finally generate the overall state feedback gain by fuzzy blending of such gains. A new modification to the original PDC method is proposed here, so that, besides the stability issue, the closed-loop performance of the system can be considered at the design stage. For this purpose, the state feedback gains are not considered constant through the linearized subsystems, rather, based on some prescribed performance criteria, several feedback gains are associated to every subsystem, and the final gain for every subsystem is obtained by fuzzy blending of such gains. The advantage is that, for example, a faster response can be obtained, for a given bound on the control input. Asymptotic stability of the closed loop system is also guaranteed by using the Lyapunov method. To illustrate the effectiveness of the new method, control of a flexible joint robot (FJR) is investigated and superiority of the designed controller over other existing methods is demonstrated.  相似文献   

2.
Hyper-exponential stability analysis and hyper-exponential stabilization of linear systems by bounded linear time-varying feedback are investigated in this paper. On the one hand, we propose some Lyapunov-like hyper-exponential stability theorems (both global and local) based on the comparison principle and the concepts of hyper-exponentially stable functions and hyper-exponentially increasing functions. On the other hand, we establish methods to design bounded linear time-varying controllers such that hyper-exponential stability of linear time-invariant systems can be guaranteed. The key design tool is the utilization of a time-varying parameter contained in the controller and the properties of solution to a parametric Lyapunov equation. Both state feedback and observer-based output feedback are accommodated. As a further result, hyper-exponential semi-global stabilization for linear systems by bounded controls is discussed. Finally, the validity of the proposed schemes is illustrated through numerical simulations on spacecraft rendezvous control system.  相似文献   

3.
This paper addresses the cooperative output feedback control of a mobile dual flexible manipulator, which is mounted at a moving platform to grasp and move a rigid object. We derive the distributed parameter model with geometric constraints for the dual flexible manipulator system by utilizing the Lagrange multiplier method and the Hamilton’s principle, which avoids the problem of control spillover. This paper considers a case where the states of system are difficult to measure directly and exploits the high gain observer theory to design the state observers for estimating the unavailable states. Then the cooperative output feedback control scheme is developed by the Lyapunov’s method, which enables the cooperative control of the flexible manipulator system. Furthermore, under the cooperative output feedback control scheme, we prove that the states of the system are uniformly bounded. Finally, the feasibility of the designed cooperative output feedback controllers is verified by numerical simulation.  相似文献   

4.
This paper addresses the problem of local exponential stabilization via boundary feedback controllers for a class of nonlinear distributed parameter processes described by a scalar semi-linear parabolic partial differential equation (PDE). Both the domain-averaged measurement form and the boundary measurement form are considered. For the boundary measurement form, the collocated boundary measurement case and the non-collocated boundary measurement case are studied, respectively. For both domain-averaged measurement case and collocated boundary measurement case, a static output feedback controller is constructed. An observer-based output feedback controller is constructed for the non-collocated boundary measurement case. It is shown by the contraction semigroup theory and the Lyapunov’s direct method that the resulting closed-loop system has a unique classical solution and is locally exponentially stable under sufficient conditions given in term of linear matrix inequalities (LMIs). The estimation of domain of attraction is also discussed for the resulting closed-loop system in this paper. Finally, the effectiveness of the proposed control methods is illustrated by a numerical example.  相似文献   

5.
This paper presents a novel iterative learning feedback control method for linear parabolic distributed parameter systems with multiple collocated piecewise observation. Multiple actuators and sensors distributed at the same position of the spatial domain are utilized to perform collocated piecewise control and measurement operations. The advantage of the proposed method is that it combines the iterative learning algorithm and feedback technique. Not only can it use the iterative learning algorithm to track the desired output trajectory, but also the feedback control approach can be utilized to achieve real-time online update. By utilizing integration by parts, triangle inequality, mean value theorem for integrals and Gronwall lemma, two sufficient conditions based on the inequality constraints for the convergence analysis of the tracking error system are presented. Some simulation experiments are provided to prove the effectiveness of the proposed method.  相似文献   

6.
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7.
This paper proposes a framework for the design of sparsely distributed output feedback discrete-time sliding mode control (ODSMC) for interconnected systems. The major target here is to develop an observer based discrete-time sliding mode controller employing a sparsely distributed control network structure in which local controllers exploit some other sub-systems’ information as well as its own local information. As the local controllers/observers have access to some other sub-systems’ states, the control performance will be improved and the applicability region will be widened compared to the decentralised structure. As the first step, a stability condition is derived for the overall closed-loop system obtained from applying ODSMC to the underlying interconnected system, by assuming a priori known structure for the control/observer network. The developed LMI based controller design scheme provides the possibility to employ different information patterns such as fully distributed, sparsely distributed and decentralised patterns. In the second step, we propose a methodology to identify a sparse control/observer network structure with the least possible number of communication links that satisfies the stability condition given in the first step. The boundedness of the obtained overall closed-loop system is analysed and a bound is derived for the augmented system state which includes the closed-loop system state and the switching function.  相似文献   

8.
This paper is concerned with the quadratic stability analysis and robust distributed controllers design of both continuous-time and discrete-time uncertain spatially interconnected systems (USISs), where uncertainties are modeled by linear fractional transformation (LFT). The well-posedness, quadratic stability, and contractiveness of USISs are properly defined for the first time. A sufficient condition employing the given system matrices is established to check the well-posedness, quadratic stability and contractiveness. This condition is simpler than the existing conditions based on the decomposition of system matrices. Based on the new condition derived, a sufficient condition is given for the existence of robust distributed controllers and a constructive method is then presented for the design of robust distributed controllers. The advantage of the proposed constructive approach is that it employs the given system matrices while the existing methods conduct the bilinear transformation on these matrices when design controllers, and consequently, the constructive approach in this paper is computationally more efficient than the existing methods. Several examples are included to demonstrate the simplicity, efficiency and applicability of the derived theoretical results.  相似文献   

9.
This paper proposes two kinds of distributed disturbance observer (DO) based consensus control laws for linear multi-agent systems (MAS) with mismatched disturbances. For a linear MAS with mismatched disturbances generated by exosystems, we design relative information based distributed DOs for each agent to obtain information of disturbances. The first method is to utilise the information of disturbances obtained by the distributed DO as a feedforward term to reject influence of exogenous disturbances for consensus results, where the gain matrix of the feedforward term is obtained via solving a matrix equation. The second method is to design an internal model based dynamic compensator to reject influence of exogenous disturbances, where the dynamic compensator is also updated by the distributed DO. The leaderless and leader-follower consensus are both considered in this paper, and rigorous proof of consensus results is also given. Finally, some numerical simulations verify effectiveness of the proposed consensus control laws.  相似文献   

10.
This paper is concerned with the stabilization of linear systems with both pointwise and distributed input delays, which can be arbitrarily large yet exactly known. The state vector used in the well-known Artstein transformation is firstly linked with the future state of the system. Pseudo-predictor feedback (PPF) approaches are then established to design memory stabilizing controllers. Necessary and sufficient conditions guaranteeing the stability of the closed-loop system are established in terms of the stability of some integral delay systems. Furthermore, since the PPF still is infinite-dimensional state feedback law and may cause difficulties in their practical implementation, truncated pseudo-predictor feedback (TPPF) approaches are established to design finite dimensional (memoryless) controllers. It is shown that the pointwise and distributed input delays can be compensated properly by the TPPF as long as the open-loop system is polynomially unstable. Finally, two numerical examples, one of which is the spacecraft rendezvous control system, are carried out to support the obtained theoretical results.  相似文献   

11.
This paper addresses the output regulation problem for a class of preview control systems, and derives a state feedback law which suppresses the steady-state error caused by the excitation from polynomial or sinusoidal exogenous inputs. Recently, the output regulation condition for the broader class of distributed parameter systems is characterized via the operator regulator equation. We show that a solution of the operator regulator equation specialized to the preview control system is obtained by solving the matrix regulator equation, and provide the state feedback law which attenuates the transient error optimally with respect to an LQ (Linear Quadratic) performance index.  相似文献   

12.
This paper deals with the exponential stabilization of first order ODE-transport PDE coupled at the boundary point. A state feedback boundary control law has been formulated with the help of the backstepping method. The main novelty of this paper is that the stabilization of the coupled system is discussed by Lyapunov theory and the appropriate observer gain is designed by using the linear matrix inequalities (LMIs). An anti-collocated observer design for the corresponding dual system is also presented. The state feedback boundary controller, observer design and the stabilization of the closed-loop system are discussed in detail with illustrative numerical examples.  相似文献   

13.
In this paper, we will consider how to stabilize a mathematical model, the Kolmogorov model, of the interactions of an n species population. The Lotka–Volterra model is a particular case of the more general Kolmogorov model. We first identify the unstable steady states of the model, then we use the feedback control based on the solutions of the Riccati equation to stabilize the linearized system. Finally we stabilize the nonlinear system by using the feedback controller obtained in the stabilization of the linearized system. We introduce the backward Euler method to approximate the feedback control nonlinear system and obtain the error estimates. Four numerical examples are given which come from the application areas.  相似文献   

14.
The study aims to explore the optimal actuator switching scheme of observer-based event-triggered state feedback control for distributed parameter systems. The performance of distributed parameter systems is improved through the observer-based event-triggered control, in which the state feedback is updated only when a triggered event happens. In such an event-triggered mechanism, the event-based closed-loop system and minimum time interval between consecutive events are bounded. Based on finite horizon linear quadratic regulator (LQR) optimal control, the optimal switching algorithm is proposed based on the event-triggered mechanism during an unfixed time interval. Finally, the proposed scheme is verified through a simulation case.  相似文献   

15.
In this paper, we investigate the output synchronization of networked SISO nonlinear systems that can be transformed into semi-strict feedback form. Due to parameter uncertainty, the agents have heterogeneous dynamics. Combined backstepping method together with graph theory, we construct an augmented Laplacian potential function for analysis and a distributed controller is designed recursively for each agent such that its output can be synchronized to its neighbors' outputs. The distributed controller of each agent has three parts: state feedback of itself, neighborhood information transmitted through the network and adaptive parameter updaters both for itself and its neighbors. Moreover, distributed tuning function is designed to minimize the order of the parameter updater. It is proved that when the undirected graph is connected, all agents’ outputs in the network can be synchronized, i.e., cooperative output synchronization of the network is realized. Simulation results are presented to verify the effectiveness of the proposed controllers.  相似文献   

16.
In this paper, the simultaneous H∞ stabilization problem is investigated for a physically interconnected large-scale system which works in multiple operation modes. A distributed wireless networked control framework is introduced, in which the distributed dynamic output feedback controllers not only use the local measurements, but also receive the neighboring controllers’ broadcasts via wireless networks. The channel fading in wireless communications is described as the Rice fading model. Our focus is on the design of the distributed controllers such that the large-scale system is mean-square stable in each operation mode and achieves a prescribed H∞ disturbance attenuation level. By employing the Lyapunov functional method and related stochastic analysis techniques, a sufficient condition on the existence of desired controllers is presented, and the parameterization of the controller gains is derived. Finally, a numerical example is utilized to illustrate the feasibility of the proposed scheme.  相似文献   

17.
本文讨论一类严格正则的单输入多输出系统输出反馈配置极点问题。通过利用非齐次线性方程组解的结构,得到容易求解的输出反馈配置极点方法;最后举例说明这种方法的有效性。  相似文献   

18.
This work investigates the problem of distributed control for large-scale systems, in which a communication network is available to exchange information. To avoid the unnecessary communication, an event-triggered control (ETC) mechanism is introduced, in which the transmission occurs only when a certain event is triggered. Under the assumption that only the output signal is available, the static output feedback (SOF) is considered in this work. The aim of the co-design is to design an SOF controller and an ETC condition simultaneously such that the overall closed-loop system is stabilized with a certain level of performance. To this end, an event-triggering scheme based on output signals is proposed to determine when the event is triggered. Then the closed-loop system is modeled as a linear perturbed system. The distributed control co-design is formulated as a convex optimization problem with linear matrix inequalities (LMIs) constraints. Finally, a numerical example is presented to show the effectiveness of the proposed design method.  相似文献   

19.
This paper investigates the formation control of interconnected second-order systems. Each agent is assumed to be capable of measuring its own absolute velocity and the relative positions with respect to its neighboring agents, whereas the target formation is described by absolute positions of all agents in a global coordinate. For such formation control problems, no distributed control policy was reported in existing literature. This paper focuses on the string connection structure of the agents and proposes a distributed control policy that takes the form of purely state feedback without incorporating any feed-forward component. The closed-loop system equation is characterized by an oscillation matrix whose entries are the feedback controller gains. Formation control is accomplished by formulating the agents’ target positions as feedback controller gains. Moreover, it is shown that for agent models described by double integrators, each of the agents located at the two endpoints of the string structure should know its own absolute position. For a class of agent models where each agent’s acceleration depends on its own position, the control laws do not need to use the absolute position. For both system models, the target formations that are asymptotically reachable by the proposed control laws are specified explicitly. Numerical simulations have been conducted to illustrate the effectiveness of the theoretical results.  相似文献   

20.
A well-known method of eigenvalue assignment by static output feedback is improved. The main result is a parametric expression for the output feedback controller gain matrix explicitly characterized by the set of non-linear system of equations obtained for the state feedback design and the set of linear equations resulting from static output feedback consideration. In practice, it is shown that all the possible controllers can be generated for exactly assigning the prescribed eigenvalues of the nominal plant by appropriate software for solving the set of non-linear system of equations thus obtained. This in turn makes it possible to select the output feedback matrix with minimum norm or other constraints. Some numerical examples are presented to illustrate the design technique.  相似文献   

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