In the last decade, the Jensen inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms of linear matrix inequalities (LMIs). However, it is also well-known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature, reducing this gap is a relevant issue and always an open problem. In this paper, we propose an alternative inequality based on the Fourier Theory, more precisely on the Wirtinger inequalities. It is shown that this resulting inequality encompasses the Jensen one and also leads to tractable LMI conditions. In order to illustrate the potential gain of employing this new inequality with respect to the Jensen one, two applications on time-delay and sampled-data stability analysis are provided.
In this paper, an adaptive controller design is studied for single-input–single-output (SISO) nonlinear systems with parameter uncertainties and the systems are enforced to subject to the full state constraints. A remarkable feature of the constrained systems is that the so-called control direction is unknown, or in other words, the signs of control gains are unknown. In the existing results, we discover that all the state constraint control results are required to determine a priori knowledge of control direction. It will be inevitable to bring about a different design procedure and a difficult task when no a priori knowledge of control direction is known. To stabilize this class of systems, two parameter adaptive controllers with Nussbaum gain technique are constructively framed to overcome the unknown control direction problem, and the novel symmetric and asymmetric Barrier Lyapunov Functions (BLFs) are adopted to guarantee that the states are not to violate their constraints. Then, the proposed BLF strategy can be to conquer the conservatism of the traditional BLF-based controls for the full state constraints. Finally, two theorems are provided to show that all the signals in the closed-loop system are bounded, the outputs are driven to follow the reference signals and all the states are ensured to remain in the predefined compact sets. The effectiveness of the proposed scheme is performed via a simulation example.
We present a survey of formation control of multi-agent systems. Focusing on the sensing capability and the interaction topology of agents, we categorize the existing results into position-, displacement-, and distance-based control. We then summarize problem formulations, discuss distinctions, and review recent results of the formation control schemes. Further we review some other results that do not fit into the categorization.
This paper investigates the adaptive sliding mode control problem of nonlinear Markovian jump systems (MJSs) with partly unknown transition probabilities. The system state components are not all unmeasured. The specific information of the model uncertainties and bounds of the nonlinear term and disturbance term are unknown in the controller design process. Moreover, any knowledge of the unknown elements existing in the transition matrix is not required. Our attention is mainly focused on designing the observer-based adaptive sliding mode controller for such a complex system. Firstly, an observer is constructed to estimate the system state. Secondly, we design an integral sliding mode surface and observer-based adaptive sliding mode controller such that the MJSs are insensitive to all admissible uncertainties and satisfy the reaching condition. The stochastic stability of the closed-loop system can be guaranteed. Finally, a numerical example is exploited to demonstrate the effectiveness of the proposed results.
In this study, an adaptive control technique is developed for a class of uncertain nonlinear parametric systems. The considered systems can be viewed as a class of nonlinear pure-feedback systems and the full state constraints are strictly required in the systems. One remarkable advantage is that only less adjustable parameters are used in the design. This advantage is first to take into account the pure-feedback systems with the full state constraints. The characteristics of the considered systems will lead to a difficult task for designing a stable controller. To this end, the mean value theorem is employed to transform the pure-feedback systems to a strict-feedback structure but non-affine terms still exist. For the transformed systems, a novel recursive design procedure is constructed to remove the difficulties for avoiding non-affine terms and guarantee that the full state constraints are not violated by introducing Barrier Lyapunov Function (BLF) with the error variables. Moreover, it is proved that all the signals in the closed-loop system are global uniformly bounded and the tracking error is remained in a bounded compact set. Two simulation studies are worked out to show the effectiveness of the proposed approach.
In this paper, the control problem is addressed for a hybrid PDE–ODE system that describes a nonuniform gantry crane system with constrained tension. A bottom payload hangs from the top gantry by connecting a flexible cable. The flexible cable is nonuniform due to the spatiotemporally varying tension applied to the system. The control objectives are: (i) to position the payload to the desired setpoint, (ii) to regulate the transverse deflection of the flexible cable, and (iii) to keep the tension values remaining in the constrained space. Cooperative control laws are proposed and the integral-barrier Lyapunov functions are employed for stability analysis of the closed-loop system. Adaption laws are developed for handling parametric uncertainties. The bounded stability is guaranteed through rigorous analysis without any simplification of the dynamics. In the end, numerical simulations are displayed to illustrate the performance of the proposed cooperative control.
The emergence of synchronization in a network of coupled oscillators is a fascinating subject of multidisciplinary research. This survey reviews the vast literature on the theory and the applications of complex oscillator networks. We focus on phase oscillator models that are widespread in real-world synchronization phenomena, that generalize the celebrated Kuramoto model, and that feature a rich phenomenology. We review the history and the countless applications of this model throughout science and engineering. We justify the importance of the widespread coupled oscillator model as a locally canonical model and describe some selected applications relevant to control scientists, including vehicle coordination, electric power networks, and clock synchronization. We introduce the reader to several synchronization notions and performance estimates. We propose analysis approaches to phase and frequency synchronization, phase balancing, pattern formation, and partial synchronization. We present the sharpest known results about synchronization in networks of homogeneous and heterogeneous oscillators, with complete or sparse interconnection topologies, and in finite-dimensional and infinite-dimensional settings. We conclude by summarizing the limitations of existing analysis methods and by highlighting some directions for future research.
This paper is concerned with the stabilization problem for a class of Markovian stochastic jump systems against sensor fault, actuator fault and input disturbances simultaneously. In the proposed approach, the original plant is first augmented into a new descriptor system, where the state vector, disturbance vector and fault vector are assembled into the state vector of the new system. Then, a novel augmented sliding mode observer is presented for the augmented system and is utilized to eliminate the effects of sensor faults and disturbances. An observer-based mode-dependent control scheme is developed to stabilize the resulting overall closed-loop jump system. A practical example is given to illustrate the effectiveness of the proposed design methodology.
In this paper, an output feedback control method with prescribed performance is proposed for single-input and single-output (SISO) switched non-strict-feedback nonlinear systems. It is assumed that nonlinear functions of the concerned systems are unknown, switching signals are unknown and arbitrary, and the states are unmeasured. A linear state observer is designed to estimate the unmeasured states, and an observer-based output feedback control scheme is developed. The key advantages of the proposed control strategy are that virtual control gains of the concerned non-strict-feedback nonlinear systems are not required to be known, and only one tuning parameter is needed. Based on Lyapunov stability theory, it is shown that all the signals in the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small residual set with the prescribed performance bound. The effectiveness of the proposed control approach is verified by a numerical example.
A novel control strategy for multi-agent coordination with event-based broadcasting is presented. In particular, each agent decides itself when to transmit its current state to its neighbors and the local control laws are based on these sampled state measurements. Three scenarios are analyzed: Networks of single-integrator agents with and without communication delays, and networks of double-integrator agents. The novel event-based scheduling strategy bounds each agent’s measurement error by a time-dependent threshold. For each scenario it is shown that the proposed control strategy guarantees either asymptotic convergence to average consensus or convergence to a ball centered at the average consensus. Moreover, it is shown that the inter-event intervals are lower-bounded by a positive constant. Numerical simulations show the effectiveness of the novel event-based control strategy and how it compares to time-scheduled control.
This paper is concerned with the problem of asynchronous filtering for discrete-time stochastic Markov jump systems with sensor nonlinearity. The sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the Bernoulli distribution. A sufficient condition is first given such that the resultant filtering error system, which is a kind of nonhomogeneous Markov jump system, is stochastically stable with a guaranteed performance index. Then the existence criterion of the desired asynchronous filter with piecewise homogeneous Markov chain is proposed in terms of a set of linear matrix inequalities. A numerical example is given to show the effectiveness and potential of the developed theoretical results.
This paper is concerned with event-triggered sampled-data consensus for distributed multi-agent systems with directed graph. A novel distributed event-triggered sampled-data transmission strategy is proposed, which allows the event-triggering condition to be intermittently examined at constant sampling instants. Based on this novel strategy, a sampled-data consensus control protocol is presented, with which the consensus of distributed multi-agent systems can be transformed into the stability of a system with a time-varying delay. Then, a sufficient condition on the consensus of the multi-agent system is derived. Correspondingly, a co-design algorithm for obtaining both the parameters of the distributed event-triggered transmission strategy and the consensus controller gain is proposed. Two numerical examples are given to show the effectiveness of the proposed method.
Whereas the upper bound lemma for matrix cross-product, introduced by and modified by , plays a key role in guiding various delay-dependent criteria for delayed systems, the Jensen inequality has become an alternative as a way of reducing the number of decision variables. It directly relaxes the integral term of quadratic quantities into the quadratic term of the integral quantities, resulting in a linear combination of positive functions weighted by the inverses of convex parameters. This paper suggests the lower bound lemma for such a combination, which achieves performance behavior identical to approaches based on the integral inequality lemma but with much less decision variables, comparable to those based on the Jensen inequality lemma.
This paper is concerned with the state estimation and sliding mode control problems for phase-type semi-Markovian jump systems. Using a supplementary variable technique and a plant transformation, a finite phase-type semi-Markov process has been transformed into a finite Markov chain, which is called its associated Markov chain. As a result, phase-type semi-Markovian jump systems can be equivalently expressed as its associated Markovian jump systems. A sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated Markovian jump systems satisfy the reaching condition. Moreover, an observer-based sliding mode control problem is investigated. Sufficient conditions are established for the solvability of the desired observer. Two numerical examples are presented to show the effectiveness of the proposed design techniques.
This paper is concerned with the problem of asynchronous l(2)-l(infinity) filtering for discrete-time stochastic Markov jump systems with sensor nonlinearity. The sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the Bernoulli distribution. A sufficient condition is first given such that the resultant filtering error system, which is a kind of nonhomogeneous Markov jump system, is stochastically stable with a guaranteed l(2)-l(infinity) performance index. Then the existence criterion of the desired asynchronous filter with piecewise homogeneous Markov chain is proposed in terms of a set of linear matrix inequalities. A numerical example is given to show the effectiveness and potential of the developed theoretical results. (C) 2013 Elsevier Ltd. All rights reserved.
Cyber-secure networked control is modeled, analyzed, and experimentally illustrated in this paper. An attack space defined by the adversary’s model knowledge, disclosure, and disruption resources is introduced. Adversaries constrained by these resources are modeled for a networked control system architecture. It is shown that attack scenarios corresponding to denial-of-service, replay, zero-dynamics, and bias injection attacks on linear time-invariant systems can be analyzed using this framework. Furthermore, the attack policy for each scenario is described and the attack’s impact is characterized using the concept of safe sets. An experimental setup based on a quadruple-tank process controlled over a wireless network is used to illustrate the attack scenarios, their consequences, and potential counter-measures.
The control algorithm hierarchy of motion control for over-actuated mechanical systems with a redundant set of effectors and actuators commonly includes three levels. First, a high-level motion control algorithm commands a vector of virtual control efforts (i.e. forces and moments) in order to meet the overall motion control objectives. Second, a control allocation algorithm coordinates the different effectors such that they together produce the desired virtual control efforts, if possible. Third, low-level control algorithms may be used to control each individual effector via its actuators. Control allocation offers the advantage of a modular design where the high-level motion control algorithm can be designed without detailed knowledge about the effectors and actuators. Important issues such as input saturation and rate constraints, actuator and effector fault tolerance, and meeting secondary objectives such as power efficiency and tear-and-wear minimization are handled within the control allocation algorithm. The objective of the present paper is to survey control allocation algorithms, motivated by the rapidly growing range of applications that have expanded from the aerospace and maritime industries, where control allocation has its roots, to automotive, mechatronics, and other industries. The survey classifies the different algorithms according to two main classes based on the use of linear or nonlinear models, respectively. The presence of physical constraints (e.g input saturation and rate constraints), operational constraints and secondary objectives makes optimization-based design a powerful approach. The simplest formulations allow explicit solutions to be computed using numerical linear algebra in combination with some logic and engineering solutions, while the more challenging formulations with nonlinear models or complex constraints and objectives call for iterative numerical optimization procedures. Experiences using the different methods in aerospace, maritime, automotive and other application areas are discussed. The paper ends with some perspectives on new applications and theoretical challenges.
Motivated by the recent and growing interest in smart grid technology, we study the operation of DC/AC inverters in an inductive microgrid. We show that a network of loads and DC/AC inverters equipped with power-frequency droop controllers can be cast as a Kuramoto model of phase-coupled oscillators. This novel description, together with results from the theory of coupled oscillators, allows us to characterize the behavior of the network of inverters and loads. Specifically, we provide a necessary and sufficient condition for the existence of a synchronized solution that is unique and locally exponentially stable. We present a selection of controller gains leading to a desirable sharing of power among the inverters, and specify the set of loads which can be serviced without violating given actuation constraints. Moreover, we propose a distributed integral controller based on averaging algorithms, which dynamically regulates the system frequency in the presence of a time-varying load. Remarkably, this distributed-averaging integral controller has the additional property that it preserves the power sharing properties of the primary droop controller. Our results hold for any acyclic network topology, and hold without assumptions on identical line admittances or voltage magnitudes.
In this paper, the recursive state estimation problem is investigated for an array of discrete time-varying coupled stochastic complex networks with missing measurements. A set of random variables satisfying certain probabilistic distributions is introduced to characterize the phenomenon of the missing measurements, where each sensor can have individual missing probability. The Taylor series expansion is employed to deal with the nonlinearities and the high-order terms of the linearization errors are estimated. The purpose of the addressed state estimation problem is to design a time-varying state estimator such that, in the presence of the missing measurements and the random disturbances, an upper bound of the estimation error covariance can be guaranteed and the explicit expression of the estimator parameters is given. By using the Riccati-like difference equations approach, the estimator parameter is characterized by the solutions to two Riccati-like difference equations. It is shown that the obtained upper bound is minimized by the designed estimator parameters and the proposed state estimation algorithm is of a recursive form suitable for online computation. Finally, an illustrative example is provided to demonstrate the feasibility and effectiveness of the developed state estimation scheme.