Showing papers in "International Journal of Control in 2013"
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TL;DR: Model-free control and the corresponding ‘intelligent’ PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account.
Abstract: ''Model-free control'' and the corresponding ''intelligent'' PID controllers (iPIDs), which already had many successful concrete applications, are presented here for the first time in an unified manner, where the new advances are taken into account. The basics of model-free control is now employing some old functional analysis and some elementary differential algebra. The estimation techniques become quite straightforward via a recent online parameter identification approach. The importance of iPIs and especially of iPs is deduced from the presence of friction. The strange industrial ubiquity of classic PID's and the great difficulty for tuning them in complex situations is deduced, via an elementary sampling, from their connections with iPIDs. Several numerical simulations are presented which include some infinite-dimensional systems. They demonstrate not only the power of our intelligent controllers but also the great simplicity for tuning them.
645 citations
TL;DR: This article is concerned with the recursive finite-horizon filtering problem for a class of nonlinear time-varying systems subject to multiplicative noises, missing measurements and quantisation effects, and the design of a recursive filter such that an upper bound for the filtering error covariance is guaranteed and such anupper bound is subsequently minimised by properly designing the filter parameters at each sampling instant.
Abstract: This article is concerned with the recursive finite-horizon filtering problem for a class of nonlinear time-varying systems subject to multiplicative noises, missing measurements and quantisation effects. The missing measurements are modelled by a series of mutually independent random variables obeying Bernoulli distributions with possibly different occurrence probabilities. The quantisation phenomenon is described by using the logarithmic function and the multiplicative noises are considered to account for the stochastic disturbances on the system states. Attention is focused on the design of a recursive filter such that, for all multiplicative noises, missing measurements as well as quantisation effects, an upper bound for the filtering error covariance is guaranteed and such an upper bound is subsequently minimised by properly designing the filter parameters at each sampling instant. The desired filter parameters are obtained by solving two Riccati-like difference equations that are of a recursive form...
324 citations
TL;DR: This note studies event-triggered control of Multi-Agent Systems with first-order integrator dynamics by considering limited communication capabilities through strict peer-to-peer non-continuous information exchange and provides both a decentralised control law and a decentralising communication policy.
Abstract: This note studies event-triggered control of Multi-Agent Systems (MAS) with first-order integrator dynamics. It extends previous work on event-triggered consensus by considering limited communication capabilities through strict peer-to-peer non-continuous information exchange. The approach provides both a decentralised control law and a decentralised communication policy. Communication events require no global information and are based only on local state errors; agents do not require a global sampling period or synchronous broadcasting as in sampled-data approaches. The proposed decentralised event-triggered control technique guarantees that the inter-event times for each agent are strictly positive. Finally, the ideas in this note are used to consider the practical scenario where agents are able to exchange only quantised measurements of their states.
222 citations
TL;DR: By constructing a common Lyapunov function, it is shown that consensus can be reached if the general algebraic connectivity and communication time duration are larger than their corresponding threshold values, respectively.
Abstract: This article investigates the second-order consensus problem of multi-agent systems with inherent delayed nonlinear dynamics and intermittent communications. Each agent is assumed to obtain the measurements of relative states between its own and the neighbours' only at a sequence of disconnected time intervals. A new kind of protocol based only on the intermittent measurements of neighbouring agents is proposed to guarantee the states of agents to reach second-order consensus under a fixed strongly connected and balanced topology. By constructing a common Lyapunov function, it is shown that consensus can be reached if the general algebraic connectivity and communication time duration are larger than their corresponding threshold values, respectively. Finally, simulation examples are provided to verify the effectiveness of the theoretical analysis.
179 citations
TL;DR: The fluid inerter presented here has advantages over mechanical ball screw devices in terms of simplicity of design and it can be readily adapted to implement various passive network layouts.
Abstract: Mechanical spring-damper network performance can often be improved by the inclusion of a third passive component called the inerter. This ideally has the characteristic that the force at the terminals is directly proportional to the relative acceleration between them. The fluid inerter presented here has advantages over mechanical ball screw devices in terms of simplicity of design. Furthermore, it can be readily adapted to implement various passive network layouts. Variable orifices and valves can be included to provide series or parallel damping. Test data from prototypes with helical tubes have been compared with models to investigate parasitic damping effects of the fluid.
159 citations
TL;DR: This article investigates the robust synchronisation problem for uncertain nonlinear chaotic systems and proposes a discontinuous Lyapunov functional based on the extended Wirtinger inequality that guarantees the robust mean-square synchronisation of chaotic systems.
Abstract: This article investigates the robust synchronisation problem for uncertain nonlinear chaotic systems. The norm-bounded uncertainties enter into the chaotic systems in random ways, and such randomly occurring uncertainties (ROUs) obey certain Bernoulli distributed white noise sequences. For this synchronisation problem, the sampled-data controller that has randomly varying sampling intervals is considered. In order to fully use the sawtooth structure characteristic of the sampling input delay, a discontinuous Lyapunov functional is proposed based on the extended Wirtinger inequality. By the Lyapunov stability theory and the linear matrix inequality (LMI) framework, the existence condition for the sample-date controller that guarantees the robust mean-square synchronisation of chaotic systems is derived in terms of LMIs. Finally, in order to show the effectiveness of our result, the proposed method is applied to two numerical examples: one is Chua's chaotic systems and the other is the hyperchaotic Rossler ...
139 citations
TL;DR: It is shown that the states of the followers can track that of the leader when there exists a single leader, and converge to a convex hull spanned by those of the leaders when there exist multiple leaders, both in finite time.
Abstract: In this article, distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances is investigated. With the aid of sliding-mode control technique, both the finite-time consensus tracking in the presence of a single leader and the finite-time containment control with multiple leaders are in detail analysed. A distinctive feature of this work is that the communication topology among the followers can be directed. It is shown that the states of the followers can track that of the leader when there exists a single leader, and converge to a convex hull spanned by those of the leaders when there exist multiple leaders, both in finite time. Moreover, the finite convergence time is explicitly presented. Numerical examples are finally given to illustrate the theoretical results.
129 citations
TL;DR: An observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm using a neural-network observer designed to estimate system states and a neuro-controller constructed via ADP method to obtain the optimal control.
Abstract: In this paper, an observer-based optimal control scheme is developed for unknown nonlinear systems using adaptive dynamic programming (ADP) algorithm. First, a neural-network (NN) observer is designed to estimate system states. Then, based on the observed states, a neuro-controller is constructed via ADP method to obtain the optimal control. In this design, two NN structures are used: a three-layer NN is used to construct the observer which can be applied to systems with higher degrees of nonlinearity and without a priori knowledge of system dynamics, and a critic NN is employed to approximate the value function. The optimal control law is computed using the critic NN and the observer NN. Uniform ultimate boundedness of the closed-loop system is guaranteed. The actor, critic, and observer structures are all implemented in real-time, continuously and simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.
104 citations
TL;DR: This paper obtains delay-free stochastic closed-loop systems and the controlled output is chosen as the tracking error and the feedback gains of the controller can be derived by solving a minimization problem.
Abstract: This paper is concerned with a tracking controller design problem for discrete-time networked predictive control systems. The control law used here is a combined state-feedback control and integral control. Since not all the states are available in practice, a local Luenberger observer is utilised to estimate the state vector. The measured output and estimated state vector are packed together and transmitted to the tracking controller via a communication channel with a limited capacity. Meanwhile, the control signal is also transmitted through a communication network.Network-induced delays on both links are considered for the signal transmission and modelled by Markov chains. Moreover, it is assumed that the elements in Markov transition matrices are subject to uncertainties. In order to fully compensate for network-induced delays, the controller generates a sequence of control signals which are dependent on each possible delay in the feedforward channel. By taking the augmentation twice, we obtain delay-...
100 citations
TL;DR: The approach is based on a new state predictor which estimates the future of states and guarantees that the prediction error converges asymptotically to zero, and the state feedback controller is then designed based on this predictor.
Abstract: This article presents a method to control and stabilise systems with pure input lag. The approach is based on a new state predictor which estimates the future of states and guarantees that the prediction error converges asymptotically to zero. The state feedback controller is then designed based on this predictor. Furthermore, a sequential structure of sub-predictors is presented for unstable systems with a long time-delay and accordingly the controller is designed for asymptotic stability. The core idea is to design a series of coupled predictors, each of which is responsible for the prediction of one small portion of the delay, such that the predictors collectively predict the states for a long time-delay. Moreover, sequential sub-predictor method is used for robust control of dead time systems in presence of uncertainty. Simulation examples are presented to verify the proposed method.
93 citations
TL;DR: By introducing the sign functions and using the generalised method of adding a power integrator, this paper successfully designs a continuous global state-feedback controller independent of time delays.
Abstract: This paper studies the global stabilisation problem for a class of high-order nonlinear systems with multiple time delays. A distinct property of the systems to be investigated is that powers on the upper bound restrictions of nonlinearities are allowed to take values on a continuous interval. By introducing the sign functions and using the generalised method of adding a power integrator, this paper successfully designs a continuous global state-feedback controller independent of time delays. Moreover, a novel Lyapunov–Krasovskii functional is constructed to prove the globally asymptotic stability of the resulting closed-loop system.
TL;DR: A novel switching surface is proposed and its finite-time stability to the origin is proved and a robust fractional control law is proposed to ensure the existence of the sliding motion in finite time.
Abstract: This paper investigates the problem of robust control of nonlinear fractional-order dynamical systems in the presence of uncertainties. First, a novel switching surface is proposed and its finite-time stability to the origin is proved. Subsequently, using the sliding mode theory, a robust fractional control law is proposed to ensure the existence of the sliding motion in finite time. We use a fractional Lyapunov stability theory to prove the stability of the system in a given finite time. In order to avoid the chattering, which is inherent in conventional sliding mode controllers, we transfer the sign function of the control input into the fractional derivative of the control signal. The proposed chattering-free sliding mode technique is then applied for stabilisation of a broad class of three-dimensional fractional-order chaotic systems via a single variable driving control input. Simulation results reveal that the proposed fractional sliding mode controller works well for chaos control of fractional-ord...
TL;DR: In this article, the optimal sensor placement for target localization and tracking in 2D and 3D was analyzed in a unified framework, and the optimal placement problems of the three sensor types were formulated as an identical parameter optimisation problem.
Abstract: This paper analytically characterises optimal sensor placements for target localisation and tracking in 2D and 3D. Three types of sensors are considered: bearing-only, range-only and received-signal-strength. The optimal placement problems of the three sensor types are formulated as an identical parameter optimisation problem and consequently analysed in a unified framework. Recently developed frame theory is applied to the optimality analysis. We prove necessary and sufficient conditions for optimal placements in 2D and 3D. A number of important analytical properties of optimal placements are further explored. In order to verify the analytical analysis, we present a gradient control law that can numerically construct generic optimal placements.
TL;DR: It is shown that consensus in the closed-loop multi-agent systems under a connected topology can be converted to the simultaneous asymptotic stability of a set of switching systems whose dimensions are the same as each agent.
Abstract: This article addresses the distributed consensus problem of linear multi-agent systems with discontinuous observations over a time-invariant undirected communication topology. Under the assumption that each agent can only intermittently share its outputs with the neighbours, a class of distributed observer-type of protocols are designed and utilised to achieve consensus. By using appropriate matrix decomposition, it is shown that consensus in the closed-loop multi-agent systems under a connected topology can be converted to the simultaneous asymptotic stability of a set of switching systems whose dimensions are the same as each agent. From a multiple Lyapunov functions approach, it is proved that there exists a protocol to guarantee consensus if the communication time rate is larger than a threshold value. Furthermore, a distributed pinning control method is employed to solve the consensus problem on an arbitrary given topology which needs not be connected. Particularly, the questions of what kind of agen...
TL;DR: In this article, the existence of a Lyapunov-Krasovskii functional is shown to be a necessary and sufficient condition for the uniform global asymptotic stability and the global exponential stability of systems described by neutral functional differential equations in Hale's form.
Abstract: In this article, we show that the existence of a Lyapunov–Krasovskii functional is necessary and sufficient condition for the uniform global asymptotic stability and the global exponential stability (GES) of time-invariant systems described by neutral functional differential equations in Hale's form. It is assumed that the difference operator is linear and strongly stable, and that the map on the right-hand side of the equation is Lipschitz on bounded sets. A link between GES and input-to-state stability is also provided.
TL;DR: This paper introduces a projection-free iterative optimisation algorithm and discusses its application to linear MPC, and discusses how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algorithm performance can be optimised by pre-computing the matrices in a parametric form.
Abstract: A key component in enabling the application of model predictive control (MPC) in fields such as automotive, aerospace, and factory automation is the availability of low-complexity fast optimisation algorithms to solve the MPC finite horizon optimal control problem in architectures with reduced computational capabilities. In this paper, we introduce a projection-free iterative optimisation algorithm and discuss its application to linear MPC. The algorithm, originally developed by Brand for non-negative quadratic programs, is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum. An acceleration technique based on a projection-free line search is also introduced, to speed-up the convergence to the optimum. The algorithm is applied to MPC through the dual of the quadratic program (QP) formulated from the MPC finite time optimal control problem. We discuss how termination conditions with guaranteed degree of suboptimality can be enforced, and how the algorithm...
TL;DR: This paper investigates the distributed consensus tracking problem for multi-agent systems with Lipschitz-type dynamics under a reference leader and proposes a class of discontinuous protocols based on the relative information between the neighbouring agents to achieve consensus tracking.
Abstract: This paper investigates the distributed consensus tracking problem for multi-agent systems with Lipschitz-type dynamics under a reference leader. It is assumed that the leader state information is only available to a subset of followers, while the bounded reference input of the leader’s is unavailable to any follower. To achieve consensus tracking, a class of discontinuous protocols based on the relative information between the neighbouring agents are proposed. Furthermore, as extensions of the former result, the robust and adaptive consensus tracking problems are studied for the case where there exist parameter uncertainties and external disturbances in the network. Finally, the effectiveness of the theoretical result is demonstrated through a network of single-link manipulators.
TL;DR: The existence and approximate controllability of a class of fractional nonlocal delay semilinear differential systems in a Hilbert space is studied by using semigroup theory, fractional calculus and Schauder's fixed point theorem.
Abstract: We study the existence and approximate controllability of a class of fractional nonlocal delay semilinear differential systems in a Hilbert space. The results are obtained by using semigroup theory, fractional calculus and Schauder’s fixed point theorem. Multi-delay controls and a fractional nonlocal condition are introduced. Furthermore, we present an appropriate set of sufficient conditions for the considered fractional nonlocal multi-delay control system to be approximately controllable. An example to illustrate the abstract results is given.
TL;DR: This work considers the control of a commercial multi-zone refrigeration system, consisting of several cooling units that share a common compressor, and is used to cool multiple areas or rooms, and proposes a sequential convex optimisation method, which typically converges in fewer than 5 or so iterations.
Abstract: We consider the control of a commercial multi-zone refrigeration system, consisting of several cooling units that share a common compressor, and is used to cool multiple areas or rooms. In each time period we choose cooling capacity to each unit and a common evaporation temperature. The goal is to minimise the total energy cost, using real-time electricity prices, while obeying temperature constraints on the zones. We propose a variation on model predictive control to achieve this goal. When the right variables are used, the dynamics of the system are linear, and the constraints are convex. The cost function, however, is nonconvex due to the temperature dependence of thermodynamic efficiency. To handle this nonconvexity we propose a sequential convex optimisation method, which typically converges in fewer than 5 or so iterations. We employ a fast convex quadratic programming solver to carry out the iterations, which is more than fast enough to run in real time. We demonstrate our method on a realistic mod...
TL;DR: This article investigates the problem of non-fragile synchronisation control for complex networks with time-varying coupling delay and missing data with a stochastic variable satisfying the Bernoulli random binary distribution.
Abstract: This article investigates the problem of non-fragile synchronisation control for complex networks with time-varying coupling delay and missing data. A stochastic variable satisfying the Bernoulli random binary distribution is utilised to model the missing data. Based on the Gronwall's inequality, an exponential synchronisation condition is obtained ensuring the exponential mean-square stability of the error system. Then a sufficient condition for designing the non-fragile synchronisation controller is proposed. Finally, a simulation example is given to show the efficiency of the proposed design methods.
TL;DR: Three different robustness analysis methods are implemented into the DOB based control systems, and the relation between the robustness of the system and bandwidth of DOB is clearly explained.
Abstract: Disturbance observer (DOB) estimates the system disturbances by using the inverse of the nominal plant model and a low pass filter (LPF). Although the LPF provides the properness in the inner-loop, it is the main design constraint of the control systems based on DOB. The bandwidth of the LPF is designed as high as possible so that the DOB can estimate the disturbances in a wider frequency range. However, its bandwidth is limited by noise and robustness of the system. The robustness limitation is directly related with the robustness analysis methods, and they significantly affect the performance of the DOB based control systems. In this paper, three different robustness analysis methods are implemented into the DOB based control systems, and the relation between the robustness of the system and bandwidth of DOB is clearly explained. The conservatism, which is the main drawback of the conventional analysis methods, on the bandwidth of DOB is removed by proposing a new real parametric uncertainty based analy...
TL;DR: This paper defends the use of a terminal cost and an explicit or implicit terminal constraint for ensuring the stability of model predictive control systems.
Abstract: This paper defends the use of a terminal cost and an explicit or implicit terminal constraint for ensuring the stability of model predictive control systems. Existing methods for ensuring stability are briefly reviewed. The necessity of a terminal constraint to satisfy certain design requirements is established. The advantages and disadvantages of employing terminal stabilising conditions are discussed.
TL;DR: A new dynamic feedback control law is given that makes the system exponential stabilisation ∀τ > 0 provided that |αj| ≠ |βj|(j = 1, 2) and the result is proved via test of exact observability of the system.
Abstract: In this paper, we consider the exponential stabilisation problem of a Timoshenko beam with delay in boundary control. Suppose that the controller outputs of the forms α1u1(t) + β1u1(t − τ) and α2u2(t) + β2u2(t − τ) where u1(t) and u2(t) are the inputs of boundary controllers. In the past, most of the stabilisation results are required αj > βj > 0, j = 1, 2. In the present paper, we shall give a new dynamic feedback control law that makes the system exponential stabilisation ∀τ > 0 provided that |αj| ≠ |βj|(j = 1, 2). The exponential stabilisation result is proved via test of exact observability of the system.
TL;DR: In this paper, the dissipative control problem is investigated for a class of discrete time-varying systems with simultaneous presence of state saturations, randomly occurring nonlinearities as well as multiple missing measurements.
Abstract: In this paper, the dissipative control problem is investigated for a class of discrete time-varying systems with simultaneous presence of state saturations, randomly occurring nonlinearities as well as multiple missing measurements. In order to render more practical significance of the system model, some Bernoulli distributed white sequences with known conditional probabilities are adopted to describe the phenomena of the randomly occurring nonlinearities and the multiple missing measurements. The purpose of the addressed problem is to design a time-varying output-feedback controller such that the dissipativity performance index is guaranteed over a given finite-horizon. By introducing a free matrix with its infinity norm less than or equal to 1, the system state is bounded by a convex hull so that some sufficient conditions can be obtained in the form of recursive nonlinear matrix inequalities. A novel controller design algorithm is then developed to deal with the recursive nonlinear matrix inequalities....
TL;DR: The recently investigated ℓasso model predictive control is applied to the terminal phase of a spacecraft rendezvous and capture mission and is demonstrated to meet tighter specifications on control precision and also avoids the risk of undesirable behaviours often associated with pureℓ1 stage costs.
Abstract: The recently investigated lasso model predictive control (MPC) is applied to the terminal phase of a spacecraft rendezvous and capture mission. The interaction between the cost function and the treatment of minimum impulse bit is also investigated. The propellant consumption with lasso MPC for the considered scenario is noticeably less than with a conventional quadratic cost and control actions are sparser in time. Propellant consumption and sparsity are competitive with those achieved using a zone-based l1 cost function, whilst requiring fewer decision variables in the optimisation problem than the latter. The lasso MPC is demonstrated to meet tighter specifications on control precision and also avoids the risk of undesirable behaviours often associated with pure l1 stage costs.
TL;DR: Design procedures of a continuous controller are provided by the method of adding a power integrator, and the stability of the resulting closed-loop system is rigorously proven with the help of the elegant choice of a Lyapunov–Krasovskii functional.
Abstract: This paper focuses on the stabilisation for a class of high-order nonlinear systems with multiple time delays. Growth restriction on system nonlinearities is further relaxed. Design procedures of a continuous controller are provided by the method of adding a power integrator, and the stability of the resulting closed-loop system is rigorously proven with the help of the elegant choice of a Lyapunov–Krasovskii functional. Finally, a simulation example is provided to demonstrate the validness of the proposed approach.
TL;DR: The proposed observer always exists when a state observer exists for the unknown input system, and furthermore, the proposed observer can exist even in some instances when an unknown input state observer does not exist.
Abstract: This article presents necessary and sufficient conditions for the existence and design of an unknown input Functional observer. The existence of the observer can be verified by computing a nullspace of a known matrix and testing some matrix rank conditions. The existence of the observer does not require the satisfaction of the observer matching condition (i.e. Equation (16) in Hou and Muller 1992, ‘Design of Observers for Linear Systems with Unknown Inputs’, IEEE Transactions on Automatic Control, 37, 871–875), is not limited to estimating scalar functionals and allows for arbitrary pole placement. The proposed observer always exists when a state observer exists for the unknown input system, and furthermore, the proposed observer can exist even in some instances when an unknown input state observer does not exist.
TL;DR: An adaptive iterative learning control method is proposed for a class of nonlinear strict-feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories and guarantees the boundedness of all the signals in the controlled system.
Abstract: An adaptive iterative learning control method is proposed for a class of nonlinear strict-feedback discrete-time systems with random initial conditions and iteration-varying desired trajectories. An n-step ahead predictor approach is employed to estimate the future states in the control design. Discrete Nussbaum gain method is utilised to deal with the lack of a priori knowledge of control directions. The proposed control algorithm guarantees the boundedness of all the signals in the controlled system. The tracking error converges to zero asymptotically along the iterative learning axis except for beginning states affected by random initial conditions. The effectiveness of the proposed control scheme is verified through numerical simulation.
TL;DR: This paper gives a reasonably detailed review of advances in stability and stabilisation of linear multidimensional (N-D) discrete systems in the frequency domain, especially in the past decade.
Abstract: This paper gives a reasonably detailed review of advances in stability and stabilisation of linear multidimensional (N-D) discrete systems in the frequency domain. The emphasis is on the recent progress, especially in the past decade. The discussion will focus on two topics: (i) stability test. Determination of whether a given N-D (N ≥ 2) system is stable; (ii) stabilisation. Parameterisation of all stabilising compensators for a stabilisable N-D system. After reviewing the progress and several state of the art methods in these two topics with illustrative examples, some related issues are also briefly mentioned at the end.
TL;DR: The min–max model predictive control method is proposed to design the control packets by incorporating the external disturbances into the optimisation problem and the input-to-state practical stability of the resulting nonlinear NCS is established by constructing a novel Lyapunov function.
Abstract: This article investigates a class of constrained nonlinear networked control systems (NCSs) subject to external disturbances, input and state constraints and network-induced constraints. From a practical perspective, the network-induced constraints considered include the time delays and packet dropouts on both the sensor-to-controller (S-C) channel and the controller-to-actuator (C-A) channel simultaneously. The min–max model predictive control method is proposed to design the control packets by incorporating the external disturbances into the optimisation problem. Moreover, the input-to-state practical stability of the resulting nonlinear NCS is established by constructing a novel Lyapunov function. Finally, the simulation results and the comparison studies are presented to demonstrate the effectiveness and improvement of the proposed method.