Showing papers in "Iet Control Theory and Applications in 2010"

Kalman filtering with state constraints: a survey of linear and nonlinear algorithms

Abstract: The Kalman filter is the minimum-variance state estimator for linear dynamic systems with Gaussian noise. Even if the noise is non-Gaussian, the Kalman filter is the best linear estimator. For nonlinear systems it is not possible, in general, to derive the optimal state estimator in closed form, but various modifications of the Kalman filter can be used to estimate the state. These modifications include the extended Kalman filter, the unscented Kalman filter, and the particle filter. Although the Kalman filter and its modifications are powerful tools for state estimation, we might have information about a system that the Kalman filter does not incorporate. For example, we may know that the states satisfy equality or inequality constraints. In this case we can modify the Kalman filter to exploit this additional information and get better filtering performance than the Kalman filter provides. This paper provides an overview of various ways to incorporate state constraints in the Kalman filter and its nonlinear modifications. If both the system and state constraints are linear, then all of these different approaches result in the same state estimate, which is the optimal constrained linear state estimate. If either the system or constraints are nonlinear, then constrained filtering is, in general, not optimal, and different approaches give different results.

Quantum control theory and applications: a survey

Abstract: This study presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and quantum incoherent control. In the area of closed-loop quantum control, this study reviews closed-loop learning control and several important issues related to quantum feedback control including quantum filtering, feedback stabilisation, linear-quadratic-Gaussian control and robust quantum control.

Trajectory tracking control design with command-filtered compensation for a quadrotor

Abstract: The design of a flight control system capable of not only stabilising attitude but also tracking a trajectory accurately for an under-actuated quadrotor aircraft is quite challenging. This study constructs the relationship between the attitude and linear acceleration of a small quadrotor unmanned aircraft and proposes a trajectory tracking control design algorithm, based on the relationship, using a new command-filtered backstepping technique to stabilise the attitude and a linear tracking differentiator to eliminate the classical inner/outer-loop structure. Finally, the validity and the effectiveness of this algorithm are demonstrated by various numerical simulations under different conditions.

Switched affine systems control design with application to DCߝDC converters

Abstract: This study presents a novel procedure for switched affine systems control design specially developed to deal with switched converters where the main goal is to attain a set of equilibrium points. The main contribution is on the determination of a switching function, which assures global stability and minimises a guaranteed quadratic cost. The implementation of the switching function taking into account only partial information is analysed and discussed with particular interest. The theoretical results are applied to buck, boost and buck-boost converters control design. Several simulations show the usefulness of the methodology and its favourable impact in a class of real-world control design problems.

Improved sliding mode control for discrete-time systems via reaching law

Abstract: In this study, the sliding mode control problem is considered for discrete-time systems. Firstly, some existing definitions on the quasi-sliding mode and reaching condition are examined. A new reaching law is proposed and the corresponding reachability is investigated. Comparisons between the proposed strategies and some existing works are also made. Finally, illustrative simulation results are provided.

Brief paper: state estimation of Takagi-Sugeno systems with unmeasurable premise variables

Abstract: This study is dedicated to the design of observers for non-linear systems described by Takagi–Sugeno (T–S) multiple models with unmeasurable premise variables. Furthermore, this T–S structure can represent a larger class of non-linear systems compared to the T–S systems with measurable premise variables. Considering the state of the system as a premise variable allows one to exactly represent the non-linear systems described by the general form x=f(x, u). Unfortunately, the developed methods for estimating the state of T–S systems with measured premise variable are not directly applicable for the systems that use the state as a premise variable. In the present paper, firstly, the design of observers for T–S systems with unmeasurable premise variable is proposed and sufficient convergence conditions are established by Lyapunov stability analysis. The linear matrix inequality (LMI) formalism is used in order to express the convergence conditions of the state estimation error in terms of LMI and to obtain the gains of the observer. Secondly, the proposed method is extended in order to attenuate energy-bounded unknown inputs such as disturbances. An academic example is proposed to compare some existing methods and the proposed one.

Brief Paper: Output-feedback adaptive dynamic surface control of stochastic non-linear systems using neural network

Abstract: For the first time, a dynamic surface control approach is proposed for a class of stochastic non-linear systems with the standard output-feedback form using neural network. The proposed approach is a stochastic vision of the existing dynamic surface control approach which can overcome the problem of 'explosion of complexity' in the backstepping design of stochastic systems. Moreover, all unknown system functions are lumped into a suitable unknown function which is compensated for using only a neural network. The proposed control approach is simpler than the existing backstepping control methods for stochastic systems. Two examples are given to illustrate the effectiveness of the proposed design approach.

Bounded control of network connectivity in multi-agent systems

Abstract: A distributed control law that guarantees connectivity maintenance in a network of multiple mobile agents is presented. The control law, which lets the agents perform formation manoeuvres, respects sensor limitations by allowing each agent to only take into account agents within its sensing radius. In contrast to previous approaches to the problem, the proposed control law does not attain infinite values whenever an edge of the communication graph tends to be lost. This is achieved via the use of decentralised navigation functions, which are bounded potential fields. The navigation functions are defined to take into account the connectivity maintenance objective. The authors first treat the case of connectivity maintenance for a static communication graph and then extend the result to the case of dynamic graphs. The results are illustrated on a formation control problem.

Robust h ∞ consensus analysis of a class of second-order multi-agent systems with uncertainty

Abstract: This study is concerned with consensus problems for a class of multi-agent systems with second-order dynamics. Some dynamic neighbour-based rules are adopted for the agents with the consideration of parameter uncertainties and external disturbances. Sufficient conditions are derived to make all agents asymptotically reach consensus while satisfying desired H∞ performance. Finally, numerical simulations are provided to show the effectiveness of our theoretical results.

Finite-time filtering for non-linear stochastic systems with partially known transition jump rates

Abstract: This study is concerned with the problem of robust finite-time filtering for a class of non-linear Markov jump systems (MJSs) with partially known information on the transition jump rates. The non-linearities in the system are parameterised by multilayer neural networks. Our attention is focused on the design of a mode-dependent full-order H∞ filter to ensure the finite-time boundedness of the filtering error system and a prescribed H∞ attenuation level for all admissible uncertainties and approximation errors of the networks. Sufficient conditions of filtering design are developed in terms of solvability of a set of linear matrix inequalities. A tunnel diode circuit is used to show the effectiveness and potentials of the proposed techniques.

Modelling and identification for non-uniformly periodically sampled-data systems

Abstract: The authors state the non-uniformly periodically sampling pattern and derives the state-space models of non-uniformly sampled-data systems with coloured noises, and further obtains the corresponding transfer function models. Difficulties of identification are that there exist unknown inner variables and unmeasurable noise terms in the information vectors. By means of the auxiliary model method, an auxiliary model based multi-innovation generalised extended stochastic gradient (SG) algorithm is presented by expanding the scalar innovation to the innovation vector and introducing the innovation length. The proposed algorithm provides higher parameter estimation accuracy and faster convergence rate than the SG algorithm due to repeatedly using the system innovation.

Global stabilisation and tracking control of underactuated surface vessels

Abstract: In this study, the authors solve the problem of uniform global asymptotic stabilisation and global exponential tracking for an underactuated ship with only two propellers. A unified backstepping design methodology is proposed to tackle both the stabilisation and tracking problems. The obvious advantage of this framework is that the controller design procedure is systematic and analytically simple. The study also addresses the tracking problem with constant bias of environmental disturbances. Simulation results are provided to validate our theoretical results.

Tracking control of pneumatic artificial muscle actuators based on sliding mode and non-linear disturbance observer

Abstract: The dynamic properties and non-linear control of the pneumatic muscle actuator (PMA) were investigated in this study for use in a specially designed hand rehabilitation device. The phenomenological model of PMA was established in the lower pressure range applicable for hand rehabilitation. The experimental results show that PMA's characteristics can be approximated by piecewise functions. In order to improve the performance and robustness of control for accurate trajectory tracking, a sliding mode control based on non-linear disturbance observer (SMCBNDO) was designed. The simulation and experimental results demonstrated that the model and the sliding mode control achieved the desired performance in tracking a desired trajectory within guaranteed accuracy. The work indicates that the model and the non-linear control proposed in this study can be applied in PMA-driven hand function rehabilitation devices requiring lower pressures.

Robust finite-time control approach for robotic manipulators

Abstract: In this study, a new robust finite-time stability control approach for robot systems is developed based on finite-time Lyapunov stability principle and proved with backstepping method. The corresponding stability analysis is presented to lay a foundation for theoretical understanding to the underlying design issues as well as safe operation for real systems. A case study of a two-link robot model is presented to demonstrate the effectiveness of the proposed approach.

Consensus control for multi-agent systems with double-integrator dynamics and time delays

Abstract: In this study, mathematical modelling and analysis for consensus problems will be conducted for a group of autonomous mobile agents with double-integrator dynamics and time-varying interconnection delays. To solve the problems, distributed control scheme for each agent will be proposed first. Then the consensus stability of the multi-agent system is obtained for the problem, where the dynamics of each agent is second-order with time-varying interconnection delays. In the convergence analysis, both fixed and switched interconnection topologies of the considered multi-agent system are investigated. Finally, some numerical examples are presented to validate the consensus algorithms.

Robust Η/ spl alpha/ stabilisation of networked control systems with packet analyser [Brief Paper]

Abstract: The authors investigate the problem of robust ℋ∞ stabilisation for a class of networked control systems (NCSs) with both network-induced delay and packet dropout In order to obtain a less conservative and robust ℋ∞ stability criterion, the authors establish an appropriate Lyapunov–Krasovskii functional and propose a relevant free-weighting matrix method endowed with extra degrees of freedom through the introduction of novel relaxation variables associated with ∫Ω xT(α)(•)x(α) dα Subsequently, on the basis of the obtained stability criterion, the authors derive the ℋ∞ stabilisation condition for NCSs with norm-bounded parameter uncertainty Furthermore, the authors provide four numerical examples to illustrate the effectiveness of the proposed approach

Robust energy-to-peak filtering for networked systems with time-varying delays and randomly missing data

Abstract: This study is concerned with the robust energy-to-peak (l2–l∞) filtering problem for a class of uncertain linear discrete-time networked control systems with time-varying delays and randomly missing data. The system matrices are assumed to reside in a convex polytope, and the time-varying delays appearing in system states are assumed to lie in a given interval. Moreover, the random data missing is supposed to satisfy the Bernoulli random binary distribution. The authors' goal is to design a full-order filter such that the filtering error dynamic system is exponentially mean-square stable for all admissible time delays and randomly missing data while a prescribed l2–l∞ performance is achieved. Sufficient delay- and parameter-dependent conditions for the existence of the filter and for the solvability of the addressed problem are given in terms of a set of linear matrix inequalities. Finally, simulation examples and comparison studies are provided to demonstrate the effectiveness of the proposed approach.

Gain-scheduled H 2 and H ∞ control of discrete-time polytopic time-varying systems

Abstract: This study presents ℋ2 and ℋ∞ performance analysis and synthesis procedures for the design of both gain-scheduled and robust static output feedback controllers for discrete-time linear systems with time-varying parameters. The obtained controllers guarantee an upper bound on the ℋ2 or ℋ∞ performance of the closed-loop system. As an immediate extension, the mixed ℋ2/ℋ∞ guaranteed cost control problem is also addressed. The scheduling parameters vary inside a polytope and are assumed to be a priori unknown, but measured in real-time. If bounds on the rate of parameter variation are known, they can be taken into account, providing less conservative results. The geometric properties of the polytopic domain are exploited to derive finite sets of linear matrix inequalities (LMIs) based on the existence of a parameter-dependent Lyapunov function. An application of the methodology to a realistic vibroacoustic problem, with experimentally obtained data, illustrates the benefits of the proposed approach and shows that the techniques can be used for real engineering problems.

Robust fault detection for continuous-time switched delay systems: an linear matrix inequality approach

Abstract: This study addresses the robust fault detection problem for continuous-time switched systems with state delays. The fault detection filter is used as the residual generator depending on the system mode. Attention is focused on designing the filter such that, for the modelling errors, the unknown inputs and the control one, the error between the residuals and the faults is minimised. The addressed fault detection filter design is converted into an auxiliary H ? filtering problem. By using the Lyapunov-Krasovskii functional method and average dwell time approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities (LMIs). Two examples are provided to demonstrate the effectiveness of the proposed method.

Sliding-mode adaptive attitude controller design for spacecrafts with thrusters

Abstract: In this study, the authors propose two non-linear attitude controllers, mainly consisting of the sliding-mode attitude tracking controller and the sliding-mode adaptive attitude tracking controller, for spacecrafts with thrusters to follow the predetermined trajectory in outer space by use of employing the spacecraft's attitude control. First, the attitude model and non-linear controllers of the attitude control system of a spacecraft are established and derived, considering the external forces suffering from the gradient torque in a gravitational field because of universal gravitation, the optical torque because of solar shining and so on, to utilise the sliding-mode and/or adaptive control theory for designing the non-linear attitude controllers. Also, we consider the variation of moment inertia matrix of a spacecraft during the whole flying course to analyse their influences for the practical controller design as the conditions of limitation and correction. Simultaneously, the authors use both the adaptive control theory and the sliding-mode control to estimate parameters and eliminate disturbances of the attitude control system. Accordingly, the non-linear attitude controllers of a spacecraft are designed while the spacecraft is flying. Finally, the authors employ the Lyapunov stability theory to fulfil the stability analysis of two non-linear controllers for the overall non-linear attitude control system. Extensive simulation results are obtained to validate the effectiveness of the proposed attitude controllers.

Robust attitude control of helicopters with actuator dynamics using neural networks

Abstract: In this study, attitude control is proposed for helicopters with actuator dynamics. For the nominal helicopter dynamics, model-based control is firstly presented to keep the desired helicopter attitude. To handle the model uncertainty and the external disturbance, radial basis function neural networks are adopted in the attitude control design. Using neural network approximation and the backstepping technique, robust attitude control is proposed with full state feedback. Considering unknown moment coefficients and the mass of helicopters, approximation-based attitude control is developed for the helicopter dynamics. In all proposed attitude control techniques, multi-input and multi-output non-linear dynamics are considered and the stability of the closed-loop system is proved via rigorous Lyapunov analysis. Extensive numerical simulation studies are given to illustrate the effectiveness of the proposed attitude control.

Brief paper: Higher order sliding mode control with self-tuning law based on integral sliding mode

Abstract: A higher order sliding mode control (SMC) with self-tuning law algorithm for uncertain non-linear systems is proposed. The method can be viewed as the finite time stabilisation based on geometric homogeneity and integral SMC. In order to reduce chattering and solve system uncertainties with unknown bound, a bipolar sigmoid function on-line adaptation and an adjustable control gain tuning approach without high-frequency switching are developed. Control system stability is ensured using the Lyapunov method. An example is given to show the effectiveness of the developed approach.

Robust adaptive sliding-mode fault-tolerant control with L 2 -gain performance for flexible spacecraft using redundant reaction wheels

Abstract: A robust adaptive fault-tolerant control approach for attitude tracking of flexible spacecraft is proposed for use in situations when there are reaction wheels/actuator failures, external disturbances and time-varying inertia-parameter uncertainties. More specifically, a robust controller based on sliding-mode control scheme is first designed to ensure that the equilibrium point in the closed-loop system is uniform ultimate bounded stability, incorporating constraints on actuator failures, whose failure time instants, patterns and values are unknown, as motivated from a practical spacecraft control application. Then, this controller is redesigned such that an assumption on a bound required of the unknown and time-varying inertia matrix is released by using online estimation for this bound. The prescribed robust performance is also evaluated by L2-gain less than a given small level for the penalty output signal. Complete stability and performance analysis are presented, and illustrative simulation results of an application to flexible spacecraft show that the high precise attitudes control and vibration suppression are successfully achieved using various scenarios of control effect failures.

Position-tracking control of underactuated autonomous underwater vehicles in the presence of unknown ocean currents

Abstract: This study addresses the problem of position-tracking control of underactuated autonomous underwater vehicles (AUVs) in the presence of unknown ocean currents in a horizontal plane. A position-tracking controller and a current observer are presented based on the Lyapunov stability theory by using the backstepping technique, respectively. The final controlled system, which arises from putting together the position-tracking controller and the observer, is proved to be globally K-exponentially stable by stability criteria for cascade system. The trajectories used for the illustration of the proposed control schemes are a circle with constant velocity and a sinusoidal curve that requires time-varying velocity. In order to demonstrate the practicability of the proposed controller, the surge force is assumed to be non-negative, and control input saturations are considered. Simulation results are presented to demonstrate the effectiveness of the proposed control schemes.

H ∞ static output feedback control for discrete-time switched linear systems with average dwell time

Abstract: This study investigates the problem of H∞ static output feedback (SOF) control for discrete-time switched linear systems with average dwell time. By the aid of multiple Lyapunov functions combined with Finsler's lemma, a switched SOF controller is designed such that the closed-loop switched system is exponentially stable and achieves a weighted L2-gain. Sufficient conditions for SOF control are derived and formulated in terms of linear matrix inequalities (LMIs). The minimal average dwell time and the corresponding SOF controller are obtained from the LMI conditions for a given system decay degree. The proposed method is less conservative than the existing ones, which is validated by a numerical example.

Improved approach to delay-dependent stability analysis of discrete-time systems with time-varying delay [Brief Paper]

Abstract: This study focuses on studying the asymptotical stability analysis problem for discrete-time systems with time-varying delay. By utilising the S-procedure and an inequality technique, a novel delay-dependent stability criterion is derived in terms of two linear matrix inequalities. Since no slack variable is introduced, less decision variables are involved in the stability condition and the burden of numerical computation is thus reduced. It is also rigorously proved that the authors' result is less conservative than some recent ones. Furthermore, the developed approach is extended to address the stability analysis problem of delayed discrete-time systems with norm-bounded uncertainties. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed results.

Brief paper: reliable control for networked control systems with probabilistic sensors and actuators faults

Abstract: This study is concerned with the reliable controller design for networked control systems (NCS) against both probabilistic sensors faults and actuators faults. The faults of each sensor or actuator occur randomly and their failure rates are governed by two sets of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of every sensor or actuator, new type of distribution-based NCS fault model is proposed. Based on the new built model, reliable controller is designed and sufficient conditions for the exponentially mean square stability (EMSS) of NCS are obtained by using Lyapunov functional method. The main contribution of the proposed fault model and methods lies with its practicality and generalisation, which contains many realistic problems in the NCS, such as probabilistic sensors or actuators failures, partial degradation, data distortion, packet dropout, network-induced delay and so on. Moreover, some existing models in the open literatures are deemed as special cases of the proposed fault model. To illustrate the implementation procedure, a vertical take-off and landing (VTOL) aircraft system is given to show the effectiveness and application of the proposed method.

Finite-time stability of linear time-varying singular impulsive systems [Brief Paper]

Abstract: In this study, the problem of finite-time stability of linear time-varying singular systems with impulses at fixed times is addressed. Sufficient conditions for linear singular impulsive systems to be finite-time stable are proposed in terms of a set of coupled matrix inequalities. Two numerical examples are given to illustrate the effectiveness of the obtained theoretical results.

New insight into internal model control filter design for load disturbance rejection

Abstract: In this study, a modified design of the internal model control (IMC) filter is proposed for improving closed-loop system performance of load disturbance rejection, especially for slow processes in industrial and chemical engineering practices. The deficiency of a conventional IMC filter design for controller tuning is revealed with regard to load disturbance rejection. By constructing one or more asymptotic canceling constraints for disturbance rejection, a modified IMC filter is proposed to reduce the influence from the time constant(s) of the process or repetitive-type load disturbance to the closed-loop disturbance rejection performance. Similar to a conventional IMC filter, there is essentially a single adjustable parameter in the proposed IMC filter, which can be monotonically tuned to meet with the compromise between the achievable disturbance rejection performance and the closed-loop system stability. Quantitative tuning formulae and guidelines for this adjustable parameter are developed in terms of the widely used first- and second-order process models with time delay. Illustrative examples are given to show the effectiveness and merits of the proposed IMC filter.

Brief Paper Robust fault-tolerant control of networked control systems with stochastic actuator failure

Abstract: Fault-tolerant control of networked control systems (NCSs) with random actuator failure is studied. An innovative model is presented for this problem. It includes three sources of uncertainties, namely uncertainties in the plant model, uncertainties in networked communications and uncertainties in possible actuator failure/malfunction. Other main features are: (i) the fault statistics of each actuator is individually quantified, and (ii) a united framework is proposed to have logic zero-order-holders embedded in the NCS. The latter enables actuators - when in normal operation - to use the latest actuating signals available to them. Based on the Lyapunov-Krasovskii functional, three theorems are proved in the study for the system stability and controller design. Theorem 1 gives a matrix inequality for the system asymptotical stability in the mean-square and is the foundation of the other two theorems. Theorem 2 shows a stability condition regarding the design of a robust state-feedback control for the system under study. Finally, Theorem 3 gives a modified stability condition that can be employed for actual design. A numerical example is presented to show how such a robust controller can be designed.