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Online ISSN 1751-8652 Print ISSN 1751-8644

IET Control Theory & Applications

Volume 6, Issue 17, 15 November 2012

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Volume 6, Issue 17

15 November 2012

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    • State-feedback stabilisation for stochastic non-holonomic systems with time-varying delays
      • Author(s): F. Gao ; F. Yuan ; Y. Wu
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2593 –2600
      • DOI:  10.1049/iet-cta.2011.0746
      • Type: Article
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      • p. 2593 –2600 (8)
        This study investigates the problem of state-feedback stabilisation for a class of stochastic non-holonomic systems in chained form with time-varying delays. By using input-state-scaling technique and backstepping recursive approach, and choosing an appropriate Lyapunov–Krasoviskii functional, a state-feedback controller is constructed. Based on switching strategy to eliminate the phenomenon of uncontrollability, the proposed controller could ensure that the closed-loop system is globally asymptotically regulated at origin in probability. A simulation example is provided to illustrate the effectiveness of the proposed method.
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      Stability and stabilisation of Markovian jump systems with time-varying delay: an input–output approach
      • Author(s): Z. Li ; Z. Fei ; H. Gao
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2601 –2610
      • DOI:  10.1049/iet-cta.2012.0458
      • Type: Article
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      • p. 2601 –2610 (10)
        This study revisits the problems of stability analysis and controller synthesis of Markovian jump systems with time-varying delay via an input–output approach. First, the system under consideration is transformed into an interconnected system, and the result on stochastic scaled small-gain condition for stochastic interconnected systems is presented, which is key idea to solve the problems considered in this study. Based on the system transformation and the stochastic scaled small-gain theorem, the stochastic stability of the original system is examined via the stochastic version of the bounded realness of the transformed forward system. The merit of the proposed approach lies in its reduced conservatism, which is made possible by a precise approximation of the time-varying delay and the stochastic scaled small-gain theorem. The proposed stability condition is demonstrated to be much less conservative than most existing results. Moreover, the problem of stabilisation is further solved with admissible controller designed via convex optimisations, whose effectiveness is also illustrated via numerical examples.
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      Domain of attraction and guaranteed cost control for non-linear quadratic systems. Part 1. Analysis
      • Author(s): F. Amato ; R. Ambrosino ; M. Ariola ; A. Merola
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2611 –2618
      • DOI:  10.1049/iet-cta.2012.0039
      • Type: Article
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      • p. 2611 –2618 (8)
        This is the first study of a two-part work devoted to the stability analysis and guaranteed cost control of the class of non-linear quadratic systems. For a given polytopic region in the state space, a sufficient condition is proposed to check whether an assigned region belongs to the domain of attraction of the zero equilibrium point. It is also shown that this problem is intimately related to the convergence and the computation of quadratic cost functions. Thanks to the main result of the study, both issues are casted in terms of feasibility problems involving linear matrix inequalities. A meaningful application example, involving the development of optimal strategies for integrated pest management, is illustrated at the end of this study.
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      Fuzzy approximation-based indirect adaptive controller for multi-input multi-output non-affine systems with unknown control direction
      • Author(s): A. Boulkroune ; M. M'Saad ; M. Farza
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2619 –2629
      • DOI:  10.1049/iet-cta.2012.0565
      • Type: Article
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      • p. 2619 –2629 (11)
        A fuzzy approximation-based indirect adaptive control is investigated for a class of unknown non-affine non-linear systems with unknown control direction. An equivalent model in affine-like form is first derived for the original non-affine system by using a Taylor series expansion. Next, a fuzzy indirect adaptive control is designed based on this affine-like equivalent model. In this control scheme, the adaptive fuzzy systems are used to appropriately approximate the equivalent affine model’s unknown non-linearities, whereas the Nussbaum gain function is used to deal with the unknown control directions (being closely related to the sign of control gain matrix). A decomposition property of the control gain matrix is fully exploited in the controller design and the stability analysis. It is proven that, under some appropriate assumptions, the proposed control scheme can achieve that all the signals in the closed-loop control system are bounded and the tracking errors converge to a small neighbourhood around zero. Effectiveness of the developed scheme is illustrated by two simulation examples.
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      Real-time control of human coagulation
      • Author(s): J.G. Makin  and  S. Narayanan
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2630 –2643
      • DOI:  10.1049/iet-cta.2011.0475
      • Type: Article
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      • p. 2630 –2643 (14)
        In previous work, the authors showed that the dynamics of human blood clotting could be fruitfully modelled and simulated as a hybrid system (HS), that is, one with interacting continuous and discrete parts. Here, the authors show that, although a complete analysis of the HS is (computationally) infeasible, analysis and control techniques can indeed be applied to a large, critical subsystem a set of about 100 ordinary differential equations. The theory is outlined behind the control techniques and then demonstrate in a series of simulations their application to control of pathological blood clotting, both hypercoagulatory (factor-V Leiden) and hypocoagulatory (hæmophilia A). In particular, steering is simulated during a clotting event of the crucial blood–protein thrombin, via the controlled injection of (recombinant) factor VIII (for hæmophilia) or the anti-coagulant heparin (for FV Leiden). It remains to remedy the shortcomings of this control technique, and to extend it to the remainder of the HS of the previous work; methods for these are proposed, and addressed in a subsequent article.
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      Adaptive fuzzy control for non-linear dynamical systems based on differential flatness theory
      • Author(s): G.G. Rigatos
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2644 –2656
      • DOI:  10.1049/iet-cta.2011.0464
      • Type: Article
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      • p. 2644 –2656 (13)
        A new approach to adaptive fuzzy control for uncertain non-linear dynamical systems, is proposed. The considered class of systems can be written in the Brunovsky (canonical) form after a transformation of their state variables and control input. The resulting control signal is shown to consist of non-linear elements, which in case of unknown system parameters can be approximated using neurofuzzy networks. An adaptation law for the neurofuzzy approximators can be computed using Lyapunov stability analysis. It is shown that the proposed adaptation law assures stability of the closed loop. Simulation experiments on benchmark non-linear dynamical systems are used to evaluate the performance of the proposed flatness-based adaptive fuzzy control scheme.
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      Dynamic observer-based robust control and fault detection for linear systems
      • Author(s): X.-J. Li  and  G.-H. Yang
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2657 –2666
      • DOI:  10.1049/iet-cta.2011.0057
      • Type: Article
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      • p. 2657 –2666 (10)
        This study is concerned with the design of dynamic observer-based robust controller that also facilitates the acquisition of information used for fault detection (FD) purpose in feedback control systems. Through introducing a weighting matrix, the combination of observer states is utilised to generate a residual signal to detect faults. The first technical contribution is to construct a new linearising change-of-variables that is able to convert the dynamic observer-based controller design problem into linear matrix inequality-based optimisation problem. The second one is to show that the proposed dynamic observer-based controller can achieve a better H∞ performance compared with the existing static (Luenberger) observer-based controller design approaches. Finally, via the simple residual structure, a convex fault detector design condition with some parameter matrices fixed is developed for guaranteeing the H− performance used to measure the fault sensitivity. An F-18 aircraft model is given to show the satisfactory FD performance and control performance.
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      Robust non-linear control design to an ionic polymer metal composite with hysteresis using operator-based approach
      • Author(s): M. Deng  and  A. Wang
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2667 –2675
      • DOI:  10.1049/iet-cta.2011.0534
      • Type: Article
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      • p. 2667 –2675 (9)
        In this article, robust non-linear control design to an ionic polymer metal composite (IPMC) with hysteresis, uncertainties and input constraints is studied. The IPMC is a novel smart polymer material, and many potential applications for low mass high displacement actuators in biomedical and robotic systems have been shown. In general, the IPMC has highly non-linear property and hysteretic behaviour, and the control input is subject to some constraints to ensure safety and longer service life of IPMC. Moreover, there exist uncertainties caused by identifying some physical parameters and approximate calculation in dynamic model. As a result, considering measurement error of parameters and model error, a practical non-linear model is obtained, and a non-linear robust control design with hysteresis, uncertainties and input constraints using operator-based robust right coprime factorisation is proposed for an IPMC setup, where, the Prandtl–Ishlinskii (PI) model is used to describe the hysteresis, and which is identified using experimental data. The effectiveness of the proposed control method based on obtained non-linear model is confirmed by simulation and experimental results.
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      Robust stability and stabilisation of discrete-time descriptor systems with uncertainties in the difference matrix
      • Author(s): W.-J. Mao
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2676 –2685
      • DOI:  10.1049/iet-cta.2011.0377
      • Type: Article
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      • p. 2676 –2685 (10)
        This study considers the problems of robust stability and stabilisation for linear discrete-time descriptor systems with norm-bounded uncertainties in all the system matrices including that in the difference matrix E. Under the assumption that the difference matrix E is rank-invariant for all admissible uncertainties, the robustness analysis problem under consideration falls into two cases: right-singular case and left-singular case. A necessary and sufficient stability condition and a sufficient stability condition are proposed for the first and second case, respectively. By using a state augmentation technique, sufficient stabilisation conditions are obtained for both cases. Furthermore, a necessary and sufficient stabilisation condition is established in the case of a non-singular matrix E. Finally, illustrative examples show that the proposed conditions are effective to design the stabilising controller for uncertain discrete-time descriptor systems with both the singular and non-singular matrixE.
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      Quantised H∞ control for sampled fuzzy systems
      Combined of vector field and linear quadratic Gaussian for the path following of a small unmanned helicopter
      • Author(s): T. Wang ; Y. Chen ; J. Liang ; C. Wang ; Y. Zhang
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2696 –2703
      • DOI:  10.1049/iet-cta.2012.0270
      • Type: Article
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      • p. 2696 –2703 (8)
        In this study, a composite fight control method for the path following of a small unmanned helicopter is proposed. The control system design adopts the hierarchical control architecture that is composed of an inner-loop, an outer-loop and a planning layer. The inner-loop controller design is based on the setpoint tracking linear quadratic Gaussian control technique which can not only stabilise the dynamics of the helicopter, but also track the reference control signals provided by the outer-loop controller well. The core part of the outer-loop controller design is based on the notion of vector field, which is used for generating the desired heading rate command. Lyapunov stability arguments are applied to demonstrate the asymptotic approximation to the desired path in the presence of wind disturbance. Experimental results are presented to verify the validity of the method.
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      Fuzzy adaptive fault-tolerant output feedback control of multi-input and multi-output non-linear systems in strict-feedback form
      • Author(s): B. Huo ; Y. Li ; S. Tong
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2704 –2715
      • DOI:  10.1049/iet-cta.2012.0435
      • Type: Article
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      • p. 2704 –2715 (12)
        This study develops an adaptive fuzzy control method for accommodating actuator faults in a class of uncertain multi-input and multi-output non-linear systems in strict-feedback form and without the requirement of their states being available for controller design. The considered faults are modelled as both loss-of-effectiveness and lock-in-place (stuck at unknown place). With the help of fuzzy logic systems to approximate the unknown non-linear functions, a fuzzy adaptive observer is developed for estimating the unmeasured states. Combining backstepping technique with non-linear tolerant-fault control theory, a novel adaptive fuzzy fault-tolerant control approach is constructed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded, and also the tracking errors between the system outputs and the reference signals converge to a small neighbourhood of zero by appropriate choice of the design parameters. Simulation results are provided to show the effectiveness of the control approach.
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      Stability and l2-gain analysis for a class of discrete-time non-linear Markovian jump systems with actuator saturation and incomplete knowledge of transition probabilities
      • Author(s): G. Song ; Y. Zhang ; S. Xu
      • Source: IET Control Theory & Applications, Volume 6, Issue 17, p. 2716 –2723
      • DOI:  10.1049/iet-cta.2012.0101
      • Type: Article
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      • p. 2716 –2723 (8)
        This study deals with the control problems of a class of discrete-time non-linear Markovian jump systems subject to saturating actuators and incomplete knowledge of transition probabilities. Modal non-linearities satisfying sector conditions are taken into consideration. Sufficient conditions that guarantee the closed-loop system to be locally stochastically stable are given. The linear matrix inequality (LMI) approach is used to analyse the closed-loop plant stability and l2-gain. Conditions in terms of LMIs are provided for obtaining an l2-gain as small as possible. A simulation example is given to illustrate the effectiveness of the proposed method.
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