Search

This study focuses in the output feedback stabilisation of constrained linear systems affected by uncertainties and noisy output measurements. The system states are restricted inside a given polytope and a classical Luenberger observer is used to reconstruct the unmeasurable states from output observations. Based on the observed states, a state feedback is proposed as the control input. The stability analysis and the control design are done using an extended version of the attractive ellipsoid method (AEM) approach. To avoid the violation of state constraints, this work proposes a barrier Lyapunov function (BLF) based analysis. The control parameters are obtained throughout the solution of some optimisation problems such that the BLF ensures an approximation of the constraints by a maximal ellipsoidal set and the AEM provides the characterisation of a minimal ultimately bounded set for the closed-loop system solutions. Numerical simulations show the advantages using the BFL-AEM methodology against classical sub-optimal controllers in academic second order and third order examples. Then, the proposed control strategy is applied over a Buck DC-DC converter. In all the cases, the method proposed here prevails over the other controllers. [ABSTRACT FROM AUTHOR]

Robust control of under-actuated mechanical systems (UMSs) with model uncertainty is still a challenging problem. For UMSs, the model parametric uncertainties make it difficult to precisely calculate the isolated equilibrium point corresponding to a fixed input. Without an accurate destination state, many set-point control methods cannot eliminate the positioning errors. An improved sliding mode control (ISMC) method is proposed to solve the robust control problem for a class of UMSs with model uncertainty and input disturbance. A balance variable is introduced in the sliding surface design to compensate for the disturbance caused by the inaccurate destination state, and the ISMC method is proposed to make the system state reach the sliding surface in finite time. Linear matrix inequality approach and particle swarm optimisation algorithm are applied to design the sliding mode surface parameters. The simulation results on an UMS are presented to show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

The problem of designing a globally optimal robust output feedback controller for time-varying polytopic uncertain systems is a well-known non-convex optimisation problem. In this paper, new sufficient conditions for both robustandswitching output-feedback control syntheses are proposed in terms of bilinear matrix inequalities (BMIs) under the multiple Lyapunov function framework. This set of synthesis conditions is further reduced to a special type of BMIs, which can be solved effectively using linear matrix inequality optimisation plus a line search. The associated robust output-feedback controller is constructed as a switching-type full-order dynamic output-feedback controller, consisting of a family of linear time-invariant subcontrollers and a min-switching logic. The proposed approach features the important property of computational efficiency with stringent performance. Its effectiveness and advantages have been demonstrated through extensive numerical studies. [ABSTRACT FROM PUBLISHER]

This paper investigates the problem of the sampled-data extended dissipative control for uncertain Markov jump systems. The systems considered are transformed into Markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach. The focus is on the design of a mode-independent sampled-data controller such that the resulting closed-loop system is mean-square exponentially stable with a given decay rate and extended dissipative. A novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality. The reduced conservatism of the criteria is demonstrated by two numerical examples. Furthermore, a sufficient condition for the existence of a desired mode-independent sampled-data controller is obtained by solving a convex optimisation problem. Finally, a resistance, inductance and capacitance (RLC) series circuit is employed to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a smooth control strategy for the regulation problem of an uncertain system, which assures uniform ultimate boundedness of the closed-loop system inside of the zero-state neighbourhood. This neighbourhood can be made arbitrarily small. To this end, a class of nonlinear proportional integral controllers orPIcontrollers was designed. The behaviour of this controller emulates very close a sliding mode controller. To accomplish this behaviour saturation functions were combined with traditionalPIcontroller. The controller did not need a high-gain controller or a sliding mode controller to accomplish robustness against unmodelled persistent perturbations. The obtained closed-solution has a finite time of convergence in a small vicinity. The corresponding stability convergence analysis was done applying the traditional Lyapunov method. Numerical simulations were carried out to assess the effectiveness of the obtained controller. [ABSTRACT FROM PUBLISHER]

In this paper, theH∞consensus control andH2robust control synthesised with transient performance problems are investigated for a group of autonomous agents with linear or linearised dynamics. Based on the relative information between neighbouring agents and a subset of absolute information of the agents, distributed controllers are proposed for bothH∞andH2cases. Compared with the existing protocols, the one presented in this article focuses on improving the transient performance of the consensus problem. By using the tools from matrix analysis and robust control theory, conditions for the existence of controllers to those problems under an undirected communication topology are provided. Then, it is shown that theH2performance limit of uncertain systems under a distributed controller equals the minimumH∞consensus index synthesised with transient performance of a single agent by using a state feedback controller, independent of the communication topology. Finally, a simulation example as an application in Raptor-90 helicopter is proposed to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

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 analysis method. The proposed methods are compared in detail, and simulation results are given to show the validation. [ABSTRACT FROM AUTHOR]

This paper focuses on the robustH∞control problem for a class of nonlinear switched systems containing neutral uncertainties with average dwell time (ADT) switching. Uncertainties are considered to be nonlinearly dependent on state and state derivative and allowed to appear in channels of state, control input and disturbance input. The robustH∞control problem of the switched system with stabilisable and unstabilisable subsystems is solvable if the stabilisable and unstabilisable subsystems satisfy certain conditions and admissible switching strategy among them. ADT and piecewise Lyapunov function approaches are applied to achieve the control design. A numerical example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM PUBLISHER]

In this paper, a robust adaptive neural control design approach is presented for a class of uncertain pure-feedback nonlinear systems. To reduce the complexity of the both controller structure and computation, only one neural network is used to approximate the lumped unknown function of the system at the last step of the recursive design process. By this approach, the complexity growing problem existing in conventional methods can be eliminated completely. Stability analysis shows that all the closed-loop system signals are uniformly ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness and merits of the proposed approach. [ABSTRACT FROM AUTHOR]

In this article, a distributed fault detection and isolation (FDI) method is developed for a class of interconnected nonlinear uncertain systems. In the distributed FDI architecture, a FDI component is designed for each subsystem in the interconnected system. For each subsystem, its corresponding local FDI component is designed by utilising local measurements and certain communicated information from neighbouring FDI components associated with subsystems that are directly interconnected to the particular subsystem under consideration. Under certain assumptions, adaptive thresholds for distributed FDI in each subsystem are derived, ensuring robustness with respect to interactions among subsystems and system modelling uncertainty. Moreover, the fault detectability and isolability conditions are rigorously investigated, characterising the class of faults in each subsystem that are detectable and isolable by the proposed distributed FDI method. Additionally, the stability and learning capability of the local adaptive fault isolation estimators designed for each subsystem is established. A simulation example of interconnected inverted pendulums mounted on carts is used to illustrate the effectiveness of the method. [ABSTRACT FROM PUBLISHER]

In this article on-line parameter estimation of dynamical systems is addressed in the context of model-based networked control systems (MB-NCSs). Stability conditions that are robust to parameter uncertainties and lack of feedback for extended intervals of time are presented. The updated model is used to control the real system the next time feedback information is unavailable. Additionally, new estimation models are proposed that offer better convergence properties than typical state-space parameter estimation methods; common assumptions such as availability of persistently exciting inputs and estimation of only a canonical form of the system are relaxed. The implementation of upgraded models in MB-NCSs results in better usage of the network by allowing longer intervals without the need for measurement updates. [ABSTRACT FROM AUTHOR]

This article considers the distributed robust control problems of uncertain linear multi-agent systems with undirected communication topologies. It is assumed that the agents have identical nominal dynamics while subject to different norm-bounded parameter uncertainties, leading to weakly heterogeneous multi-agent systems. Distributed controllers are designed for both continuous- and discrete-time multi-agent systems, based on the relative states of neighbouring agents and a subset of absolute states of the agents. It is shown for both the continuous- and discrete-time cases that the distributed robust control problems under such controllers in the sense of quadratic stability are equivalent to the H ∞ control problems of a set of decoupled linear systems having the same dimensions as a single agent. A two-step algorithm is presented to construct the distributed controller for the continuous-time case, which does not involve any conservatism and meanwhile decouples the feedback gain design from the communication topology. Furthermore, a sufficient existence condition in terms of linear matrix inequalities is derived for the distributed discrete-time controller. Finally, the distributed robust H ∞ control problems of uncertain linear multi-agent systems subject to external disturbances are discussed. [ABSTRACT FROM PUBLISHER]

Sufficient conditions are derived for the robust stability of discrete-time, switched, linear systems with dwell time in the presence of polytopic type parameter uncertainty. A Lyapunov function, in quadratic form, is assigned to each of the subsystems. This function is allowed to be time-varying and piecewise linear during the dwell time and it becomes time invariant afterwards. Asymptotic stability conditions are obtained in terms of linear matrix inequalities for the nominal set of subsystems. These conditions are then extended to the case where the subsystems encounter polytopic type parameter uncertainties. The developed method is applied to l 2-gain analysis where a bounded real lemma is derived, and to H ∞ control and estimation, both for the nominal and the uncertain cases. [ABSTRACT FROM PUBLISHER]

This article presents the design of a robust controller for uncertain systems whose parameters are bounded by intervals. For that, we propose to combine the standard H ∞ approach with interval tools in order to ensure robust performances. The main advantages of the proposed approach are: (1) the natural and ease of modelling of the uncertain parameters, thanks to intervals, and (2) the derivation of a low-order controller since its structure can be fixed a priori and the order is lower than the system order. In particular, we demonstrate that a PID-structure can be used to control a nth order interval system. The approach is then applied to design a robust controller for a piezoelectric actuator and the experimental results effectively show its efficiency. [ABSTRACT FROM AUTHOR]

This article investigates the robust admissibility of uncertain discrete-time switched singular systems. First, the admissibility is introduced, by using the switched Lyapunov function, for singular systems. Sufficient conditions for robust admissibility of uncertain switched singular systems are presented in strict linear matrix inequalities formulation. Robust admissibility condition designs for both state feedback and static output control feedback are then derived. Numerical examples are provided to illustrate our approach. [ABSTRACT FROM PUBLISHER]

Block-oriented models (BOMs) have shown to be appealing and efficient as nonlinear representations for many applications. They are at the same time valid and simple models in a more extensive region than time-invariant linear models. In this work, Wiener models are considered. They are one of the most diffused BOMs, and their structure consists in a linear dynamics in cascade with a nonlinear static block. Particularly, the problem of control of these systems in the presence of uncertainty is treated. The proposed methodology makes use of a robust identification procedure in order to obtain a robust model to represent the uncertain system. This model is then employed to design a model predictive controller. The mathematical problem involved in the controller design is formulated in the context of the existing linear matrix inequalities (LMI) theory. The main feature of this approach is that it takes advantage of the static nature of the nonlinearity, which allows to solve the control problem by focusing only in the linear dynamics. This formulation results in a simplified design procedure, because the original nonlinear model predictive control (MPC) problem turns into a linear one. [ABSTRACT FROM AUTHOR]

We propose a variant of the recently introduced strategy for stabilisation with limited information by D. Liberzon and J.P. Hespanha and analyse its robustness properties. We show that, if the nominal plant can be made input-to-state stable with respect to measurement errors, parameter uncertainty and exogenous disturbances, then this robustness is preserved with this quantised feedback. More precisely, if a sufficient bandwidth is available on the communication network, then the resulting closed loop is shown to be semiglobally input-to-state practically stable. [ABSTRACT FROM AUTHOR]

This article presents a novel robust iterative learning control algorithm (ILC) for linear systems in the presence of multiple time-invariant parametric uncertainties.The robust design problem is formulated as a min-max problem with a quadratic performance criterion subject to constraints of the iterative control input update. Then, we propose a new methodology to find a sub-optimal solution of the min-max problem. By finding an upper bound of the worst-case performance, the min-max problem is relaxed to be a minimisation problem. Applying Lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities (LMIs). An LMI-based ILC algorithm is given afterward and the convergence of the control input as well as the system error are proved. Finally, we apply the proposed ILC to a generic example and a distillation column. The numerical results reveal the effectiveness of the LMI-based algorithm. [ABSTRACT FROM AUTHOR]

This article proposes a new approach to robustify an input-output linearisation controller. The robustification is achieved by estimating the uncertainties and external unmeasurable disturbances using a novel uncertainty and disturbance estimator. A significant feature of the proposed approach is that it does not need any information about the uncertainties. The stability of the system and the estimator is established. Effectiveness of the proposed approach is demonstrated through application to the wing rock motion control problem. [ABSTRACT FROM AUTHOR]

This paper focuses on uncertain pendulum-like systems subject to norm constraint structured uncertainties, and addresses the robust gradient-like behaviour analysis and synthesis problems for such systems. By applying the structured singular value of an operator to structured uncertainty, the results on robust analysis for the gradient-like behaviour of uncertain pendulum-like systems are obtained. Based on the analysis results, using KYP lemma, a dynamic output feedback controller for the closed loop system guaranteeing gradient-like behaviour is designed and the controller parameters are explicitly expressed by a set of feasible solutions of corresponding linear matrix inequalities. Finally two numerical examples are presented to demonstrate the applicability and validity of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we study the limitations of the capability of the feedback mechanism in dealing with structural uncertainty for a class of pth order non-linear autoregressive control systems. The size of the structural uncertainty is characterized by multiple Lipschitz constants (say L1,L2,...,Lp) of the uncertain non-linear function. It is shown that if L1,L2,...,Lp satisfy certain algebraic conditions, then there exists no globally stabilizing feedback control law for the corresponding uncertain systems. The result here is an extension of the previous result obtained by Zhang and Guo (2002). [ABSTRACT FROM AUTHOR]

This paper describes the synthesis of robust output feedback H∞ control for a class of uncertain Markovian jump linear systems with time-delays which are time-varying and depend on the system modes of operation. Under the assumption of known bounds of system uncertainties and the control system gain variations, we present sufficient conditions on the existence of robust stochastic stability and γ-disturbance H∞ attenuation. Through the changes of variables and Schur complements, these sufficient conditions can be rewritten in a set of coupled linear matrix inequalities, with which, robust control can be easily constructed. As an added advantage, the control design depends only on [image omitted], the measured parameter of Markovian jumping at time t, which might be corrupted by measurement noises. Numerical examples are provided to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

A robust stability criterion for multivariable discrete-time variable structure control is proposed. When a variable structure controller is designed and implemented as a sampled-data system, achieving robustness to uncertainties can become difficult. To ameliorate the situation, an uncertainty estimator, also formulated within the variable structure framework, can be used as an embedded discrete-time variable structure controller. This approach requires a bounded changing rate of the uncertainties to ensure robust stability. However, when uncertainties vary as a function of state variables, which occurs with parametric uncertainties, it is not practical to assume such a bound. In this paper, uncertainties are assumed to consist of external disturbances and parametric uncertainties. An uncertainty compensator is used to deal with the former, and a robust stability criterion is developed using the small gain theorem for the latter. [ABSTRACT FROM AUTHOR]