Reliable control for positive switched systems with random nonlinearities

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 boundedness of interval type-2 fuzzy systems with time delay and actuator faults

ABSTRACTThis paper is concerned with the problem of observer-based reliable passive control for uncertain Takagi–Sugeno (T–S) fuzzy systems with time-delay and actuator faults. By employing Lyapunov stability theory, fault treatment method and linear matrix inequalities (LMIs), a sufficient condition on the existence of an observer-based reliable passive controller is given. Further, the LMI conditions are proposed for the observer-based reliable passive controller design. The gain of reliable controller and observer can be obtained by solving the proposed LMIs. Using the reliable passive controller, the closed-loop system is not only internally stable but also strictly passive even though some actuator components fail and system state fails to be measured completely. Finally, a truck-trailer system example is given to verify the effectiveness and advantages of the designed approach.

LMI approach to reliable H∞ control of linear systems

This paper considers the problem of adaptive reliable guaranteed cost controller design for linear time-delay systems against actuator faults via dynamic output feedback. Based on indirect adaptive method, a new reliable dynamic output feedback controller is established. The controller gains are affinely dependent on the estimations of fault parameters, which are updating automatically according to the proposed adaptive laws. New delay-dependent sufficient conditions for the existence of the reliable guaranteed cost dynamic output feedback controller are derived in terms of linear matrix inequalities, which have less conservativeness than the corresponding reliable dynamic output feedback controller with fixed gains. An example is presented to show the effectiveness of the proposed method.

Error-constrained reliable tracking control for discrete time-varying systems subject to quantization effects

Successful use of a reliable controller requires a fault detector to detect sensor faults such that the sensor can be removed from the closed-loop if it is faulty. If it could be expected that a sensor would completely fail such that it would not emit any signal then a fault detector would not be required and the reliable controller should operate as it was designed for this situation. Integrating a fault detector with a controller introduces tradeoffs that have to be made between the controller and fault detector performance. This can make the H∞ design harder since weighting choice is more crucial. Where there is more than one fault to be detected there must be frequency separation between the fault models and the other weightings which further restricts a successful design. It was shown by Niemann and Stoustrup (1997) that for uncertain systems the integrated design of a controller a fault detection filter should have a smaller fault error than separate designs. In this paper the integration of a fault detector with a reliable controller was explored. The convenience of a single H∞ design must be balanced against the complexity of that design and the difficulties in choosing frequency weighting functions to satisfy all the design objectives.

This study investigates reliable output tracking control issues. Both passive and active reliable control laws are proposed using variable structure control (VSC) technique. These reliable controllers need not the solution of Hamilton-Jacobi equation or inequality, which are essentials in optimal approaches such as reliable LQR and H-infinity designs. As a matter of fact, this approach is able to relax the computational load. The proposed reliable designs are also applied to bank-to-turn missile systems to illustrate their benefits.

SummaryThis paper presents a nonfragile reliable control approach to positive switched systems with actuator faults and saturation. In order to guarantee the reliability of the controller, the controller gain matrix is chosen as the sum of a normal gain matrix and a gain perturbation matrix. A nonfragile reliable control is first proposed for the considered systems using a gain matrix decomposition technique. Then, the presented nonfragile control design approach is developed for the systems with exogenous disturbances. An approach to compute the normal gain matrix and the gain perturbation matrix is also provided. Under the obtained controller, the resulting closed‐loop systems are positive and L1‐gain stable. Meanwhile, all the states will stay inside a cone. All presented conditions are described via linear programming. Finally, two examples are provided to verify the effectiveness of the theory findings.

The problem of robust reliable control with multi-objective requirements and static-output-feedback (SOF) form is studied for a class of uncertain nonlinear systems subject to vector-bounded nonlinear dynamics, norm-bounded disturbances and actuator faults or the loss of actuator effectiveness. Based on the Lyapunov stability theory and multi-objective optimization strategy, a sufficient condition for the reliable controller design with SOF-form is developed. It can guarantee the robust stability, the given magnitude constraints on control input and system output, the prescribed level on the disturbance attenuation and the optimized quadratic cost performance of the closed-loop system under all possible faults. Thus, the comprehensive performance of the post-fault system is ensured by the designed controller. Finally, a numerical example is provided to verify the effectiveness of our proposed design algorithm.

Reliable control for networked control systems with probabilistic actuator fault and random delays

Reliable Control of Uncertain Nonlinear Systems

This paper develops some new reliable controller design methods for finite and infinite horizon cases with nonzero initial conditions using an H/sub /spl infin//-like performance measure with weightings on initial and final states. For the state-feedback case, it gives necessary and sufficient conditions for the existence of the reliable controller for outages in a prespecified subset of actuators. For the output-feedback case, it gives sufficient conditions for reliable controller design for outages in preselected subsets of actuators or sensors.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

In this paper, the reliable control problem is studied for a class of discrete linear Markovian jump singular systems with actuator failures. A more practical model of actuator failures than outage is considered. It is important that the transition probabilities of the jumping process are assumed to be partly unknown. The failures of actuator are quantified by a variable taking values in a given interval. The purpose of the addressed reliable control problem is to design a reliable controller based on the state feedback method such that the closed-loop systems are asymptotically mean-square stable disturbance attenuation not only when all actuators are operational, but also in case of some actuator failures. The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs). A numerical example is provided to demonstrate the effectiveness of the proposed design approach.

This paper presents a method of designing robust H ∞ reliable controllers for a class of Lipschitz nonlinear delay switched systems. External disturbances and parameter uncertainties in the systems are assumed that they are unknown time-varying and norm-bounded. When faults exist on actuators, robust H ∞ reliable controllers are proposed by using Lyapunov stability theory and dwell time approach so that the closed-loop systems are globally exponentially stable with a guaranteed H ∞ performance level γ, which are based on switching strategy. Solutions of robust H ∞ reliable controllers can be achieved by linear matrix inequalities (LMIs) and finite dimensional convex optimization. A numerical example indicates that the proposed scheme is feasible and effective that can achieve the closed-loop system integrity in the presence of actuator failures.