Reliable control for discrete-time Markovian jump singular systems with partly unknown transition probabilities

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

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.

This paper concerns the reliable guaranteed cost control problem of nonlinear systems with time-varying state delays and actuator failures for a given quadratic cost function. The problem is to design a delay-dependent reliable guaranteed cost state feedback control law which can tolerate actuator failures, such that the closed-loop cost function value is not more than a specified upper bound. Based on the linear matrix inequality (LMI) approach, a sufficient condition for the existence of reliable guaranteed cost controllers is derived. Furthermore, a convex optimization problem with LMI constraints is formulated to design the optimal reliable guaranteed cost controller which minimizes the upper bound of the closed-loop system cost. A numerical example is given to illustrate the proposed method.

This thesis is concerned with the dissipative control and filtering problems of singular systems. Four classes of singular systems are considered: delay-free singular systems, singular systems with constant time-delay, uncertain singular systems with time-varying delay and sensor failures, and singular Markovian jump systems with actuator failures.
\nFor delay-free singular systems, the system augmentation approach is employed to study the dissipative control and filtering problems. First, the approach is used to solve the dissipative control problem by static output-feedback for standard state-space systems which are the special cases of singular systems. For a continuous-time standard state-space system, the closed-loop system is represented in an augmented system form. Based on the augmented system, a necessary and sufficient dissipativity condition is proposed, which decouples the Lyapunov matrix and controller matrix. To further separate the Lyapunov matrix and the system matrices, an equivalent condition is obtained by introducing some slack matrices. Then, a necessary and sufficient condition for the existence of a static output-feedback controller is proposed, and an iterative algorithm is given to solve the condition. For discrete-time singular systems, by giving an equivalent representation of the solution set, a necessary and sufficient dissipativity condition is proposed in terms of strict linear matrix inequality (LMI) which can be easily solved by standard commercial software. Then a state-feedback controller design method is given based on the augmentation system approach. The method is extended to the static output-feedback control problem and the reduced-order dissipative filtering problem.
\nFor continuous-time singular time-delay systems, the problem of state-feedback dissipative control is considered. An improved delay-dependent dissipativity condition in terms of LMIs is established by employing the delay-partitioning technique, which guarantees a singular system to be admissible and dissipative. Based on this, a delay-dependent sufficient condition for the existence of a state-feedback controller is proposed to guarantee the admissibility and dissipativity of the closed-loop system. In addition to delay-dependence, the obtained results are also dependent on the level of dissipativity. Moreover, the results obtained unify existing results on H∞ performance analysis and passivity analysis for singular systems.
\nFor discrete-time singular systems with polytopic uncertainties, time-varying delay and sensor failures, the problem of robust reliable dissipative filtering is considered. The filter is designed by the reciprocally convex approach such that the filtering error singular system is admissible and strictly (Q, S, R)-dissipative. For singular systems with time-varying delay and sensor failures, a sufficient condition of reliable dissipative analysis is obtained in terms of LMIs. Then the result is extended to the uncertain case by introducing some variables to decouple the Lyapunov matrices and the filtering error system matrices. Moreover, a desired filter for uncertain singular systems with time-varying delay and sensor failures is obtained by solving a set of LMIs.
\nFor continuous-time singular Markovian jump systems with actuator failures, the problem of reliable dissipative control is addressed. Attention is focused on the state-feedback controller design method such that the closed-loop system is admissible and strictly (Q, S, R)-dissipative. A sufficient condition is obtained in terms of strict LMIs. Moreover, the results obtained unify existing results on H∞control and passive control on singular Markovian jump systems.

This paper deals with the problem of reliable guaranteed cost control problem for nonlinear singular systems governed by a set of differential-algebraic equations. A more practical model of actuator failures than outage is adopted. The objective is to design a reliable guaranteed cost state feedback law, which can tolerant actuator failure, such that the cost function of the closed-loop system is guaranteed to be no more than a certain upper bound. Based on the Hamilton-Jacobi inequality (HJI), the sufficient condition of existence and design method of desiring reliable controller is presented. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

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.

ABSTRACTThis paper investigates the reliable sampled-data control problem for a class of singular networked cascade control systems with randomly occurring actuator failures, time-varying delay and disturbances. In particular, the randomly occurring actuator failures describes the phenomenon of the actuator failure appearing in a random way and is modelled by a Bernoulli distributed white noise sequences with a known conditional probability. The main purpose of this work is to design a reliable sampled-data controller such that an optimised upper bound of the predefined performance index is well guaranteed for the systems under consideration even in the presence of both the randomly occurring actuator failures and disturbances. The resulting controllers are reliable in the sense that they will provide guaranteed stochastically admissible and performance index when all actuators are operational as well as when some actuators experiences failure. Finally, two numerical examples are given to exhibit the effectiveness of the proposed control scheme.

The problem of reliable Hinfin control based on dynamic output feedback is investigated for time-varying delayed systems against actuator failure. By means of variables switchover, two linear matrix inequalities(LMIs) which are the sufficient condition of the existing of reliable Hinfin controller are given. At the same time, the design approaches of dynamic output feedback controller are presented. The resultant control system is asymptotically stable with anti-disturbance performance of given Hinfin-norm bounds despite any outages within a prespecified subset of actuators. A numerical example shows the validity of the design method proposed.

Reliable Control of Uncertain Nonlinear Systems

We consider a reliable decentralized supervisory control problem for discrete event systems in the conditional architecture. This reliable decentralized control problem requires synthesizing local supervisors such that a given specification can be achieved without blocking even if local control decisions of some local supervisors are not available for making the global control decision. We introduce a notion of reliable conditional-coobservability and show that reliable conditional-coobservability together with reliable controllability and L m (G)-closedness is a necessary and sufficient condition for the existence of a solution to the reliable decentralized control problem. In addition, we develop a method for verifying reliable conditional-coobservability.

Robust reliable stabilization of stochastic switched nonlinear systems under asynchronous switching

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.

Robust reliable guaranteed cost control for uncertain singular systems with time-delay

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.

LMI approach to reliable H∞ control of linear systems