Finite-horizon reliable control with randomly occurring uncertainties and nonlinearities subject to output quantization

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.

The decentralized robust servomechanism problem (DRSP) for large flexible space structures (LFSS) under sensor and actuator failures is considered. Failure conditions are modelled by failure matrices. This permits a unified treatment of sensor and actuator failures. For colocated LFSS, stabilization, tracking of constant set points, and regulating constant disturbances can be simultaneously handled using a decentralized tuning PID output-feedback controller. Necessary and sufficient conditions for solvability of the DRSP for colocated LFSS under sensor and actuator failures are derived. Two detailed examples demonstrate the effectiveness of the controller.

In this study, the finite-time control problem is studied for discrete time-varying systems with randomly occurring non-linearity and missing measurements. The randomly occurring non-linearity is modelled according to a Bernoulli distributed white sequence with a known conditional probability. The missing measurements phenomenon is assumed to occur in a random way and the missing probabilities are time-varying with known upper and lower bounds. Two sufficient conditions are established for the existence of the state feedback and output feedback controllers, which guarantee the finite-time stochastic stability of the closed-loop systems. The recursive linear matrix inequality approach is employed to design the desired controller gains. A numerical example is provided to illustrate the effectiveness of the obtained results.

This paper is concerned with the synthesis of constant output feedback law which possesses integrity against failures of actuator and sensor. For a linear time-invariant system, the redundancy of actuators and sensors is analyzed firstly. In the situation where actuators and sensors are redundant, the modes of open loop system which are outside a desired region of Complex plane (e.g. the open left complex plane) may remain controllable and observable after the failures of some actuator and sensor. For every such situation of permissible actuator or sensor failures, if a constant output feedback law can make the poles of close loop system in the desired region, then the feedback law is said to possess high integrity against actuator and sensor failures, A proper objective function is proposed in this paper. By using the parameter optimization method, the output feedback law possessing high integrity can be generated. A computer program is developed on the IBM PC. For a linear time invariant model of double effect evaporator and a model of a plane, the output feedback laws which possess integrity are obtained by the program. These examples illustrate the effectiveness of the method proposed in this paper. The method does not require that the open loop system is asymptotically stable, this is one of the main advantages of the method.

H∞ control for time-delay systems with randomly occurring nonlinearities subject to sensor saturations, missing measurements and channel fadings

This paper investigates the problem of robust passive control for networked fuzzy systems, where randomly occurring uncertainties, variable sampling intervals, and constant network-induced delay are taken into account. A discontinuous Lyapunov functional is introduced for the closed-loop systems, which takes full advantage of the sawtooth structure of the time-varying interval delay induced by sample-and-hold and signal transmission. A sufficient condition is proposed to ensure the closed-loop system to be robustly stochastically passive. Then, the problem of robust passive control is solved. Two examples are utilized to illustrate the advantages and effectiveness of the results that are proposed in this paper.

The issue of fault-tolerant decentralized control is investigated for large-scale civil engineering structures. Considering the correlation of the sub-control system, the sensor failures and the actuator failures, a sufficient condition for decentralized stabilizability is proposed for the class system of discrete-time systems with delay interconnections by using the Lyapunov stability theory and the linear matrix inequality (LMI) approach. It is shown that this condition is equivalent to the feasibility problem of the linear matrix inequality. Furthermore, a decentralized state feedback control law is derived as a convex optimization problem, and the latter can be solved by using existing efficient convex optimization techniques. The obtained controller enables the closed-loop systems to be stable. Considering sensor failures and the actuator failures, the ASCE 9-story benchmark building is selected as a numerical example to evaluate the control performance of the partially independent decentralized control and overlapping decentralized control. Numerical simulation results indicate that the proposed small gain decentralized stabilization control (LMI-SGDSC) algorithm performs as well as the traditional centralized control, and the overlapping decentralized control has a greater level of reliability. The fault tolerant decentralized control (LMI-SGFTDSC) achieves satisfactory control effects.

Dynamic event-triggered [formula omitted] state estimation for delayed complex networks with randomly occurring nonlinearities

The unmanned aerial vehicle (UAV) has been developing rapidly recently, and the safety and the reliability of the UAV are significant to the mission execution and the life of UAV. Sensor and actuator failures of a UAV are one of the most common malfunctions, threating the safety and life of the UAV. Fault-tolerant control technology is an effective method to improve the reliability and safety of UAV, which also contributes to vehicle health management (VHM). This paper deals with the sliding mode fault-tolerant control of the UAV, considering the failures of sensor and actuator. Firstly, a terminal sliding surface is designed to ensure the state of the system on the sliding mode surface throughout the control process based on the simplified coupling dynamic model. Then, the sliding mode control (SMC) method combined with the RBF neural network algorithm is used to design the parameters of the sliding mode controller, and with this, the efficiency of the design process is improved and system chattering is minimized. Finally, the Simulink simulations are carried out using a fault tolerance controller under the conditions where accelerometer sensor, gyroscope sensor or actuator failures is assumed. The results show that the proposed control strategy is quite an effective method for the control of UAVs with accelerometer sensor, gyroscope sensor or actuator failures.

This paper mainly focuses on the finite-horizon H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for a class of discrete time-varying systems with delays and randomly varying sensor saturations. A set of binary switching sequences taking values of 1 and 0 is introduced to account for the stochastic phenomenon of sensor saturations which occurs and influences the dynamics of the system in a probabilistic way. By utilizing the stochastic analysis and matrix inequality techniques, sufficient criteria are derived in terms of a set of recursive linear matrix inequalities (RLMIs) under which the filtering error dynamics achieves the prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance over a finite horizon. Moreover, at each time point k, the time-varying filter parameters can be solved iteratively according to the explicit solutions of the RLMIs. Finally, a numerical simulation is given to illustrate the effectiveness of the obtained results.

The integrity design problem of fault tolerant control for networked control system (NCS) with actuator failures and data packet dropouts is investigated. The data packet dropouts in both sensor-controller (S-C) and controller-actuator (C-A) links are described by two switches, which can be modeled as a discrete event system with known rate. After introducing the matrix of actuator failure, the closed-loop NCS is developed, which can be viewed as asynchronous dynamical systems (ADSs). Then, the sufficiency of exponential stability for the NCS is obtained based on the theory of ADSs. The output feedback controllers that can guarantee system stability are also proposed. Finally, two numerical examples are given to demonstrate the validity of our proposed approach.

For a class of uncertain nonlinear systems with actuator failure, a dynamic-scaling output feedback control approach is proposed to address the adaptive practical tracking problem. Compared with existing nonlinear fault-tolerant control methods, a pair of new adaptive observer and control law are developed and the main innovations lie in: (i) novel time-varying coupled matrix inequalities are introduced to deal with the actuator failure; (ii) a non-identification adaptive gain is used to compensate the actuator failure, unknown control coefficients and nonlinear parameters in nonlinearities; (iii) our control approach is non-backstepping, which achieves the global output feedback control of nonlinear systems beyond the classic output-feedback form.

In passive redundancy, redundant control devices such as sensors, compensators, and actuators are used in industry to assure reliability against failures. Passive redundancy assures that even if some devices fail, the control system remains stable. Some results on the use of passive redundancy for reliability against compensator or actuator failures are already in existence. The objective of this paper is to explore the possibility of using passive redundancy to protect against sensor failures, which has never before been examined. First, the most fundamental failure mode of sensors is considered and reliability against sensor failures in passive redundancy is defined. Next, the possibility of using passive redundancy with the simplest and most thoroughly conventional studied control system configuration, i.e., the parallel configuration, is studied. Solving the essential problem of this configuration leads to an effective control system configuration. © 1997 Scripta Technica, Inc. 80(5): 96–104, 1997.

The author parameterizes the set of all controllers such that the standard unity-feedback system is stable in the presence of arbitrary sensor or actuator failures. The characterization of controllers in this parameterization is not independent of the failures. Linear, time-invariant, multi-input, multi-output feedback systems are discussed. Two classes of failures are considered, the failure of one connection and the failure of any number of connections provided that at least one connection does not fail. >

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.