Fault-tolerant Control Of Nonlinear Systems With Saturation Constraints

With the development of modern control technology,the control systems with saturation constraints has attracted enormous attention.The saturation phenomena occurring in control systems are classified into actuators saturation and sensors saturation,which presents respectively the bounded outputs of actuators or sensors during the control process.In the traditional designs,the saturation effects have not been taken into consideration,so when the saturation occurs in the systems,it will result in the degradation of the system performance or even system instability.The global stability of closed-loop systems cannot be guaranteed for system analysis and design when actuators saturation occurs.That is to say stability can only be guaranteed in a bounded region.In the existing results,system analysis and controller design under actuators saturation is the main stream.However,in some complex systems such as aircrafts,spacecrafts where actuators saturation and actuators faults always occur at the same time,the fault-tolerant ability is extremely important.That is to say,the reliability and safety are essential in modern control theory.But,until now,only a few researchers have considered the actuators saturation,sensors saturation and fault-tolerant controller design problem.The main contents are summarized as follows:(1)Reliable control of a class of strict feedback nonlinear systems with actuators constraints.The considered nonlinear systems are of Branovsky form with input saturations,under two assumptions,a computation method for a domain of attraction is proposed,based on which it is proved that in the domain of attraction,the control effect will not exceed the saturation boundary.Then,by applying the Backstepping technique,a state feedback control is presented to guarantee the stability of the closed-loop system based on the Lassue-Yoshizawa's Lemma.(2)Adaptive reliable control of a class of strict feedback nonlinear sytems with actuators hysteresis.Consider the classical Duhem model for hysteresis,the dissertation applies the adaptive Backstepping method to the controller design to eliminate the effect of saturation on the closed-loop systems.The proposed approach does not need the exact knowledge about the expression of hysteresis.It is shown that the presented controller can achieve a quick tracking to the given servo-signal with a small tracking error in a pre-given region.It is guaranteed that all signals can be kept bounded which achieve the ideal control objective and it is proved that the closed-loop system is stable by Lyapunov theory.(3)Cost guaranteed fault-tolerant control of a class of polynomial nonlinear continuous systems with loss-in-effect actuators faults.This chapter considers a polytopic actuators fault model and the nonlinear system is built up in a polynomial function in system state.To transform the fault-tolerant controller design problem into a solvable semi-definite programming,this chapter introduces an index to qualify the effect of the nonlinear terms.Combining the above mentioned index with the L2 cost index,the original fault-tolerant control problem is transformed into a multi-objective optimization problem.Then the optimization problem is solved effectively by Sum of squares(SOS)algorithm.Compared with the existing results,the proposed method has a convex form and does not need to be solved iteratively and thus is more reliable.(4)Robust fault-tolerant control of a class of polynomial nonlinear discrete systems with loss-in-effect actuators faults.The proposed method can guarantee the performance even in the presence of the actuators faults and actuators saturation.The novelty lies in two aspects:First,to transform the fault-tolerant controller design under actuators saturation constraint,a index is given to quality the effect of the nonlinear terms with a resultant semi-definite programming;Second,the combination with the robust index,the original fault-tolerant control problem is transformed into a multi-objective optimization problem which is in a form of polynomial matrix inequalities.Then this chapter presents an optimization method to solve the programming to give a practical solution to the passive fault-tolerant control problem.(5)Simultaneous fault detection and control for a class of Ito stochastic systems with time-delay and sensors saturation.This chapter presents a full-order dynamic output feedback controller to achieve the ideal fault-tolerant and fault detection objectives.The main contribution is:for stochastic systems the multi-objective controller design problem can be dealt with by multi-Lyaponov functional method;the proposed dynamic output feedback controller design condition is given in a form of linear matrix inequalities;in the proposed framework of simultaneous fault detection and control,a better performance is obtained for both control and detection.