Chih Chiang Chen

Study of Nonsingular Fast Terminal Sliding-Mode Fault-Tolerant Control

This paper studies fault-tolerant control (FTC) designs based on nonsingular terminal sliding-mode control and nonsingular fast terminal sliding-mode control (NFTSMC). The proposed active FTC laws are shown to be able to achieve fault-tolerant objectives and maintain stabilization performance even when some of the actuators fail to operate. In comparison to existing sliding-mode control (SMC) fault-tolerant designs, the proposed schemes not only can retain the advantages of traditional SMC, including fast response, easy implementation, and robustness to disturbances/uncertainties, but also make the system states reach the control objective point in a finite amount of time. Moreover, they also resolve the potential singularity phenomena in traditional terminal and faster terminal SMC designs; meanwhile, the proposed NFTSMC fault-tolerant scheme also possesses the benefit of faster state convergence speed of NFTSMC. Finally, the proposed analytical results are also applied to the attitude control of a spacecraft. Simulation results demonstrate the benefits of the proposed schemes.

Nonlinear Reliable Control With Application to a Vehicle Antilock Brake System

This paper explores the design of active reliable control systems for a class of uncertain nonlinear affine systems using an integral-type sliding mode control (ISMC) scheme. The presented scheme not only maintains the main advantages of the ISMC design, including robustness, rapid response and easy implementation, but it can also tolerate some actuator faults when fault detection and diagnosis information is available. In this study, the uncertainties and/or disturbances are not required to be of the matched type; however, when they are matched, the state trajectories of the nominal healthy subsystem and the uncertain faulty system are identical. As a result, engineers can predictively address the matched uncertain faulty system performance in light of the performance of the nominal healthy subsystem. The analytic results are also applied to the study of a vehicle brake reliable control system. Simulation results demonstrate the benefits of the proposed scheme.

Study of Nonlinear Integral Sliding Mode Fault-Tolerant Control

This paper studies an active fault-tolerant control (FTC) design based on an integral sliding mode control (ISMC) strategy for a class of uncertain nonlinear systems. It is shown that under the proposed scheme, the closed-loop system can tolerate certain allowable actuator faults whenever fault detection and diagnosis information is available, and the scheme also retains the main advantages of the ISMC technique. These advantages include robustness, rapid response, and ease of implementation. Moreover, the state response of the resulting closed-loop system under normal operation and different fault conditions is predictable from the response of a preselected fault-free certain system, which can be determined by the designer. Consequently, the engineer has the flexibility in selecting an (optimal) control law for the preselected system according to the system requirements. The analytical results obtained are also applied to the attitude control of a spacecraft. The simulation results clearly demonstrate the benefits of the proposed scheme.

Robust Guidance Law via Integral-Sliding-Mode Scheme

B ECAUSE of the growing demand to minimize the threat of missile attacks, the study of guidance laws for antimissile systems has attracted considerable attention [1–7]. Among those existing studies, the proportional-navigation (PN) law and its generalization (e.g., ideal PN [1] and realistic true PN [2]) have been widely used for intercepting nonmaneuvering or low-maneuvering target due to the advantages of simplicity and easy implementation. Specifically, the PN law has been shown to be an optimal design in minimizing miss distance (MD) for the nonmaneuvering target [3]. However, the performance of PN and its generalization will become worse, and lack of robustness as the target’s maneuverability increases [4]. To overcome such a disadvantage, various control techniques have been recently employed to construct suitable guidance laws for the missile interception, such as the slidingmode-control (SMC)-based design [5–7], the optimal-controlbased scheme [3], and the state-dependent Riccati-equation-based guidance laws [8]. The SMC approach is known to have the advantages of rapid response, easy implementation, and strong robustness [5–7,9,10]. However, the conventional SMC scheme inevitably has to undergo a period of reaching phase, which might result in an undesirable high gain effect and be sensitive to model uncertainties and/or external disturbances (MUED) [10,11]. Instead, the integral SMC (ISMC) design was recently shown to be more effective in improving system performance [10,11]. One is that the maximum control magnitude required for the ISMC is usually smaller than that for the SMC because the maximum control magnitude of a typical SMC design usually occurs at the beginning of the reaching phase, but there is no reaching phase for the ISMC scheme. In addition, the effect of mismatched uncertainty will not be amplified in the sense of Euclidean norm by properly setting of the sliding-manifold parameters in the ISMC design. Moreover, the state responses of the nominal system and the matched-type uncertain system are identical via the ISMCapproach if the system states remain lying on the sliding manifold. In fact, the last two properties will be very helpful to provide the engineer with extra degree of freedom in the design of a suitable controller for the nominal system, and hence, creating a desired state trajectory for the uncertain system to follow. Thus, the performance of the uncertain system will be predictable. Such an advantage is generally not provided by using other nonlinear control techniques. Although an existing result [6] has proposed to employ the SMC scheme for missile-guidance control, however, that design inescapably experiences a reaching-phase period, which will suffer the aforementioned drawbacks, and the state performance of the uncertain system is not predictable from that of the nominal system. Motivated by the aforementioned benefits, this study will investigate the guidance-law design via the ISMC scheme.

Smooth output feedback stabilization of a class of planar switched nonlinear systems under arbitrary switchings

Abstract Smooth output feedback stabilization problem for a family of planar switched nonlinear systems is addressed. First, based on the adding a power integrator technique, the tasks of finding a common Lyapunov function and designing state feedback stabilizing control laws are accomplished simultaneously. Then, combining the state feedback control laws and the reduced-order nonlinear observers, output feedback control laws are designed to globally stabilize the switched nonlinear system under arbitrary switchings, whose subsystems may have uncontrollable/unobservable Jacobian linearizations.

Global Stabilization for a Class of Genuinely Nonlinear Systems With a Time-Varying Power: An Interval Homogeneous Domination Approach

This paper addresses the problem of global state feedback stabilization for a class of genuinely nonlinear systems with a time-varying power. By revamping the so-called adding a power integrator technique and the homogeneous domination approach, a new design method called interval homogeneous domination approach is proposed to delicately design a state feedback control law that renders the nonlinear systems globally asymptotically stable. The novelty of the proposed scheme owes to the systematic fashion that provides a distinct perspective to solve the stabilization problem for the nonlinear systems with a time-varying power.

Global Output Feedback Stabilization of a Class of Nonlinear Systems With Unknown Measurement Sensitivity

This note investigates the problem of global output feedback stabilization for a class of nonlinear systems with unknown measurement sensitivity. A new design method, namely dual-domination approach, is proposed to explicitly construct a state observer as well as an output feedback control law, which globally asymptotically stabilizes the nonlinear systems. The novelty of this note owes to a distinct perspective in coping with unknown measurement sensitivity which has previously been a hurdle to solve the global output feedback stabilization problem of the nonlinear systems.

On Existence of Stabilizing Switching Laws within a Class of Unstable Linear Systems

The equivalence of two conditions, condition (3) and condition (4) stated in Problem Statement section, regarding the existence of stabilizing switching laws between two unstable linear systems first appeared in (Feron 1996). Although Feron never published this result, it has been referenced in almost every survey on switched systems; see, for example, (Liberzon and Morse 1999). This paper proposes another way to prove the equivalence of two conditions regarding the existence of stabilizing switching laws between two unstable linear systems. One is effective for theoretical derivation, while the other is implementable, and a class of stabilizing switching laws have been explicitly constructed by Wicks et al. (1994). With the help of the equivalent relation, a condition for the existence of controllers and stabilizing switching laws between two unstabilizable linear control systems is then proposed. Then, the study is further extended to the issue concerning the construction of quadratically stabilizing switching laws among unstable linear systems and unstabilizable linear control systems. The obtained results are employed to study the existence of control laws and quadratically stabilizing switching laws within a class of unstabilizable linear control systems. The numerical examples are illustrated and simulated to show the feasibility and effectiveness of the proposed methods.

Global Output Feedback Stabilization for a Class of Nonlinear Cascade Systems

This paper focuses on the problem of global output feedback stabilization for a class of nonlinear cascade systems with time-varying output function. By using double-domination approach, an output feedback controller is developed to guarantee the global asymptotic stability of closed-loop system. The novel control strategy successfully constructs a unified Lyapunov function, which is suitable for both upper-triangular and lower-triangular systems. Finally, two numerical examples are provided to illustrate the effectiveness of a control strategy.

A new approach to stabilisation of a class of nonlinear systems with an output constraint

ABSTRACT This paper investigates the problem of state-feedback stabilisation for a class of high-order nonlinear systems with an output constraint. A novel tangent-type barrier Lyapunov function is first developed to cope with the output constraint. Then, by introducing the sign function and incorporating the developed tangent-type barrier Lyapunov function, the celebrated adding a power integrator technique is revamped to systematically design a continuous state feedback stabilising controller that prevents violation of the output constraint during operation. The novelty of this paper is the development of an unified design procedure, which can tackle the stabilisation task of the systems with/without the output constraint simultaneously.