Yew-Wen Liang

Reliable control of nonlinear systems

In this paper, we extend Veillettes results (1995) to the study of reliable linear-quadratic regulator problem for nonlinear systems. This is achieved by employing the Hamilton-Jacobi inequality in the nonlinear case instead of algebraic Riccati equation in the linear one. The proposed state-feedback controllers are shown to be able to tolerate the outage of actuators within a prespecified subset of actuators. Both the gain margins of guaranteeing system stability and retaining a performance bound are estimated.

Study of VSC Reliable Designs With Application to Spacecraft Attitude Stabilization

This brief investigates variable structure reliable control (VSRC) issues of a set of second-order nonlinear systems and their application to spacecraft attitude stabilization. Both passive and active reliable designs are presented. To achieve the active task, an observer to identify faults as they occur in the spacecraft actuators is also presented. These VSRC laws do not require the solution of a Hamilton-Jacobi (HJ) equation, which is essential in the optimal approaches such as linear quadratic Riccati (LQR) and Hinfin reliable designs. As a matter of fact, this approach can relax the computational burden for solving the HJ equation. Simulation results regarding spacecraft attitude stabilization with comparisons among the VSRCs and the LQR reliable designs are also given. It is shown from these simulations that the active VSRC is the most flexible, robust and effective method because it does not need to prespecify susceptible actuators and because it allows more space for the control parameter adjustment

A Study of T–S Model-Based SMC Scheme With Application to Robot Control

In light of the remarkable benefits and numerous applications of the Takagi-Sugeno (T-S) fuzzy system modeling method and the sliding mode control (SMC) technique, this paper aims to study the design of robust controllers for a set of second-order systems using a combination of these two approaches. The combined scheme is shown to have the merits of both approaches. It alleviates not only the online computational burden by using the T-S fuzzy system model to approximate the original nonlinear one (since most of the system parameters of the T-S model can be computed offline) but also preserves the advantages of rapid response and robustness characteristic of the classic SMC schemes. Moreover, the combined scheme does not need to online compute any nonlinear term of the original dynamics, and the increase in the number of fuzzy rules does not create extra online computational burdens for the scheme. The proposed analytical results are also applied to the control of a two-link robot manipulator and compared with the results using classic SMC design. Simulation results demonstrate the benefits of the proposed scheme.

Reliable Control of Nonlinear Systems via Variable Structure Scheme

This study proposes a class of variable structure stabilizing laws which make the closed-loop system be capable of tolerating the abnormal operation of actuators within a pre-specified subset of actuators. The ranges of acceptable change in control gain magnitude that preserves systems stability are estimated for the whole set of actuators. These ranges are shown to be able to be made larger than those obtained by linear quadratic regulator (LQR) reliable design (Veillette, 1995, and Liang, 2000) by the choice of control parameters. Besides, this approach does not need the solution of Hamilton-Jacobi (HJ) equation or inequality, which is essential for optimal approaches such as LQR and H infin reliable designs. As a matter of fact, this approach can also relax the computational burden for solving the HJ equation or inequality

T–S Model-Based SMC Reliable Design for a Class of Nonlinear Control Systems

This paper studies the robust reliable control issues based on the Takagi-Sugeno (T-S) fuzzy system modeling method and the sliding-mode control (SMC) technique. The combined scheme is shown to have the merits of both approaches. It not only alleviates the online computational burden by using the T-S fuzzy model to implement the original nonlinear system (since most of the system parameters of the T-S model can be offline computed) but also preserves the advantages of the SMC schemes, including rapid response and robustness. Moreover, the combined scheme does not require online computation of any nonlinear term of the original dynamics, and the increase in the partition number of the region of premise variables does not create extra online computational burdens for the scheme. Under the design, the control mission can continue safely without prompt external support, even when some of the actuators fail to operate. Meanwhile, both the active and the passive reliable designs are presented. The proposed analytical results are also applied to the attitude control of a spacecraft. Simulation results demonstrate the benefits of the proposed scheme.

Nonlinear Control for Missile Terminal Guidance

Variable Structure Control (VSC) technique is applied to the design of robust homing missile guidance laws. In the design procedure, the target’s maneuver is assumed to be unpredictable and is considered as disturbances. Guidance laws are then proposed to achieve the interception performance for both cases of longitude-axis control being available and unavailable. The proposed guidance laws are continuous which alleviate chattering drawback by classic VSC design. Results are obtained and compared with those by realistic true proportional navigation design to illustrate the benefits of the proposed design. @S0022-0434~00!00604-3#

Reliable control of nonlinear systems via variable structure scheme

This study proposes a class of reliable Variable Structure Control (VSC) laws, which are shown to be able to tolerate the outage of actuators within a prespecified subset of actuators. The gain margins of guaranteeing system stability are estimated, which depend on control parameters and are larger than those obtained by LQR reliable design. In addition, this approach does-not need to solve the Hamilton-Jacobi equation or inequality, which is known difficult to solve and is an essential part in the reliable LQR and H/sub /spl infin// designs. As a matter of fact, this approach can also relax the computational load for solving the Hamilton-Jacobi inequality.

Analysis of SDC matrices for successfully implementing the SDRE scheme

Abstract The state-dependent Riccati equation (SDRE) approach for stabilization of nonlinear affine systems was recently reported to be effective in many practical applications; however, there is no guideline on the construction of state-dependent coefficient (SDC) matrix when the SDRE solvability condition is violated, which may result in the SDRE scheme being terminated. In this study, we present several easy checking conditions so that the SDRE scheme can be successfully implemented. Additionally, when the presented checking conditions are satisfied, the sets of all feasible SDC matrices and their structures are explicitly depicted for the planar system.

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.

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.