Duan Guang-ren

Integrated Guidance and Control of Homing Missiles Against Ground Fixed Targets

Abstract This paper presents a scheme of integrated guidance and autopilot design for homing missiles against ground fixed targets. An integrated guidance and control model in the pitch plane is formulated and further changed into a normal form by nonlinear coordinate transformation. By adopting the sliding mode control approach, an adaptive nonlinear control law of the system is designed so that the missile can hit the target accurately with a desired impact attitude angle. The stability analysis of the closed-loop system is also conducted. The numerical simulation has confirmed the usefulness of the proposed design scheme.

On the Parametric Solution to the Second-Order Sylvester Matrix Equation EVF2−AVF−CV=BW

This paper considers the solution to a class of the second-order Sylvester matrix equation EVF2−AVF−CV=BW. Under the controllability of the matrix triple (E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrix F in a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the second-order Sylvester matrix equation, and can perform important functions in many analysis and design problems in control systems theory. As a demonstration, an illustrative example is given to show the effectiveness of the proposed solution.

Global stabilizing controller design for linear time-varying systems and its application on BTT missiles

Abstract A parametric method for the gain-scheduled controller design of a linear time-varying system is given. According to the proposed scheduling method, the performance between adjacent characteristic points is preserved by the invariant eigenvalues and the gradually varying eigenvectors. A sufficient stability criterion is given by constructing a series of Lyapunov functions based on the selected discrete characteristic points. An important contribution is that it provides a simple and feasible approach for the design of gain-scheduled controllers for linear time-varying systems, which can guarantee both the global stability and the desired closed-loop performance of the resulted system. The method is applied to the design of a BTT missile autopilot and the simulation results show that the method is superior to the traditional one in sense of either global stability or system performance.

Guaranteed cost control with constructing switching law of uncertain discrete-time switched systems

Abstract A guaranteed cost control problem for a class of linear discrete-time switched systems with norm-bounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a state feedback control law, such that, the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties under the constructed switching rule. A sufficient condition for the existence of guaranteed cost controllers and switching rules is derived based on the Lyapunov theory together with the linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMI constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.

A Parametric Lyapunov Equation Approach to the Design of Low Gain Feedback

Low gain feedback has found several applications in constrained control systems, robust control and nonlinear control. Low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero. Such feedback gains can be constructed either by an eigenstructure assignment algorithm or through the solution of a parametric algebraic Riccati equation (ARE). The eigenstructure assignment approach leads to feedback gains in the form of a matrix polynomial in the parameter, while the ARE approach requires the solution of an ARE for each value of the parameter. This paper proposes an alternative approach to low gain feedback design based on the solution of a parametric Lyapunov equation. Such an approach possesses the advantages of both the eigenstructure assignment approach and the ARE based approach. It also avoids the possible numerical stiffness in solving a parametric ARE and the structural decomposition of the open loop system that is required by the eigenstructure assignment approach.

Stochastic stabilizability and passive control for time-delay systems with Markovian jumping parameters

This paper deals with the stochastic stabilizability and passive control for a class of linear time-delay systems with Markov jumping parameters and Brownian motions. The transition of the jumping parameters in systems is governed by a finite-state Markov process. A sufficient condition on stochastic stabilizability is established based on stability theory in stochastic differential equations. In terms of a set of coupled linear matrix inequalities, stochastic passive controllers are designed to stochastically stabilize the given systems with passive performance constraints. A numerical example demonstrates the effect of the proposed design approach.

Robust guaranteed cost observer design for uncertain descriptor systems with state delays and Markovian jumping parameters

This paper investigates the robust guaranteed cost observer design for a class of linear descriptor systems with state delays and Markovian jumping parameters. The system under study involves time delays, jumping parameters and uncertainties. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless observers such that for all uncertainties the resulting augmented system is regular, impulse free, robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost observers is derived. Robust guaranteed cost filters are designed in terms of linear matrix inequalities (LMIs). A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost observer.

On some classes of control-oriented model of air-breathing hypersonic vehicles

The system modeling and controller design for air-breathing hypersonic vehicles have always been one of the most highly challenging tasks to the development of hypersonic flight technologies due to the unique characteristics of the vehicle dynamics. In this paper, we first provide an overview of three major classes of control-oriented models of air-breathing hypersonic vehicles in existing literatures. Moreover, explicitly analytical mathematical expressions and basic dynamic characteristics as well as applications in control system design of these models are presented. And then, hierarchical and internal relations of different kind of models are analyzed. Finally, recent results and future trends of control-oriented modeling for flight control design of air-breathing hypersonic vehicles are summarized.

Exponential stability of nonlinear ito differential systems with time-delay and Markovian switching

The exponential stability of nonlinear Ito differential systems with time-delay and Markovian switching is studied. According to the theory of stability of stochastic systems and Ito differential formula, by choosing proper stochastic Lyapunov function, applying generalized Ito formula, some sufficient conditions of exponential stability of such system was obtained, which improved existed results, with less conversations.

Delay-Dependent Robust Passive Control for Uncertain Discrete T-S Fuzzy Time-Delay Systems

This paper deals with the problems of robust stabilization and robust passive control for uncertain discrete Takagi-Sugeno (T-S) fuzzy time-delay systems. The parametric uncertainty is assumed to be norm bounded. Based on Lyapunov stability theory, a sufficient condition on the existence of delay-dependent robust passive controllers is derived firstly. Then, with the help of linear matrix inequality (LMI) method, delay-dependent robust passive controllers are designed such that for all admissible uncertainties and time delays, the closed-loop system is robustly stable and satisfies the given passive performance. A numerical example demonstrates the effectiveness of the proposed design method.