Yupeng Qiao

STABILITY OF SWITCHED POLYNOMIAL SYSTEMS

This paper investigates the stability of (switched) polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a (switched) polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some su±cient conditions for the global stability of polynomial systems.

Attitude control of missile via Fliess expansion and model predictive control

This paper considers the attitude control of missile. We convert the problem into an output tracking one of nonlinear systems via control with finite admissible values. First, the Fliess functional expansion is used to describe the outputs. Then under piece-wise admissible value control and the quadratic criteria, the optimal control is obtained using model predictive control. The method developed is used to the attitude control of missile. Simulation results show the effectiveness of the proposed method.

Linearization of switched non-linear systems

The problem of static state feedback linearization of switched non-linear systems is investigated. First, we consider the regular state feedback linearization. In this case, the single-input switched system is considered first. A necessary and sufficient condition is provided, which contains an uncertain single variable function. Then the result is extended to a multiple input case. Secondly, the problem of non-regular static state feedback linearization is considered. Using semi-tensor product, some easily verifiable sufficient conditions are obtained. Then some examples are presented to illustrate the linearization process.The problem of static state feedback linearization of switched non-linear systems is investigated. First, we consider the regular state feedback linearization. In this case, the single-input switched system is considered first. A necessary and sufficient condition is provided, which contains an uncertain single variable function. Then the result is extended to a multiple input case. Secondly, the problem of non-regular static state feedback linearization is considered. Using semi-tensor product, some easily verifiable sufficient conditions are obtained. Then some examples are presented to illustrate the linearization process.

Robust formation control of a class of multi-agent systems by output regulation approach

In this paper, we study the robust formation control problem of a class of multi-agent systems based on the generalized internal model principle. We show that this problem finally boils down to a robust stabilization problem of a nonlinear system, the solution of which can be solved by using the existing robust stabilization technique. The efficiency of the proposed design method is verified by one typical formation control problem of multi-agent systems.

FINITE FLIESS FUNCTIONAL EXPANSION AND ITS APPLICATION TO FLIGHT CONTROL OF MISSILES

This paper addresses output tracking of nonlinear systems via state feedback and Fliess expansion. Under the full row rank assumption on the “decoupling matrix,� it is shown that a suitable state feedback can be designed such that the Fliess expansion of the closed-loop system contains only finite terms. A significant advantage of this form is that it avoids the truncation error in numerical calculation of Fliess expansions. As an application, this expansion is invoked to solve the problem of attitude control of missiles. Piecewise constant control is designed on each sampling interval to realize tracking optimization. Numerical simulations demonstrate the efficacy of the proposed control scheme.

Attitude control of missiles via finite-terms Fliess expansion

This paper investigates the attitude control of missiles. We use the decomposed Fliess functional expansion of input-output decomposable systems to describe the outputs. Then under piece-wise constant admissible value controls, the optimal control on finite time durations can be obtained. The method tremendously reduces the complexity of computation and makes the online control design available. The effectiveness of the proposed method is shown by numerical simulations.

Design of control invariant sets of planar systems

Control invariant sets play a key role in model predictive control. Using Lyapunov function, a technique is proposed to design control invariant sets of planar systems in a precise form. First, it is designed for a linear system in Brunovsky canonical form. Then, the result is extended to general linear systems. Finally, the nonlinear control systems are considered, and some sufficient conditions and design techniques are also obtained. Numerical examples are presented to illustrate the proposed design methods.