Switching control system based on robust model reference adaptive control

For conventional adaptive control, time-varying parametric uncertainty and unmodeled dynamics are ticklish problems, which will lead to undesirable performance or even instability and nonrobust behavior, respectively. In this study, a class of discrete-time switched systems with unmodeled dynamics is taken into consideration. Moreover, nonlinear systems are here supposed to be approximated with the class of switched systems considered in this paper, and thereby switching control design is investigated for both switched systems and nonlinear systems to assure stability and performance. For robustness against unmodeled dynamics and uncertainty, robust model reference adaptive control (RMRAC) law is developed as the basis of controller design for each individual subsystem in the switched systems or nonlinear systems. Meanwhile, two different switching laws are presented for switched systems and nonlinear systems, respectively. Thereby, the authors incorporate the corresponding switching law into the RMRAC law to construct two schemes of switching control respectively for the two kinds of controlled systems. Both closed-loop analyses and simulation examples are provided to illustrate the validity of the two proposed switching control schemes. Furthermore, as to the proposed scheme for nonlinear systems, its potential for practical application is demonstrated through simulations of longitudinal control for F-16 aircraft.     

A criterion for testing whether a difference ideal is prime

This paper presents a criterion for testing the irreducibility of a polynomial over an algebraic extension field. Using this criterion and the characteristic set method, the authors give a criterion for testing whether certain difference ascending chains are strong irreducible, and as a consequence, whether the saturation ideals of these ascending chains are prime ideals.     

Stabilization of switched linear systems with constrained inputs

The stabilization of switched linear systems with constrained inputs(SLSCI) is considered. The authors design admissible linear state feedbacks and the switching rule which has a minimal dwell time(MDT) to stabilized the system.First,for each subsystem with constrained inputs,a stabilizing linear state feedback and an invariant set of the closed-loop system are simultaneously constructed, such that the input constraints are satisfied if and only if the closed-loop system’s states lie inside this set.Then,by constructing a quadratic Lyapunov function for each closed-loop subsystem,an MDT is deduced and an MDT-based switching strategy is presented to ensure the stability of the switched system.     

一类非线性切换系统基于观测器的稳定性分析

针对在实际工程系统中状态不可观测的困难,考虑了同时包含李普希兹非线性干扰项和不确定项的切换系统的稳定性问题.在一定的假设条件下,讨论了系统的滑模观测器.在不确定项满足匹配条件的情况下,基于滑模观测器的设计,利用多李亚普诺夫函数方法得到了保证误差切换系统渐近稳定的充分条件,所设计的滑模观测器成为切换系统的渐近稳定的观测器.这为非线性切换系统利用观测器进行稳定性分析提供了一个新视角.最后通过仿真算例验证了所提方案的正确有效性.     

Robust H∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions

The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.     

Nonlinear Sampled-Data Systems with a Generalized Hold Polynomial-Function for Fast Sampling Rates

It is well-known that such non-conventional digital control schemes, such as generalized sampled-data hold functions, have clear advantages over the conventional single-rate digital control systems. However, they have theoretical negative aspects that deviation of the input can lead to intersample oscillations or intersample ripples. This paper investigates the zero dynamics of sampleddata models, as the sampling period tends to zero, composed of a new generalized hold polynomial function, a nonlinear continuous-time plant and a sampler in cascade. For a new design of generalized hold circuit, the authors give the approximate expression of the resulting sampled-data systems as power series with respect to a sampling period up to the some order term on the basis of the normal form representation for the nonlinear continuous-time systems, and remarkable improvements in the stability properties of discrete system zero dynamics may be achieved by using proper adjustment. Of particular interest are the stability conditions of sampling zero dynamics in the case of a new hold proposed. Also, an insightful interpretation of the obtained sampled-data models can be made in terms of minimal intersample ripple by design, where the ordinary multirate sampled systems have a poor intersample behavior. It has shown that the intersample behavior arising from the multirate input polynomial function can be localised by appropriately selecting the design parameters based on the stability condition of the sampling zero dynamics. The results presented here generalize the well-known notion of sampling zero dynamics from the linear case to nonlinear systems.     

On the stability analysis of switched nonlinear systems with time varying delay under arbitrary switching

This paper addresses the stability problem for a class of switched nonlinear time varying delay systems modeled by delay differential equations. By transforming the system representation under the arrow form and using a new constructed Lyapunov function, the aggregation techniques, the Borne-Gentina practical stability criterion associated with the properties, new delay-independent stability conditions of the considered systems are established. Compared with the existing results in this area, the obtained result is explicit, simple to use and allows us to avoid the problem of searching a common Lyapunov function. Finally, an example is provided, with numerical simulations, to demonstrate the effectiveness of the proposed method.     

关于一类线性时不变切换系统的脉冲控制

针对一类线性时不变脉冲切换系统,利用Lyapunov函数导出了一种有效的控制方法.首先,建立了这类系统在任意切换率下稳定与渐近稳定的充分条件;然后,给出了这类系统在设定的切换率下指数稳定的判别准则;最后,给出了一个数值例子及仿真来阐明结论的正确性.     

Exponential stability of linear distributed parameter switched systems with time-delay

In this paper, the exponential stability analysis for ODE switched systems with time delay is extended to distributed parameter switched systems (DPSS) in Hilbert space. For a given family of exponential stable subsystems, this paper focuses on finding conditions to guarantee the overall DPSS’ exponential stability. Based on semigroup theory, by applying piecewise Lyapunov-Krasovskii functionals method incorporated average dwell time approach, sufficient conditions for exponential stability are derived. These conditions are given in the form of linear operator inequalities (LOIs) where the decision variables are operators in Hilbert space, and the stability properties depend on switching rule. Being applied to heat switched propagation equations, these LOIs are reduced to standard Linear Matrix Inequalities (LMIs). Finally, a numerical example is given to illustrate the effectiveness of the proposed result.     

线性切换系统的周期性平稳性分析

研究了线性切换系统的周期性和稳定性规律,给出线性切换系统周期性的充要条件及平稳性的充分性判据．为基于混合动态系统Ｐｅｔｒｉ网模型的混合控制器参数验证和设计提供了依据．     

Generating exact nonlinear ranking functions by symbolic-numeric hybrid method

This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments. The authors first transform the problem into a parameterized polynomial optimization problem, and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming (SDP). A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function, and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs. At last, the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.     

Input-to-State Stability of Switched Nonlinear Delay Systems Based on a Novel Lyapunov-Krasovskii Functional Method

In this paper, the input-to-state stability (ISS) analysis is addressed for switched nonlinear delay systems. By introducing a novel Lyapunov-Krasovskii functional with indefinite derivative and the merging switching signal techniques, some new criteria are established for switched nonlinear delay systems under asynchronous switching, which extends the existing results to the nonlinear systems with switching rules and delays. The ISS problem is also considered under synchronous switching for switched nonlinear systems by employing the similar techniques. Finally, a nonlinear delay model is provided to show the effectiveness of the proposed results.     

Robust H∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions

The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.     

Robust Stabilization of Non-minimum Phase Switched Nonlinear Systems with Uncertainty

This paper investigates the problem of robust stabilization of a class of switched nonlinear system with uncertain dynamics where each subsystem represents a non-minimum phase. The authors first construct a stabilizing sliding mode controller for each subsystem to stabilize individually its own unstable internal dynamics. Then, a switching strategy is introduced to select the most appropriate diffeomorphism through an infinity of diffeomorphisms. Sufficient conditions are specifically given for the exponential stability and the exponential upper bound of the trajectory of the switched subsystem,which guarantees the global asymptotical stability of the resulting switched system. Obviously, the proposed control approach can improvemore the transient state, compared to a feedback linearization based on only one diffeomorphism. Simulation studies illustrate the effectiveness of the suggested approach.     

不确定切换系统基于切换时间的动态输出反馈鲁棒H∞控制

借助平均驻留时间方法，讨论了一类不确定切换系统的动态输出反馈鲁棒H_∞控制问题。利用多Lyapunov函数法，以线性矩阵不等式的形式给出了使得该类闭环系统的动态输出反馈控制器存在的充分条件。同时,构建了基于切换驻留时间的切换律。在综合考虑最优化干扰抑制性能指标γ和求解的简便性后，给出了动态输出反馈控制器的设计算法。进一步的，将所得结果推广到任意切换律的情况。     

Efficiently counting affine roots of mixed trigonometric polynomial systems

Estimating the number of isolated roots of a polynomial system is not only a fundamental study theme in algebraic geometry but also an important subproblem of homotopy methods for solving polynomial systems. For the mixed trigonometric polynomial systems, which are more general than polynomial systems and rather frequently occur in many applications, the classical B′ezout number and the multihomogeneous B′ezout number are the best known upper bounds on the number of isolated roots. However, for the deficient mixed trigonometric polynomial systems, these two upper bounds are far greater than the actual number of isolated roots. The BKK bound is known as the most accurate upper bound on the number of isolated roots of a polynomial system. However, the extension of the definition of the BKK bound allowing it to treat mixed trigonometric polynomial systems is very difficult due to the existence of sine and cosine functions. In this paper, two new upper bounds on the number of isolated roots of a mixed trigonometric polynomial system are defined and the corresponding efficient algorithms for calculating them are presented. Numerical tests are also given to show the accuracy of these two definitions, and numerically prove they can provide tighter upper bounds on the number of isolated roots of a mixed trigonometric polynomial system than the existing upper bounds, and also the authors compare the computational time for calculating these two upper bounds.     

Robust exponential stability of switched interval interconnected systems with unbounded delay

In this paper, a class of switched interval interconnected systems with unbounded delay were investigated. On the assumption that the interconnected functions of the systems satisfied the global Lipschitz condition, by using vector Lyapunov methods and M-matrix theory, the integrodifferential inequalities with unbounded delay were constructed. By the stability analysis of the integrodifferential inequalities, the sufficient conditions to ensure the robust exponential stability of the interval interconnected systems were obtained. By using average dwell time approach, conditions for guaranteeing the robust exponential stability of the switched delay interval interconnected systems were derived. Finally, two numerical examples were given to illustrate the correction and effectiveness of the proposed theory.     

一类介质访问约束下的网络控制系统设计

针对多输入多输出的网络控制系统,传感器和执行器为时间驱动,由于网络资源的有限性,在每个传输周期内,系统往往只有部分传感器和执行器得到网络介质访问权,与远程控制器进行数据传输,这称为网络控制系统的介质访问约束性,它极大地影响到系统的稳定性和控制性能,成为网络控制中亟待解决的问题。针对这一问题将网络控制系统建模为输出矩阵和输入矩阵随介质约束改变的切换系统,并利用切换系统分析方法和稳定性理论,设计了切换观测器和基于观测器的状态反馈控制器,分析了周期调度下该网络控制闭环系统的稳定性,最后通过仿真验证了这种方法的有效性。     

Stability conditions of complex switched systems with unstable subsystems

New stability conditions for complex switched systems are presented. We propose the concepts of attractive region and semi-attractive region, which are used as a tool for analyzing the stability of switched systems with unstable subsystems. Based on attractive region the sufficient conditions with less conservative for stability of switched systems have been established, there is no limitation for all members of the system set to be stable. Since our results have considered and utilized the decreasing span of oscillating solutions of the switched systems, they are more practical than the other presented ones of stability of switched systems, and need not resort to multiple Lyapunov functions.     

Robust Finite-Time Stability and Stabilization of a Class of Fractional-Order Switched Nonlinear Systems

This paper deals with the problem of finite-time boundedness and finite-time stabilization boundedness of fractional-order switched nonlinear systems with exogenous inputs. By constructing a simple Lyapunov-like function and using some properties of Caputo derivative, the authors obtain some new sufficient conditions for the problem via linear matrix inequalities, which can be efficiently solved by using existing convex algorithms. A constructive geometric is used to design switching laws amongst the subsystems. The obtained results are more general and useful than some existing works, and cover them as special cases, in which only linear fractional-order systems were presented. Numerical examples are provided to demonstrate the effectiveness of the proposed results.