Mixed model identification for linear time‐invariant systems with mixed noises in frequency domain

In this paper, we present a new method for frequency domain identification of discrete linear time‐invariant systems. We take consideration of the case where the output noises are mixed or unknown. In order to deal with this problem, a new mixed model structure is used correspondingly. The augmented Lagrangian method (ALM) is combined in selection of poles for the shifted Cauchy kernels to get solutions to the optimal problem. Simulations show the proposed method can get efficient approximation to the original systems.     

On uniform controller design for linear switched systems

Traditional method to design a controller for each subsystem of switched systems will increase the complexity of the controller’s realization. Hence this paper gives sufficient conditions for designing a uniform output feedback controller for linear switched systems, and this common controller can be used for all subsystems of the switched systems. Then the output stabilization problem for a particular class of linear switched systems under this uniform output feedback controller has been studied. An illustrative example is given in order to highlight the proposed method.     

Adaptive-observer-based output-constrained tracking of a class of arbitrarily switched uncertain non-affine nonlinear systems

This paper addresses an adaptive output-feedback tracking problem of arbitrarily switched pure-feedback nonlinear systems with time-varying output constraints and unknown control directions. In this work, the tracking problem of switched non-affine nonlinear systems with output constraints is transformed into the stabilization problem of switched unconstrained affine systems. The main contribution of this paper is to present a universal formula for constructing an adaptive state-observer-based tracking controller with only two adaptive parameters by using the common Lyapunov function method. These adaptive parameters in the proposed control scheme are derived using the function approximation technique and a priori knowledge of the signs of control gain functions is not required. The theoretical analysis is presented for the Lyapunov stability and the constraint satisfaction of the resulting closed-loop system in the presence of arbitrary switchings.     

Output Feedback Model Predictive Tracking Control Using a Slope Bounded Nonlinear Model

In this paper, an output feedback model predictive tracking control method is proposed for constrained nonlinear systems, which are described by a slope bounded model. In order to solve the problem, we consider the finite horizon cost function for an off-set free tracking control of the system. For reference tracking, the steady state is calculated by solving by quadratic programming and a nonlinear estimator is designed to predict the state from output measurements. The optimized control input sequences are obtained by minimizing the upper bound of the cost function with a terminal weighting matrix. The cost monotonicity guarantees that tracking and estimation errors go to zero. The proposed control law can easily be obtained by solving a convex optimization problem satisfying several linear matrix inequalities. In order to show the effectiveness of the proposed method, a novel slope bounded nonlinear model-based predictive control method is applied to the set-point tracking problem of solid oxide fuel cell systems. Simulations are also given to demonstrate the tracking performance of the proposed method.     

On the Computation of Optimal Static Output Feedback Controllers for Discrete-Time Systems

In this article, we consider the static output feedback problem for discrete-time systems when complete set of state variables is not available. It has been reported that quasi-Newton methods have substandard performance on this problem. A structured quasi-Newton method with trust region globalization is analyzed and studied for solving this problem. Moreover, the classical Anderson-Moore method is enhanced by using the trust region mechanism to ensure global convergence instead of the line search technique. The algorithms are tested numerically on test problems of engineering applications.     

A relation between the output regulation and the observer design for nonlinear systems

Output regulation and observer design are two important problems for nonlinear systems, and there is a vast literature addressing each problem separately in the control literature. Isidori and Byrnes [1] have solved the output regulation problem for nonlinear systems with a Poisson stable exosystem, and Sundarapandian [2] has solved the exponential observer design problem for Lyapunov stable nonlinear systems. In this paper, we demonstrate that for a special class of Lyapunov stable nonlinear systems, namely neutrally stable systems, the exponential observer design problem can be solved by converting it into an output regulation problem and then solving the new problem using the output regulation techniques of Isidori and Byrnes [1]. Finally, we present the corresponding results for the discrete-time case.     

Decentralized iterative learning control for a class of large scale interconnected dynamical systems

The problem of decentralized iterative learning control for a class of large scale interconnected dynamical systems is considered. In this paper, it is assumed that the considered large scale dynamical systems are linear time-varying, and the interconnections between each subsystem are unknown. For such a class of uncertain large scale interconnected dynamical systems, a method is presented whereby a class of decentralized local iterative learning control schemes is constructed. It is also shown that under some given conditions, the constructed decentralized local iterative learning controllers can guarantee the asymptotic convergence of the local output error between the given desired local output and the actual local output of each subsystem through the iterative learning process. Finally, as a numerical example, the system coupled by two inverted pendulums is given to illustrate the application of the proposed decentralized iterative learning control schemes.     

Adaptive fuzzy backstepping control for a class of MIMO switched nonlinear systems with unknown control directions

In this article, an adaptive fuzzy output tracking control approach is proposed for a class of multiple‐input and multiple‐output uncertain switched nonlinear systems with unknown control directions and under arbitrary switchings. In the control design, fuzzy logic systems are used to identify the unknown switched nonlinear systems. A Nussbaum gain function is introduced into the control design and the unknown control direction problem is solved. Under the framework of the backstepping control design, fuzzy adaptive control and common Lyapunov function stability theory, a new adaptive fuzzy output tracking control method is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed‐loop system are bounded and the tracking error remains an adjustable neighborhood of the origin. A numerical example is provided to illustrate the effectiveness of the proposed approach. © 2015 Wiley Periodicals, Inc. Complexity 21: 155–166, 2016     

On the fractional-order extended Kalman filter and its application to chaotic cryptography in noisy environment

In this paper via a novel method of discretized continuous-time Kalman filter, the problem of synchronization and cryptography in fractional-order systems has been investigated in presence of noisy environment for process and output signals. The fractional-order Kalman filter equation, applicable for linear systems, and its extension called the extended Kalman filter, which can be used for nonlinear systems, are derived. The result is utilized for chaos synchronization with the aim of cryptography while the transmitter system is fractional-order, and both the transmitter and transmission channel are noisy. The fractional-order stochastic chaotic Chen system is then presented to apply the proposed method for chaotic signal cryptography. The results show the effectiveness of the proposed method.     

非线性奇异摄动系统的输出调节问题

本文讨论了一类非线性奇异摄动系统的输出调节器问题 .在一些合理的假设条件下 ,综合利用奇异摄动和几何方法 ,我们给出了问题可解的充分必要条件 .     

最小能量控制与Lg样条函数

本文考察了一类带有泛函约束的线性系统的最小能量控制问题与Lg样条插值函数的对应关系.得到了求解最优控制——样条函数的递推算法;并建立了最优控制问题解法Ⅱ,指出文献[1]的解法可作为它的特例.     

Fuzzy delayed output feedback synchronization for time-delayed chaotic systems

In this paper, we propose a new fuzzy delayed output feedback synchronization (FDOFS) method for time-delayed chaotic systems. Based on Lyapunov–Krasovskii theory, T–S fuzzy model, and delayed feedback control scheme, the FDOFS controller is designed and an analytic expression of the controller is shown. The proposed controller can guarantee asymptotical synchronization of both drive and response systems. The FDOFS controller can be obtained by solving the linear matrix inequality (LMI) problem. A numerical example for time-delayed Lorenz system is presented to demonstrate the validity of the proposed FDOFS method.     

Determination of the analytical parametric relationship for output spectrum of Volterra systems based on its parametric characteristics

The output frequency response function (OFRF) of Volterra systems can be described as a polynomial function of model parameters. However, the analytical determination of the OFRF is very computationally intensive, especially for higher order OFRF. To circumvent this problem, a numerical method can be adopted, provided that a series of simulation or experimental data for this polynomial function are given. In this study, it is theoretically shown that the analytical parametric relationship of OFRF up to any order can be determined accurately by using a simple Least Square method and every specific component of the output spectrum can also be determined explicitly, based on the OFRF's parametric characteristics. Practical techniques to obtain a unique and accurate solution for the Least Square method are discussed. This study provides a fundamental result for the determination of the analytical parametric relationship for this kind of system polynomial functions by using numerical methods.     

Design of dynamic controller for neutral differential systems with delay in control input

In this paper, the design problem of dynamic output feedback controller for asymptotic stabilization of a class of neutral systems have been considered. A criterion for the existence of such controllers is derived based on the linear matrix inequality (LMI) approach combined with the Lyapunov method. A parameterized characterization of the controllers is given in terms of the feasible solutions to the LMIs, which can be solved by various convex optimization algorithms. A numerical example is given to illustrate the proposed design method.     

Positive real control for 2-D discrete delayed systems via output feedback controllers

This paper considers the problem of positive real control for two-dimensional (2-D) discrete delayed systems in the Fornasini–Marchesini second local state-space model. Attention is focused on the design of dynamic output feedback controllers, which guarantee that the closed-loop system is asymptotically stable and the closed-loop transfer function is extended strictly positive real. We first present a sufficient condition for extended strictly positive realness of 2-D discrete delayed systems. Based on this, a sufficient condition for the solvability of the positive real control problem is obtained in terms of a linear matrix inequality (LMI). When the LMI is feasible, an explicit parametrization of a desired output feedback controller is presented. Finally, we provide a numerical example to demonstrate the application of the proposed method.     

Finding multiple roots of a box-constrained system of nonlinear equations with a biased random-key genetic algorithm

Several numerical methods for solving nonlinear systems of equations assume that derivative information is available. Furthermore, these approaches usually do not consider the problem of finding all solutions to a nonlinear system. Rather, most methods output a single solution. In this paper, we address the problem of finding all roots of a system of equations. Our method makes use of a biased random-key genetic algorithm (BRKGA). Given a nonlinear system, we construct a corresponding optimization problem, which we solve multiple times, making use of a BRKGA, with areas of repulsion around roots that have already been found. The heuristic makes no use of derivative information. We illustrate the approach on seven nonlinear equations systems with multiple roots from the literature.     

New Algorithm for Computing LQ Suboptimal Output Feedback Gains of Decentralized Control Systems

In this paper, the problem of computing the suboptimal output feedback gains of decentralized control systems is investigated. First, the problem is formulated. Then, the gradient matrices based on the index function are derived and a new algorithm is established based on some nice properties. This algorithm shows that a suboptimal gain can be computed by solving several ordinary differential equations (ODEs). In order to find an initial condition for the ODEs, an algorithm for finding a stabilizing output feedback gain is exploited, and the convergence of this algorithm is discussed. Finally, an example is given to illustrate the proposed algorithm.     

Dynamic output guaranteed cost controller for neutral systems with input delay

In this paper, we consider a design problem of dynamic output guaranteed cost controller (GCC) of a class of neutral systems with input delay. A quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov second method, two stability criteria for existence of the controller are derived in terms of matrix inequalities. The solutions of the matrix inequalities can be easily obtained using existing efficient convex optimization techniques. A numerical example is given to illustrate the proposed design method.     

On Dynamic Output Feedback Guaranteed Cost Control of Uncertain Discrete-Delay Systems: LMI Optimization Approach

In this paper, we consider a design problem of dynamic output feedback controller for guaranteed cost stabilization of discrete-delay systems with norm-bounded time-varying parameter uncertainties. A linear-quadratic cost function is considered as a performance measure for the closed-loop system. Based on the Lyapunov second method, several stability criteria for the existence of the controller are derived in terms of linear matrix inequalities (LMIs). The solutions of the LMIs can be obtained easily using existing efficient convex optimization techniques. A numerical example is given to illustrate the proposed method.     

线性系统的输出反馈特征结构配置——具有不可控不可观模态的情形

本文考虑具有不可控不可观模态的线性系统的输出反馈特征结构配置问题。根据文中给出的矩阵方程AV＋BW＝VF的一种显式参数解，得到了线性系统的输出反馈特征结构配置的一种参数化方法，本文没有对系统附加能控能观条件，在[AB]能控的条件下，本文得到的矩阵方程的解是文[5]中定理2的结果，在[AB]能控且[AC]能观的条件下，本文得到的输出反馈特征结构配置方法是文[6]在系统为定常时算法Ⅱ的结果。