Approximate Controllability for Degenerate Heat Equation with Bilinear Control

This paper investigates the nonnegative approximate controllability for the one-dimensional degenerate heat equation governed by bilinear control.Both non-controllability and approximate controllability are studied for the system.If the control is restricted to act on a fixed domain,it is not controllable.If the control is allowed to mobile,it is approximately controllable.

Non-fragile guaranteed cost control of discrete-time fuzzy bilinear system

This paper focuses on the problem of non-fragile guaranteed cost control for a class of T-S discrete-time fuzzy bilinear systems（DFBS）.Based on the parallel distributed compensation（PDC） approach,the sufficient conditions are derived such that the closed-loop system is asymptotically stable and the cost function value is no more than a certain upper bound in the presence of the additive controller gain perturbations.The non-fragile guaranteed cost controller can be obtained by solving a set of bilinear matrix inequalities（BMIs）.The Van de Vusse model is utilized to demonstrate the validity and effectiveness of the proposed approach.

BILINEAR PREDICTIVE CONTROL USING HIERARCHICAL OPTIMIZATION

Based on the Decomposition-Coordination principle, a hierarchical optimization algorithm is put forward for predictive control of bilinear systems. Time consuming is an usual problem of hierarchieal optimization algorithms, this paper tries to improve the online computational efficiency by taking the advantage of the characteristics of bilinear system itself. The effectiveness is shown by the simulation results.

Design of switched controllers for discrete singular bilinear systems

In this paper, switched controllers are designed for a class of nonlinear discrete singular systems and a class of discrete singular bilinear systems. An invariant principle is presented for such switched nonlinear singular systems. The invariant principle and the switched controllers are used to globally stabilize a class of singular bilinear systems that are not open-loop stable.

Static output feedback control for discrete-time fuzzy bilinear system

The problem of designing fuzzy static output feedback controller for T-S discrete-time fuzzy bilinear system （DFBS） is presented. Based on parallel distribution compensation method, some sufficient conditions are derived to guarantee the stability of the overall fuzzy system. The stabilization conditions are further formulated into linear matrix inequality （LMI） so that the desired controller can be easily obtained by using the Matlab LMI toolbox. In comparison with the existing results, the drawbacks, such as coordinate transformation, same output matrices, have been elim- inated. Finally, a simulation example shows that the approach is effective.

Feedback Linearization Optimal Control Approach for Bilinear Systems in CSTR Chemical Reactor

This paper considers the optimal control problem for the bilinear system based on state feedback. Based on the concept of relative order of the output with respect to the input, first we change a bilinear system to a pseudo linear system model through the coordinate transformation. Then based on the theory of linear quadratic optimal control, the optimal controller is designed by solving the Riccati equation and introducing state feedback with state prediction. At last, the simulation results in CSTR Chemical reactor show the effectiveness of the method.

Optimal Control for Time-Delay Bilinear Systems with Sinusoidal Disturbances

This paper considers the optimal control problem for time-delay bilinear systems affected by sinusoidal disturbances with known frequency and measurable amplitude and phase. Firstly, using the differential homeomorphism, a time-delay bilinear system affected by sinusoidal disturbances is changed to a time-delay pseudo linear system through the coordinate transformation. Then the system with time-delay in control variable is transformed to a linear controllable system without delay using model transformation. At last based on the theory of linear quadratic optimal control, an optimal control law which is used to eliminate the influence of the disturbances is derived from a Riccati equation and Matrix equations. The simulation results show the effectiveness of the method.

H_∞ Control of Bio-dissimilation Process of Glycerol to 1,3-Propanediol

A robust controller is designed by using the bilinear transformation and H∞ mixed sensitivity method for bio-dissimilation process of glycerol to 1,3-propanediol. Under the controller the system works near an optimal steady-state for the volumetric productivity of 1,3-propanediol attaining its maximization. The design procedure is carried out by tuning the transformation parameter and DC gain of the performance weighted function, which is an iterative and optimal search process. Simulation results are presented which show that the designed robust controller not only ensures the robust stability of the system in face of the parametric variations in the model, but also makes the system have a favourable robust tracking performance. The validity of the proposed H∞ controller has been tested.

BMI Approach to the Interconnected Stability and Cooperative Control of Linear Systems

这份报纸学习互连的稳定性和大规模线性系统的合作控制。用双线性的矩阵不平等(BMI ) 的技术，必要、足够的条件为互连的稳定性和二个分系统的合作稳定被给。就算分系统不是稳定的，系统能合作地被稳定，这被显示出就算分系统不是稳定的。我们假定分系统的稳定性不是必要的。而且，设计的问题相连，合作控制器用 BMI 限制被变换成优化问题。解决这些问题，某些最佳的交替的算法被建议，并且为算法的集中的证明被介绍。最后，几个例子被给说明优化结果。

Robust H_∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H_∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality（BMI）,which ensures a prescribed stochastic robust H_∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.

Implementing Broadcast Encryption Scheme Using Bilinear Map and Group Characteristic

This paper introduced a novel method for implementing broadcast encryption. Our scheme takes advantages of bilinear map and group characteristic, and shifts most of the storage overhead to the public device instead of storing in the tamper-proof device which is a major problem on current implementation. Furthermore, the broadcast keys in our scheme could be reused periodically resulting in more operational efficiency.

Output feedback controller design for uncertain piecewise linear systems

This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities （BMIs）. The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities （LMIs） which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.

Implementation of Control Algorithms in Small Embedded Systems

This work describes how a control algorithm can be implemented in a small (8-bit) microcontroller for the main purpose of merging embedded systems and control theory in electrical engineering undergraduate classes. Two different methods for discretizing the control expression are compared: Euler transformation and bilinear transformation. The sampling rate’s impact on the algorithm is discussed and theoretical results are verified by an application to a temperature control system in a heating plant. Four control algorithms are compared: PID and PI algorithms discretized with Euler and bilinear transformation, respectively. It is shown that for the heating plant used in this work, a bilinear PI algorithm implemented in a small 8-bit microcontroller outperforms a commercial controller from Panasonic. It is also demonstrated that all the derived algorithms can be implemented using integer calculations only, obviating the need for expensive and time-consuming floating-point calculations. This work bridges the gap between control theory equations and the implementation of control systems in small embedded systems with no inherent floating-point processing power.

三相电压型PWM整流器控制技术分析

阐述三相电压型PWM整流器的工作原理、拓扑结构及控制策略,分析三相电压型PWM整流器的控制结构、双闭环整流系统的控制方法。通过仿真和实验验证控制策略的正确性和有效性。

不确定非线性系统基于偏差分离的双线性控制

非线性和不确定性是制约控制系统性能的主要因素,为此出现了许多方法都试图克服这些因素的影响.本文提出一种基于偏差分离的双线性控制策略,在线获取模型偏差信息,并采用简单的双线性控制结构,具有很好的工程意义.论文证明了双线性控制系统指数渐近稳定的充分条件.仿真结果表明所提出的双线性控制策略的有效性.

双线性系统的自适应控制及其在谷氨酸pH值控制中的应用

对一类双线性系统，建立了自适应控制算法，给出了算法的稳定性证明．该算法也适用于非最小相位的双线性系统．在谷氨酸ｐＨ值控制中的实际应用表明，它具有良好的动态、静态性能和抗干扰能力，比ＰＩＤ控制具有更高的控制质量．

A PRIORI ERROR ESTIMATE AND SUPERCONVERGENCE ANALYSIS FOR AN OPTIMAL CONTROL PROBLEM OF BILINEAR TYPE

In this paper, we investigate a priori error estimates and superconvergence properties for a model optimal control problem of bilinear type, which includes some parameter estimation application. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We derive a priori error estimates and superconvergence analysis for both the control and the state approximations. We also give the optimal L^2-norm error estimates and the almost optimal L^∞-norm estimates about the state and co-state. The results can be readily used for constructing a posteriori error estimators in adaptive finite element approximation of such optimal control problems.