A partial parameterization of nonlinear output feedback controllers for saturated linear systems

This paper addresses the stabilization problem of linear systems subject to input saturation. The major purpose is to introduce nonlinearity into control laws so as to expand the design freedom for performance enhancement. To this end, a new approach is developed which involves a partial differential matrix inequality (PDMI). A class of stabilizing feedback laws is explicitly obtained by solving this PDMI analytically and the feedback laws are parameterized by a nonlinear function. Further, it is revealed that any linear observer can be used to realize the output feedback stabilization. Numerical examples, including the seek control of a hard disk drive, show that the introduced nonlinearity does contribute to the improvement of system performance. The application to integral control is also discussed.     

Nonlinear feedback control with global stabilization

Hamilton-Jacobi-Bellman theory is shown to provide a unified framework for nonlinear feedback control laws for special classes of nonlinear systems. These classes include Jurdjevic-Quinn type systems, as well as minimum phase systems with relative degree {1, 1, ..., 1}. Several examples are given to illustrate these results. For the controlled Lorenz equation, results obtained by Vincent and Yu are extended. Next, for spacecraft angular velocity stabilization with two torque inputs, a family of nonlinear feedback control laws that globally asymptotically stabilize angular velocity is established. Special cases of this family of control laws include generalizations of the locally stabilizing control laws of Brockett and Aeyels to global stabilization as well as the globally stabilizing control laws of Irving and Crouch and Byrnes and Isidori. Finally, the results are applied to spacecraft angular velocity stabilization with only one torque input. These last results extend control laws given by Outbib and Sallet.     

关于不确定对称组合系统的稳定化

研究不确定对称组合系统的二次稳定化问题,给出这类系统可二次稳定的一些充分条件 及计算反馈控制律的方法.这些条件的检验和反馈控制律的计算都由两个低阶系统关于相应 问题的求解来完成.     

不确定非完整动力学系统的指数镇定

研究具有未知惯性参数非完整动力学系统的镇定问题,基于非连续变换和动力学方程的性质,设计出两类非线地指数镇定律－鲁棒控制和自适应控制律。将其用于一类移动机器人的位姿镇定,仿真结果验证了所提出控制方法的有效性。     

Output feedback stabilization for stochastic nonholonomic systems with nonlinear drifts and Markovian switching

This paper investigates the output feedback stabilization of stochastic nonholonomic systems which have both nonlinear drifts and Markovian switching. The state‐scaling and backstepping techniques are exploited in the design of control laws. The output feedback stabilizing control laws and switching control strategy are proposed so that the closed‐loop system can be stabilized in probability in the large. In the end, an example of nonholonomic mobile robots is provided to illustrate the effectiveness of control laws.     

Global time-varying stabilization of underactuated surface vessel

This note considers the stabilization problem of an underactuated surface vessel. Three global smooth time-varying control laws are proposed with the aid of different techniques. The first proposed control law makes the state of the closed-loop system asymptotically converge to zero, while the second and the third control laws make the state of the closed-loop system globally exponentially converge to zero. Moreover, the exponential convergence rate of the state of the closed-loop system can be arbitrarily assigned with the third control law. Simulation results show that the proposed control laws are effective.     

Relaxed stabilization conditions for continuous-time Takagi-Sugeno fuzzy control systems

This paper deals with the stabilization of continuous-time Takagi-Sugeno (T-S) fuzzy control systems. Based on fuzzy Lyapunov functions and nonparallel distributed compensation (non-PDC) control laws, new stabilization conditions are represented in the form of linear matrix inequalities (LMIs). The theoretical proof shows that the proposed conditions can provide less conservatism than the existing results in the literature. Moreover, in order to demonstrate the effectiveness of the non-PDC control laws, the problem of H_∞ controller design for T-S fuzzy systems is also studied. Simulation examples are given to illustrate the merits of the proposed methods.     

Decentralized stabilization via game theoretic methods

Game theoretic ideas are employed in establishing the tradeoffs between control effort and ‘degree’ of stabilization for a class of feedback controls. These control laws are particularly suited for decentralized stabilization of interconnected systems.     

An impulsive‐switched‐system approach to aperiodic sampled‐data systems with time‐delay control

This paper devotes to the stability of aperiodic sampled‐data systems with time‐delay control, where the delays can impose a positive effect on the stability of the systems. The systems are modeled as impulsive switched systems with fixed switching laws. A novel separation theorem is presented to determine the Schur property of a matrix product and then used to obtain a less conservative stability criterion for the impulsive switched systems with fixed switching laws. By the separation theorem and a loop‐functional approach, some new stability and stabilization criteria for aperiodic sampled‐data systems with time‐delay control are provided in terms of linear matrix inequalities. Finally, the stability and stabilization results are tested on some classical numerical examples to illustrate the efficiency of the proposed method.     

Global stabilization of discrete‐time feedforward time‐delay systems by bounded controls

This paper studies the problem of global stabilization of a family of discrete‐time feedforward time‐delay systems with bounded controls. Two classes of nonlinear control laws are established based on a special canonical form of the considered system. The proposed control laws use not only the current states but also the delayed states for feedback and, moreover, contain some free parameters. These advantages can help to improve the transient performance of the closed‐loop system significantly. A practical example is given for illustration.     

基于线性矩阵不等式的不确定关联系统的分散鲁棒镇定

应用线性矩阵不等式（LMI）方法研究不确定性关联大系统的分散便棒镇定问题。系统中不稳定项具有数值界,可不满足匹配条件。基于不确定项的表达形式,给出了其可分散状态反馈镇定的充分条件,即一组LMIs有解。在此基础上,通过求第一凸优化问题,提出了具有较小反馈增益的分散稳定化状态反馈控制律的设计方法。仿真示例说明了该方法的有效性和优越性。     

一类切换系统极限环的反馈镇定研究

利用多Lyapunov函数法讨论一类切换系统极限环的反馈镇定问题．首先给出切换系统极限环的有界状态反馈、有界输出反馈以及动态反馈镇定定理;然后利用Jurdjevic—Quinn方法给出反馈控制器的具体形式,并证明了在给定反馈控制器的作用下,切换系统的极限环渐近稳定．仿真例子验证了结论的正确性．     

Synthesis of decoupling laws for attitude stabilization of a spacecraft

The problem of attitude stabilization of a spacecraft is considered. A method for solving the problem of accurate pole placement is proposed. The decoupling control laws for attitude stabilization of a spacecraft are synthesized using the proposed method.     

Stabilization of nonholonomic chained systems via nonregular feedback linearization

This paper addresses the problem of feedback stabilization of nonholonomic chained systems within the framework of nonregular feedback linearization. Firstly, the nonsmooth version of nonregular feedback linearization is formulated, and a criterion for nonregular feedback linearization is provided. Then, it is proved that the chained form is linearizable via nonregular feedback control, thus enable us to design feedback control laws using standard techniques for linear systems. The obtained discontinuous control laws guarantee convergence of the closed-loop system with exponential rates. Finally, simulation results are presented to show the effectiveness of the approach.     

Boundary Stabilization of a Cosserat Elastic Body

Boundary stabilization of vibrating three‐dimensional Cosserat elastic solids are studied using mathematical tools, such as operator theory and semigroup techniques. The advantages of the boundary control laws for both boundary stabilization problems are investigated. The boundary stabilization problems are studied using a Lyapunov stability method and LaSalle's invariant set theorem. Numerical simulations are provided to illustrate the effectiveness and performance of the designed control scheme.     

On the stabilization of feedforward systems with bounded control

For the global asymptotic stabilization of nonlinear—controllable in the first approximation—cascades consisting of a globally asymptotically—locally exponentially stable system driving a stable system, a Lyapunov-like design is proposed. This yields (bounded) control laws, where the control magnitude can be chosen arbitrarily large. This result provides an alternative to classical forwarding.     

Supervisory control of air–fuel ratio in spark ignition engines

The problem of air–fuel ratio stabilization in spark ignition engines is addressed in this paper. The proposed strategy consists of proper switching among two control laws to improve quality of the closed-loop system. The first control law is based on an a priori off-line identified engine model and ensures robust and reliable stabilization of the system at large, while the second control law is adaptive, it provides on-line adaptive adjustment to the current fluctuations and improves accuracy of the closed-loop system. The supervisor realizes a switching rule between these control laws providing better performance of regulation. Results of implementation on two vehicles are reported and discussed.     

Nonlinear control design for linear differential inclusions via convex hull of quadratics

This paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions (LDIs). A recently introduced non-quadratic Lyapunov function, the convex hull of quadratics, will be used for the construction of nonlinear state feedback laws. Design objectives include stabilization with maximal convergence rate, disturbance rejection with minimal reachable set and least L₂ gain. Conditions for stabilization and performances are derived in terms of bilinear matrix inequalities (BMIs), which cover the existing linear matrix inequality (LMI) conditions as special cases. Numerical examples demonstrate the advantages of using nonlinear feedback control over linear feedback control for LDIs. It is also observed through numerical computation that nonlinear control strategies help to reduce control effort substantially.     

Adaptive stabilization of uncertain dynamic non-holonomic systems

This paper investigates the stabilization problem of uncertain dynamic non-holonomic chained systems with unknown constant inertia parameters. Globally time-varying adaptive stabilizing control laws for such systems are presented. The application of it to a non-holonomic wheeled mobile robot is described. Simulation results show that the proposed approach is effective.     

Saturated stabilization and tracking of a nonholonomic mobile robot

This paper presents a framework to deal with the problem of global stabilization and global tracking control for the kinematic model of a wheeled mobile robot in the presence of input saturations. A model-based control design strategy is developed via a simple application of passivity and normalization. Saturated, Lipschitz continuous, time-varying feedback laws are obtained and illustrated in a number of compelling simulations.