Robust tracking control design for uncertain robotic systems with persistent bounded disturbances

In this study, a robust nonlinear L_∞‐gain tracking control design for uncertain robotic systems is proposed under persistent bounded disturbances. The design objective is that the peak of the tracking error in time domain must be as small as possible under persistent bounded disturbances. Since the nonlinear L_∞ ‐gain optimal tracking control cannot be solved directly, the nonlinear L_∞ ‐gain optimal tracking problem is transformed into a nonlinear L_∞ ‐gain tracking problem by given a prescribed disturbance attenuation level for the L_∞ ‐gain tracking performance. To guarantee that the L_∞ ‐gain tracking performance can be achieved for the uncertain robotic systems, a sliding‐mode scheme is introduced to eliminate the effect of the parameter uncertainties. By virtue of the skew‐symmetric property of the robotic systems, sufficient conditions are developed for solving the robust L_∞ ‐gain tracking control problems in terms of an algebraic equation instead of a differential equation. The proposed method is simple and the algebraic equation can be solved analytically. Therefore, the proposed robust L_∞ ‐gain tracking control scheme is suitable for practical control design of uncertain robotic systems. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Anti-disturbance control for time-varying delay Markovian jump nonlinear systems with multiple disturbances

In this paper, the problem of composite anti-disturbance resilient control is addressed for time-varying delay Markovian jump nonlinear systems with multiple disturbances. The disturbances are assumed to include two parts: the first one in the input channel is described by an external system with perturbations; the second one is supposed to be bounded H₂ norm. By combining disturbance observer and L₂–L_∞ control method, the disturbances are attenuated and rejected, simultaneously, and the desired dynamic performance can be obtained for time-varying delay Markovian jump nonlinear systems. Moreover, the gains of the resilient controller and the observer are acquired by applying linear matrix inequalities (LMIs) technology. Finally, an application example is presented to show the effectiveness of the proposed approach.     

基于力/力矩信息的面向位控机器人的阻抗控制

为了克服末端接触点距离力传感器中心较远时,力传感器测量实际接触力的局限性,分析实际作用力与测量力/力矩值之间的关系,利用力传感器信息或力矩信息得到位置控制方向和力控制方向.根据位控与力控方向对机器人末端进行参考轨迹规划,在阻抗控制律中应用参考比例因子调节参考轨迹.基于力误差信息通过模糊推理调节参考比例因子的大小,使生成的参考轨迹适应未知表面的变化.实验结果表明,所提出的控制方法能实现未知工件表面的恒力跟踪.     

Adaptive nonlinear excitation control with L2 disturbance attenuation for power systems

This paper presents a design approach to nonlinear feedback excitation control of power systems with unknown disturbance and unknown parameters. It is shown that the stabilizing control law with desired L₂ gain from the disturbance to a penalty signal can be designed by a recursive way without linearization. A state feedback law is presented for the case of the system with known parameters, and then the control law is extended to adaptive controller for the case when the parameters of the electrical dynamics of the power system are unknown. Simulation results demonstrate that the proposed controllers guarantee transient stability of the system regardless of the system parameters and faults.     

L1 adaptive control for general partial differential equation (PDE) systems

This paper addresses the L₁ adaptive control problem for general Partial Differential Equation (PDE) systems. Since direct computation and analysis on PDE systems are difficult and time-consuming, it is preferred to transform the PDE systems into Ordinary Differential Equation (ODE) systems. In this paper, a polynomial interpolation approximation method is utilized to formulate the infinite dimensional PDE as a high-order ODE first. To further reduce its dimension, an eigenvalue-based technique is employed to derive a system of low-order ODEs, which is incorporated with unmodeled dynamics described as bounded-input, bounded-output (BIBO) stable. To establish the equivalence with original PDE, the reduced-order ODE system is augmented with nonlinear time-varying uncertainties. On the basis of the reduced-order ODE system, a dynamic state predictor consisting of a linear system plus adaptive estimated parameters is developed. An adaptive law will update uncertainty estimates such that the estimation error between predicted state and real state is driven to zero at each time-step. And a control law is designed for uncertainty handling and good tracking delivery. Simulation results demonstrate the effectiveness of the proposed modeling and control framework.     

Robust control for nonlinear systems with structured 2-gain bounded uncertainty

This paper focuses on the problem of robust control design for uncertain nonlinear systems with ₂-gain bounded dynamic uncertainty and periodically time-varying memoryless uncertainty. The robust performance problem is solved via nonlinear ^∞ control with scaling factors. It is shown that the scaling factors can be functions of state variables in contrast with linear robust control.     

Low-rank matrix decomposition in L1-norm by dynamic systems

Low-rank matrix approximation is used in many applications of computer vision, and is frequently implemented by singular value decomposition under L₂-norm sense. To resist outliers and handle matrix with missing entries, a few methods have been proposed for low-rank matrix approximation in L₁ norm. However, the methods suffer from computational efficiency or optimization capability. Thus, in this paper we propose a solution using dynamic system to perform low-rank approximation under L₁-norm sense. From the state vector of the system, two low-rank matrices are distilled, and the product of the two low-rank matrices approximates to the given measurement matrix with missing entries, in L₁ norm. With the evolution of the system, the approximation accuracy improves step by step. The system involves a parameter, whose influences on the computational time and the final optimized two low-rank matrices are theoretically studied and experimentally valuated. The efficiency and approximation accuracy of the proposed algorithm are demonstrated by a large number of numerical tests on synthetic data and by two real datasets. Compared with state-of-the-art algorithms, the newly proposed one is competitive.     

Robust stabilization of nonlinear systems via stable kernel representations with L2-gain bounded uncertainty

The approach to robust stabilization of linear systems using normalized left coprime factorizations with _∞ bounded uncertainty is generalized to nonlinear systems. A nonlinear perturbation model is derived, based on the concept of a stable kernel representation of nonlinear systems. The robust stabilization problem is then translated into a nonlinear disturbance feedforward _∞ optimal control problem, whose solution depends on the solvability of a single Hamilton-Jacobi equation.     

A mixed H2/H∞ adaptive tracking control for constrained non-holonomic systems

In this study, a PID type controller incorporating an adaptive control scheme for the mixed H₂/H_∞ tracking performance is developed for constrained non-holonomic mechanical systems under unknown or uncertain plant parameters and external disturbances. By virtue of the skew-symmetric property of the non-holonomic mechanical systems and an adequate choice of a state variable transformation, sufficient conditions are developed for the adaptive mixed H₂/H_∞ tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled non-linear differential equations. The coupled algebraic equations can be solved analytically.     

Robust consensus algorithm for multi-agent systems with exogenous disturbances under convergence conditions

In this paper, a robust consensus algorithm is developed and sufficient conditions for convergence to consensus are proposed for a multi-agent system (MAS) with exogenous disturbances subject to partial information. By utilizing H_∞ robust control, differential game theory and a design-based approach, the consensus problem of the MAS with exogenous bounded interference is resolved and the disturbances are restrained, simultaneously. Attention is focused on designing an H_∞ robust controller (the robust consensus algorithm) based on minimisation of our proposed rational and individual cost functions according to goals of the MAS. Furthermore, sufficient conditions for convergence of the robust consensus algorithm are given. An example is employed to demonstrate that our results are effective and more capable to restrain exogenous disturbances than the existing literature.     

Robust L1 output tracking control for uncertain networked control systems described by T-S fuzzy model with distributed delays

This paper concentrates on investigating the robust L₁ output tracking control problem for the networked control systems described by Takagi–Sugeno fuzzy model with distributed delays and uncertainties. First, according to the parallel distributed compensation and Lyapunov theory, a fuzzy delay-dependent and basis-dependent Lyapunov–Krasovskii function that contributes to reducing the conservatism is constructed. Second, the L₁ performance criterion guaranteeing the asymptotic stability of the corresponding tracking control system and satisfying the prescribed tracking performance is derived. Furthermore, the output tracking control problem is converted into a convex optimisation problem. Finally, the results from simulation certify the effectiveness of the designed controller.     

Positive filtering for continuous-time positive systems under L1 performance

In this paper, we address the positive filtering problem for positive continuous-time systems under the L₁-induced performance. A pair of positive filters with error-bounding feature is proposed to estimate the output of positive systems. A novel characterisation is first obtained to ensure that the filtering error system is asymptotically stable with a prescribed L₁-induced performance. Then, necessary and sufficient conditions for the existence of required filters are presented, and the obtained results are expressed in terms of linear programming problems, which can be easily checked by standard software. Finally, a numerical example is given to illustrate the effectiveness of the proposed design procedures.     

Quadratic stabilisation with H∞-norm bound of non-linear discrete-time uncertain systems with bounded control

The paper addresses the problem of quadratic stabilisability with H_∞-norm bound of uncertain discrete-time control-affine systems by norm-bounded controls. Both structured parameter uncertainties and unstructured exogenous disturbances are taken into account. The given definition of quadratic stabilisability is a generalisation of that used for linear systems so far. A necessary condition of the stabilisability is formulated. A state feedback control satisfying an a priori constraint is proposed for the solution of the formulated H_∞ problem. The proposed method may be applicable even in such cases when the linearisation technique cannot be used.     

含状态时滞及执行器饱和不确定系统反馈镇定及L2增益分析

研究了具有控制饱和状态时滞不确定系统的L₂控制问题, 提出了状态反馈方法, 利用Lyapunov函数可获得时滞相关的线性矩阵不等式. 线性矩阵不等式条件可保证闭环系统无干扰时鲁棒内稳定性和在某椭球内预先给定的有干扰时L₂性能水平, 该不等式通过引入辅助矩阵解除了执行器饱和对系统的影响而更易于实现且减小了保守性. 采用线性矩阵不等式技术, 将控制器存在的充分条件转化为凸优化问题. 在此基础上设计了系统的状态反馈控制器, 最后用数值仿真验证了所提出方法的可行性.     

Model reference adaptive control for nonminimum phase systems

In this paper we define a new model reference adaptive control problem which allows a large amount of plant uncertainty. Instead of the usual goal of asymptotic error regulation, here we require that the limit superior of the magnitude of the error be less than a predefined constant times the limit superior of the magnitude of the external reference input. This provides a natural way to incorporate uncertainty which includes nonminimum phase systems.     

General quadratic performance analysis and synthesis of differential algebraic equation (DAE) systems

In this paper, control of linear differential-algebraic-equation systems, subject to general quadratic constraints, is considered. This setup, especially, includes the H_∞ control problem and the design for strict passivity. Based on linear matrix inequality (LMI) analysis conditions, LMI synthesis conditions for the existence of linear output feedback controllers are derived by means of a linearizing change of variables. This approach is constructive: a procedure for the determination of controller parameterizations is given on the basis of the solution of the LMI synthesis conditions. A discussion of the possible applications of the presented results concludes the paper.     

On globally stable adaptive control providing l 1 tracking performance for linear discrete-time systems

Existing adaptive control algorithms at best guarantee that the tracking error is a l ₂ sequence. This paper presents globally stable adaptive control algorithms for linear discrete-time systems providing l ₁ tracking performance. Two algorithms with different degree of complexity are proposed, one for the case of known control directions, and a separate algorithm for the case of unknown control directions. It is demonstrated that in both cases the tracking error is l ₁ sequence, while the input and output signals are uniformly bounded.     

Robust H∞ control for linear discrete-time systems with norm-bounded time-varying uncertainty

The problem of robust H_∞ analysis and synthesis for linear discrete-time systems with norm-bounded time-varying uncertainty is studied in this paper. It will be shown that this problem is equivalent to the problem of H_∞ analysis and synthesis of an auxiliary system. The necessary and sufficient conditions for the equivalency are proved. Thus the original problem can be solved by existing H_∞ control methods.     

Robust H∞ filtering with error variance constraints for discrete time-varying systems with uncertainty

The robust H_∞ filtering problem with error variance constraints is considered for discrete time-varying systems subject to norm-bounded parameter uncertainties in both the state and the output matrices of the state-space model. Sufficient conditions for a finite-horizon filter to satisfy state estimation error variance constraints as well as prescribed H_∞ performance for all admissible perturbations are given in terms of two discrete Riccati difference equations, which are of a form suitable for recursive computation. The results are extended to cover the case of stationary filtering over an infinite-horizon for uncertain time-invariant systems.     

Delay-dependent robust H∞ control for uncertain systems with a state-delay

A robust H_∞ control for uncertain linear systems with a state-delay is described. Systems with norm-bounded parameter uncertainties are considered and linear memoryless state feedback controllers are obtained. Firstly, a delay-dependent bounded real lemma for systems with a state-delay is presented in terms of linear matrix inequalities (LMIs). By taking a new Lyapunov-Krasovsii functional, neither model transformation nor bounding for cross terms is required to obtain delay-dependent results. Secondly, based on the bounded real lemma obtained, delay-dependent condition for the existence of robust H_∞ control is presented in terms of nonlinear matrix inequalities. In order to solve these nonlinear matrix inequalities, an iterative algorithm involving convex optimization is proposed. Numerical examples show that the proposed methods are much less conservative than existing results.