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.     

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.     

四旋翼无人机L1 自适应块控反步姿态控制器设计

针对四旋翼无人机的姿态控制问题,提出一种L1自适应块控反步控制方法.将四旋翼姿态运动模型转化为一类多输入多输出不确定非线性系统的形式;根据该系统严格反馈的结构特点,对外回路设计了块控反步控制器;针对内回路存在的外部干扰和内部参数摄动等不确定性,引入L1自适应控制思想补偿其影响.稳定性分析表明闭环系统内所有信号一致有界.仿真和姿态稳定实验验证了所提控制策略的有效性和鲁棒性.     

On nonlinear H ∞ sliding mode control for a class of nonlinear cascade systems

In this work two main robust control strategies, the sliding mode control (SMC) and nonlinear H ^∞ control, are integrated to function in a complementary manner for tracking control tasks. The SMC handles matched L ^∞[0,∞) type system uncertainties with known bounding functions. H ^∞ control deals with unmatched disturbances of L ₂[0,∞) type where the upper-bound knowledge is not available. The new control method is designed for a class of nonlinear uncertain systems with two cascade subsystems. Nonlinear H ^∞ control is applied to the first subsystem in the presence of unmatched disturbances. Through solving a Hamilton-Jacoby inequality, the nonlinear H ^∞ control law for the first subsystem well defines a nonlinear switching surface. By virtue of nonlinear H ^∞ control, the resulting sliding manifold in the sliding phase possesses the desired L ₂ gain property and to a certain extend the optimality. Associated with the new switching surface, the SMC is applied to the second subsystem to accomplish the tracking task, and ensure the L ₂ gain robustness in the reaching phase. Two illustrative examples are given to show the effectiveness of the proposed robust control scheme.     

Robust fuzzy stabilization of dithered chaotic systems using island-based random optimization algorithm

Applying dither to highly nonlinear systems may suppress chaotic phenomena, but dynamic performance, such as convergence rate and disturbance attenuation, is usually not guaranteed. This paper presents a dithered H_∞ robust fuzzy control scheme to stabilize chaotic systems that ensures disturbance attenuation bounds. In the proposed scheme, Takagi-Sugeno (T-S) fuzzy linear models are used to describe the relaxed models of the dithered chaotic system, and fuzzy controllers are designed based on an extension to the concept of parallel distributed compensation (PDC). Sufficient condition for the existence of the H_∞ robust fuzzy controllers is presented in terms of a novel linear matrix inequalities (LMI) form which takes full consideration of modeling error and disturbances, but cannot be solved by the standard procedures. In order to solve the LMI problem and to identify the chaotic systems as T-S fuzzy modes, we propose a compound optimization strategy called the island-based random-walk algorithm (IRA). The algorithm is composed of a set of communicating random-walk optimization procedures concatenated with the down-hill simplex method. The design procedure and validity of the proposed scheme is demonstrated via numerical simulation of the dithered fuzzy control of a chaotic system.     

一种可保证瞬态特性的改进的鲁棒模型参考自适应控制

针对典型的鲁棒模型参考自适应控制中瞬态性能无法得到保障的问题, 提出一种改进的鲁棒模型参考自适应控制器. 该控制器在标准的鲁棒自适应控制中加入??_∞ 补偿器, 以抑制闭环自适应系统中参数估计误差和不确定扰动对系统输出跟踪性能造成的不利影响. 理论分析和仿真验证表明, 所提出的控制器不但保留了典型鲁棒模型参考自适应控制的理想特性, 并且通过设计适当的??∞ 补偿器使得闭环系统的瞬态性得到了较大的改善, 其改善的程度依赖于??∞ 补偿器性能指标的大小.

     

并联混合有源电力滤波器自适应L2增益鲁棒控制

为了抑制外界未知扰动和参数摄动对并联混合有源电力滤波器(SHAPF) 系统性能的影响, 提出一种新型的自适应L₂ 增益鲁棒控制策略. 首先建立含有扰动和参数摄动的SHAPF 欧拉-拉格朗日(EL) 数学模型, 得到了SHAPF 在dq 坐标系下的误差动态模型; 然后通过构造适当的Lyapunov 函数设计参数自适应控制率, 实现了对系统参数摄动的补偿, 进而利用阻尼注入方法设计系统的L₂增益鲁棒控制器, 以保证闭环系统的 gamma  耗散性. 仿真实验验证了所提出策略的正确性和有效性.

     

Stability and robustness analysis of MIMO MRAC using Kp = L 2 D 2 S 2 factorization

For a class of MIMO systems with input and output unmodeled dynamics, bounded disturbances and any relative degree, using the idea of K_p = L ₂ D ₂ S ₂ factorization, the design and analysis of robust direct model reference adaptive control are further investigated in this article. By establishing the L_p and L _2δ relationship properties between the input and output, multivariable swapping lemmas and relating all the signals in the closed-loop system with the normalizing signal, stability and robustness of adaptive system are analyzed rigorously. Compared with the existing results, the proof procedure is more compact and simple. A simulation example verifies the effectiveness of the control scheme.     

A robust output-feedback adaptive dynamic surface control for linear systems with input disturbance

In this paper, a robust output-feedback adaptive control is proposed for linear time-invariant (LTI) singleinput single-output (SISO) plants with unmeasurable input disturbance. Using dynamic surface control (DSC) technique, it is shown that the explosion of complexity problem in backstepping control can be eliminated. Furthermore, the proposed adaptive DSC scheme has the following merits: 1) by introducing an initialization technique, the L∞ performance of system tracking error can be guaranteed even if the plant high-frequency gain is unknown and the input disturbance exists, and 2) the adaptive law is necessary only at the first design step, which significantly reduces the design procedure. It is proved that with the proposed scheme, all the closed-loop signals are semiglobally uniformly ultimately bounded. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.     

Adaptive H_∞ Synchronization of Master-slave Systems with Mixed Time-varying Delays and Nonlinear Perturbations： An LMI Approach

This paper proposes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays comprising different discrete and distributed time delays. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and an adaptation law including the master-slave parameters are established for designing a delayed synchronization law in terms of linear matrix inequalities(LMIs). The time-varying controller guarantees the H _∞ synchronization of the two coupled master and slave systems regardless of their initial states. Particularly, it is shown that the synchronization speed can be controlled by adjusting the updated gain of the synchronization signal. Two numerical examples are given to demonstrate the effectiveness of the method.     

TCSC 系统的自适应minimax 干扰抑制控制器设计

针对含有未知外部干扰和不确定参数的非线性晶闸管控制串联补偿器(TCSC) 系统, 提出一种L₂增益干扰抑制算法. 将minimax 方法引入耗散Hamilton 系统, 消除了不等式假设条件的约束; 构造检验函数, 推算出系统所能承受的最大干扰程度, 降低了传统干扰处理方法的保守性; 采用参数映射方法设计自适应律, 提高了参数跟踪效率. 最后通过机械功率和对地短路故障的仿真结果表明了所提出的控制方案能够有效改善系统的暂态性能.

     

Adaptive H2/H∞ tracking control for a class of uncertain robotic systems

This paper addresses the problem of designing mixed H₂/H_∞ tracking control for a large class of uncertain robotic systems. Nonlinear H_∞ control theory, H₂ control theory and intelligent adaptive control algorithm are combined to construct a hybrid adaptive/robust H₂/H_∞ tracking control scheme. One adaptive neural network system is constructed to approximate the behaviour of uncertain robot dynamics, and the other adaptive control algorithm is designed to estimate the behaviour of the modelled disturbance. Moreover, a robust H_∞ control algorithm is designed to attenuate the effects of the unmodelled disturbance. Only a set of algebraic matrix Riccati-like equations is required to implement the proposed mixed H₂/H_∞ tracking controller, and so an explicit and closed-form solution is obtained. Consequently, the mixed H₂/H_∞ adaptive/robust tracking controller developed here can be analytically computed and easily implemented. Finally, simulations are presented to illustrate the effectiveness of the proposed control algorithm.     

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 adaptive self-structuring fuzzy control design for nonaffine,nonlinear systems

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L ₂ tracking performance to stabilise the closed-loop system. This L ₂ tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.     

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.     

Inverse optimal sliding mode control of spacecraft with coupled translation and attitude dynamics

This paper proposes two robust inverse optimal control schemes for spacecraft with coupled translation and attitude dynamics in the presence of external disturbances. For the first controller, an inverse optimal control law is designed based on Sontag-type formula and the control Lyapunov function. Then a robust inverse optimal position and attitude controller is designed by using a new second-order integral sliding mode control method to combine a sliding mode control with the derived inverse optimal control. The global asymptotic stability of the proposed control law is proved by using the second method of Lyapunov. For the other control law, a nonlinear H_∞ inverse optimal controller for spacecraft position and attitude tracking motion is developed to achieve the design conditions of controller gains that the control law becomes suboptimal H_∞ state feedback control. The ultimate boundedness of system state is proved by using the Lyapunov stability theory. Both developed robust inverse optimal controllers can minimise a performance index and ensure the stability of the closed-loop system and external disturbance attenuation. An example of position and attitude tracking manoeuvres is presented and simulation results are included to show the performance of the proposed controllers.     

L1 adaptive output‐feedback control of multivariable nonlinear systems subject to constraints using online optimization

In this paper, an L₁ adaptive output‐feedback controller is developed for multivariable nonlinear systems subject to constraints using online optimization. In the L₁ adaptive architecture, an adaptive law will update the adaptive parameters that represent the nonlinear uncertainties such that the estimation error between the predicted state and the real state is driven to zero at every integration time step. Of course, neglection of the unknowns for solving the error dynamic equations will introduce an estimation error in the adaptive parameters. The magnitude of this error can be lessened by choosing a proper sampling time step. A control law is designed to compensate the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. Model predictive control is introduced to solve a receding horizon optimization problem with various constraints maintained. Numerical examples are given to illustrate the design procedures, and the simulation results demonstrate the availability and feasibility of the developed framework.     

Robust Recurrent Neural Network Control of Biped Robot

In this paper, a recurrent neural network (RNN) control scheme is proposed for a biped robot trajectory tracking system. An adaptive online training algorithm is optimized to improve the transient response of the network via so-called conic sector theorem. Furthermore, L ₂-stability of weight estimation error of RNN is guaranteed such that the robustness of the controller is ensured in the presence of uncertainties. In consideration of practical applications, the algorithm is developed in the discrete-time domain. Simulations for a seven-link robot model are presented to justify the advantage of the proposed approach. We give comparisons between the standard PD control and the proposed RNN compensation method.     

基于参数依赖滚动时域H∞控制的高超声速飞行器控制

针对输入受限的高超声速飞行器强耦合、强非线性以及严重不确定性的特点,提出一种参数依赖滚动时域?∞控制(PD-RHHC)的方法.首先在考虑控制输入约束的条件下,引入参数依赖Lyapunov函数和松弛因子并提出了基于LMI优化的PD-RHHC;然后采用函数替换方法,结合张量积模型转换方法实现高超声速飞行器(HSV)纵向非线性弹性模型的LPV描述,并将PD-RHHC应用到高超声速飞行器纵向控制中,以实现HSV在大飞行包线内的机动飞行;最后通过仿真实验验证了所提出算法的有效性.     

Adaptive H_∞ Control for Nonlinear Hamiltonian Systems with Time Delay and Parametric Uncertainties

This paper addresses the adaptive H∞ control problem for a class of nonlinear Hamiltonian systems with time delay and parametric uncertainties. The uncertainties under consideration are some small parameter perturbations involved in the structure of the Hamiltonian system. Both delay-independent and delay-dependent criteria are established based on the dissipative structural properties of the Hamiltonian systems and the Lyapunov-Krasovskii functional approach. In order to construct the adaptive H∞controller, the situation that the parameter perturbation is inexistent in the system is also studied and the controller is designed.The adaptive H∞ control problem is solved under some sufficient conditions which ensure the asymptotic stability and the L2 gain performance of the resulted closed-loop system. Numerical example is given to illustrate the applicability of the theoretical results.