On-line identification scheme using adaptive filters

An on-line scheme for identifying a linear process is proposed which consists of a linear time-varying filter and a parameter update algorithm. The disturbances affecting the process, its input and its output, belong to a general class of signals which are a mixture of stochastic and deterministic signal processes generated by some linear time-invariant system excited by white noise and the Dirac delta function, respectively. The process and the disturbance signal models are not restricted to be asymptotically stable. Either a probing input signal or a normal operating input signal can be employed. The probing signal consists of a finite number of sinusoidal signals (exponentially increasing sinusoidal signals for unstable processes) of distinct frequencies. When a normal operating signal is used, an adaptive scheme is employed to tune the parameters of the filters to the distinct frequency components of the signal. The convergence of the parameter estimates to their true value is established.     

Adaptive model predictive control for a class of constrained linear systems based on the comparison model

This paper proposes an adaptive model predictive control (MPC) algorithm for a class of constrained linear systems, which estimates system parameters on-line and produces the control input satisfying input/state constraints for possible parameter estimation errors. The key idea is to combine the robust MPC method based on the comparison model with an adaptive parameter estimation method suitable for MPC. To this end, first, a new parameter update method based on the moving horizon estimation is proposed, which allows to predict an estimation error bound over the prediction horizon. Second, an adaptive MPC algorithm is developed by combining the on-line parameter estimation with an MPC method based on the comparison model, suitably modified to cope with the time-varying case. This method guarantees feasibility and stability of the closed-loop system in the presence of state/input constraints. A numerical example is given to demonstrate its effectiveness.     

Practical adaptive output tracking of high-order lower-triangular nonlinear systems: Modular design using feedback domination method

In this paper, a new modular design technique for globally and practically adaptive output tracking of high-order lower-triangular nonlinear systems is proposed. This technique is not based on certainty equivalence principle and completely uses feedback domination method for these linearly parameterized systems. Contrary to the methods based on adding a power integrator technique, for adaptive control of high-order lower-triangular nonlinear systems, in which the choice of a parameter update law is limited to a Lyapunov-type algorithm, the present method does not have this restriction and uses the swapping identifier as its parameter update law. The modularity of designing the controller and the identifier in this method, which relies on control design using feedback domination approach, is completely different from modular design in Immersion and invariance (I&I) based method, which relies on identifier design and desired features of parameter identification. Finally an example illustrates the feasibility and efficiency of the proposed method.     

Adaptive Reliable <Emphasis Type="Italic">H</Emphasis><Subscript>∞</Subscript> Control of Uncertain Affine Nonlinear Systems

For general input affine nonlinear systems, robust reliable control designs are commonly available that compensate the actuator faults in pure outage mode. In this paper, a more general and complex problem is considered and an adaptive reliable H_∞ controller is designed for a class of uncertain input affine nonlinear systems in the presence of actuators fault. The key element of the work is the introduction of a novel adaptive mechanism that estimates the faults which are modeled as an outage or loss of effectiveness and stabilizes the overall system. Incorporating with the parameter projection algorithm and the solution of Hamilton-Jacobi-Inequality (HJI), the proposed method combines adaptive reliable control and robust H_∞ control techniques. A numerical approach is developed based on the Taylor series expansion for solving the HJI. Various simulation examples are given to illustrate the effectiveness of the proposed adaptive reliable H_∞ control scheme over the conventional H_∞ control and reliable H_∞ control method.     

基于系统浸入和流形不变自适应方法的静止无功补偿器非线性鲁棒自适应控制方法

本文提出一种将系统浸入和流形不变(I&I)自适应控制方法与L2-增益抑制鲁棒控制方法相结合的静止无功补偿器(SVC)的非线性鲁棒自适应控制方法.所提方法首先通过参数估计误差和鲁棒控制律的设计,使得所构造的表示参数估计误差函数的流形不变且吸引,从而使参数估计误差在这一流形上收敛于零.然后,通过所设计的可调参数对参数估计误差的收敛性能进行控制,以此来保证参数估计器对不确定参数的自适应估计能力.最后,采用自适应逆推算法推导鲁棒控制律,并通过使不确定外部扰动满足从输入到输出的耗散性来保证系统对不确定扰动的鲁棒性.仿真结果表明,利用所提方法设计的SVC控制器和参数替换律在参数估计、发电机功角动态响应方面优于传统自适应逆推算法,从而提高了输电系统的稳定水平.     

Recursive exponentially weighted PLS and its applications to adaptive control and prediction

A new and fast recursive, exponentially weighted PLS algorithm which provides greatly improved parameter estimates in most process situations is presented. The potential of this algorithm is illustrated with two process examples: (i) adaptive control of a two by two simulated multivariable continuous stirred tank reactor; and (ii) updating of a prediction model for an industrial flotation circuit. The performance of the recursive PLS algorithm is shown to be much better than that of the recursive least squares algorithm. The main advantage of the recursive PLS algorithm is that it does not suffer from the problems associated with correlated variables and short data windows. During adaptive control, it provided satisfactory control when the recursive least squares algorithm experienced difficulties (i.e., ‘blew’ up) due to the ill-conditioned covariance matrix, (X^TX)_t. For the industrial soft sensor application, the new algorithm provided much improved estimates of all ten response variables.     

Adaptive backstepping control of wheeled inverted pendulum with velocity estimator

In this paper, we introduce a backstepping control design of a wheeled inverted pendulum. Based on a second-order motion equation of the body angle, an adaptive integral backstepping controller is designed to stabilize the body angle. It is shown that the σ-modification rule in the adaptive update law guarantees the boundedness of the errors in estimating the time-varying signal that is an output of a linear system with every bounded input signal. Then, the stabilizing controller for the wheel angle is constructed by a PD-type positive feedback. The derived controller requires the full-state measurements. In the output feedback case, the K filter or the observer backstepping is needed. However, the structure of the controller becomes complicated. We propose a non-model-based differentiator based on the adaptive update law. Since the non-model-based differentiator does not require any knowledge of the dynamic structure of the signal, we can use it as a velocity estimator for unknown nonlinear systems. Therefore, we replaced the velocity measurement with the estimates by the non-model-based differentiator. Finally, simulation results for the proposed controller are presented.     

非线性主动悬架系统自适应最优控制

针对非线性主动悬架系统多性能指标综合优化问题,提出一类自适应最优控制方法.首先,通过引入一阶低通滤波操作,利用系统输入输出构建结构简单且调节参数少的一类未知非线性动态估计器,在线估计系统未知非线性动态;其次,构建包含乘驾舒适度、悬架行程空间及输入能耗的性能指标函数,采用单层神经网络对最优性能指标函数进行在线逼近,并得到新的哈密尔顿函数;为实现在线求解,构建一类新的基于参数估计误差信息的自适应律,在线更新神经网络权值并计算最优控制律;最后,理论分析闭环系统稳定性和收敛性,并通过专业软件Carsim与Matlab/Simulink搭建的联合仿真平台给出的对比仿真结果,验证所提出方法可有效解决主动悬架系统多目标性能优化控制问题,提升主动悬架系统综合性能.     

Stochastic Optimal Design for Unknown Linear Discrete‐Time System Zero‐Sum Games in Input‐Output form Under Communication Constraints

In this paper, stochastic optimal strategy for unknown linear discrete‐time system quadratic zero‐sum games in input‐output form with communication imperfections such as network‐induced delays and packet losses, otherwise referred to as networked control system (NCS) zero‐sum games, relating to the H_∞ optimal control problem is solved in a forward‐in‐time manner. First, the linear discrete‐time zero sum state space representation is transformed into a linear NCS in the state space form after incorporating random delays and packet losses and then into the input‐output form. Subsequently, the stochastic optimal approach, referred to as adaptive dynamic programming (ADP), is introduced which estimates the cost or value function to solve the infinite horizon optimal regulation of unknown linear NCS quadratic zero‐sum games in the presence of communication imperfections. The optimal control and worst case disturbance inputs are derived based on the estimated value function in the absence of state measurements. An update law for tuning the unknown parameters of the value function estimator is derived and Lyapunov theory is used to show that all signals are asymptotically stable (AS) and that the estimated control and disturbance signals converge to optimal control and worst case disturbances, respectively. Simulation results are included to verify the theoretical claims.     

Adaptive iterative learning control for a class of non-linearly parameterised systems with input saturations

In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov–Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L²_{[0, T]} convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.     

Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.     

Robust tracking design based on adaptive fuzzy control of uncertain nonlinear MIMO systems with time delayed states

It is proposed here to use a robust tracking design based on adaptive fuzzy control technique to control a class of multi-input-multi-output (MIMO) nonlinear systems with time delayed uncertainty in which each uncertainty is assumed to be bounded by an unknown gain. This technique will overcome modeling inaccuracies, such as drag and friction losses, effect of time delayed uncertainty, as well as parameter uncertainties. The proposed control law is based on indirect adaptive fuzzy control. A fuzzy model is used to approximate the dynamics of the nonlinear MIMO system; then, two on-line estimation schemes are developed to overcome the nonlinearities and identify the gains of the delayed state uncertainties, simultaneously. The advantage of employing an adaptive fuzzy system is the use of linear analytical results instead of estimating nonlinear system functions with an online update law. The adaptive fuzzy scheme uses a Variable Structure (VS) scheme to resolve the system uncertainties, time delayed uncertainty and the external disturbances such that H_∞ tracking performance is achieved. The control laws are derived based on a Lyapunov criterion and the Riccati-inequality such that all states of the system are uniformly ultimately bounded (UUB). Therefore, the effect can be reduced to any prescribed level to achieve H _∞ tracking performance. A two-connected inverted pendulums system on carts and a two-degree-of-freedom mass-spring-damper system are used to validate the performance of the proposed fuzzy technique for the control of MIMO nonlinear systems.     

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.     

Adaptive one-step-ahead control for non-minimum phase systems with input magnitude and rate constraints

The adaptive control design for linear stable plants with input magnitude and rate constraints is addressed. The proposed algorithm adopts the self-tuning regulator (STR) adaptive control principle with one-step-ahead control as its underlying control design. An important governing equation relating the prediction error to the 'input discrepancy' between adaptive control and the corresponding non-adaptive control is identified, independent of how the parameter estimates are attained. Together with the convergence property of least-square type estimation algorithm, the governing equation leads to a successful analysis on the convergence and tracking performance of the adaptive constrained one-step-ahead controller. Specifically, globally input matching property is maintained in the sense that the adaptive constrained control asymptotically matches its corresponding non-adaptive one. Furthermore, the desired tracking performance of the adaptive controller can be achieved asymptotically if the corresponding non-adaptive control is eventually out of the constraints. The proposed adaptive control is applicable to both minimum and non-minimum phase stable systems.     

考虑参数和负载不确定性的内置式永磁同步电机自适应反步控制

提出一种??_?? = 0 的内置式永磁同步电机的自适应反步控制方法. 通过定义虚拟控制变量和选择适当的Lyapunov 函数, 导出系统控制律及参数自适应律. 该方法能够根据自适应参数估计器实时估计出的负载转矩和定子电阻对控制输出进行动态校正, 从而提高转速控制精度和系统的抗扰能力. 仿真结果表明, 系统能够快速跟踪参考转速, 并对负载扰动和参数变化具有较强的鲁棒性.

     

Adaptive control of flexible link manipulators using a pseudolink dynamic model

This paper presents a novel adaptive control scheme for a lightweight manipulator arm governed by electric motors. The controller design is based on the dynamic model of the arm in a quasi-static approximation which consists of the transports subsystem and the motor equations corrected for the elastic compliance of the plant. A passivity property of the flexible electromechanical system is established and an adaptive motor controller is developed which contains the rigid manipulator controller as a part. The motor controller updates all unknown rigid manipulator parameters as well as elastic parameters and ensures global asymptotic stability of the tracking errors with all signals in the system remaining bounded. Projecting of parameter estimates is used in the update law to avoid possible singularities when generating control input. Simulation results for a single-link elastic arm confirm the validity and demonstrate advantages of the proposed method.     

Optimal PID Controller Autotuning Design for MIMO Nonlinear Systems Based on the Adaptive SLP Algorithm

In this paper, an adaptive swarm learning process (SLP) algorithm for designing the optimal proportional integral and derivative (PID) parameter for a multiple-input multiple-output (MIMO) control system is proposed. The SLP algorithm is proposed to improve the performance and convergence of PID parameter autotuning by applying the swarm algorithm and the learning process. The adaptive SLP algorithm improves the stability, performance and robustness of the traditional SLP algorithm to apply it to a MIMO control system. It can update the online weights of the SLP algorithm caused by the errors in the settling time, rise time and overshoot of the system based on a stable learning rate. The gradient descent is applied to update the weights. The stable learning rate is verified based on the Lyapunov stability theorem. Additionally, simulations are performed to verify the superiority of the algorithm in terms of performance and robustness. Results that compare the adaptive SLP algorithm with the traditional SLP, a neural network (NN), the genetic algorithm (GA), the particle swarm and optimization (PSO) algorithm and the kidney-inspired algorithm (KIA) based on a two-wheel inverted pendulum system are presented. With respect to performance and robustness, the adaptive SLP algorithm provides a better response than the traditional SLP, NN, GA, PSO and KIA.

     

Adaptive dynamic surface control for a class of output-feedback nonlinear systems with guaranteed ℒ∞ tracking performance

In this article, an output-feedback adaptive dynamic surface control (DSC) is proposed for a class of nonlinear systems. It is proved that, by using the new scheme, the explosion of the complexity problem in a traditional backstepping design can be eliminated, the semi-global stability of a closed-loop system can be guaranteed and, in particular, by choosing the design parameters and initialising the filters and the update law properly, we show that the ?_∞ performance of the system-tracking error can be achieved without over-parametrisation. Another advantage of the proposed scheme compared with those traditional backstepping control and current adaptive DSC schemes, whose adaptive control law is obtained through a series of steps recursively, is that the adaptive law is needed only at the first design step, and therefore significantly reduces the design procedure.     

A variable step-size selective partial update LMS algorithm

Selective partial update of the adaptive filter coefficients has been a popular method for reducing the computational complexity of least mean-square (LMS)-type adaptive algorithms. These algorithms use a fixed step-size that forces a performance compromise between fast convergence speed and small steady state misadjustment. This paper proposes a variable step-size (VSS) selective partial update LMS algorithm, where the VSS is an approximation of an optimal derived one. The VSS equations are controlled by only one parameter, and do not require any a priori information about the statistics of the system environment. Mean-square performance analysis will be provided for independent and identically distributed (i.i.d.) input signals, and an expression for the algorithm steady state excess mean-square error (MSE) will be presented. Simulation experiments are conducted to compare the proposed algorithm with existing full-update VSS LMS algorithms, which indicate that the proposed algorithm performs as well as these algorithms while requiring less computational complexity.