A switching periodic adaptive control approach for time‐varying parameters with unknown periodicity

Periodic variations are encountered in many real systems, which can exist in the system parameters, as a disturbance or as the tracking objective. However, there exist a great number of situations where the periodicity is not known in advance. Hence, how to compensate for the effects of time‐varying parameters with unknown periodicity remains a challenge for the controller design. In this paper, we proposed a switching periodic adaptive control approach for continuous‐time nonlinear parametric systems with periodic uncertainties in which the period and bound are not known in advance. We utilized a fully saturated periodic adaptation law to identify the unknown periodic parameters in a pointwise manner. In addition, we provided a logic‐based switching scheme to estimate the unknown period and bound online simultaneously. By virtue of Lyapunov stability analysis, we show that the asymptotic convergence can be guaranteed irrespective of the initial conditions. Finally, we carried out numerical simulations to demonstrate the efficacy of the switching periodic adaptive control algorithm. The proposed approach can be applied to parametric nonlinear systems with time‐varying parameters of unknown periodicity irrespective of the types of periodic uncertainties. Copyright © 2015 John Wiley & Sons, Ltd.     

Application specific integrated circuit solution for multi‐input multi‐output piecewise‐affine functions

This paper presents a fully digital architecture and its application specific integrated circuit implementation for computing multi‐input multi‐output (MIMO) piecewise‐affine (PWA) functions. The work considers both PWA functions defined over regular hyperrectangular and simplicial partitions of the input domains and also lattice PWA representations. The proposed architecture is able to implement PWA functions following different realization strategies, using a common structure with a minimized number of blocks, thus reducing power consumption and hardware resources. Experimental results obtained with application specific integrated circuit (ASIC) integrated in a 90‐nm complementary metal‐oxide semiconductor standard technology are provided. The proposed architecture is compared with other digital architectures in the state of the art habitually used to implement model predictive control applications. The proposal is superior in power consumption (saving up to 86%) and economy of hardware resources (saving up to 40% in comparison with a mere replication of the three representations) to other proposals described in literature, being ready to be used in applications where high‐performance and minimum unitary cost are required. Copyright © 2015 John Wiley & Sons, Ltd.     

柔性直流输电系统显式模型预测低复杂度控制技术

建立电压源型换流器的高压直流输电系统三阶分段仿射系统模型。针对传统的模型预测控制需要滚动优化的缺点,应用显式模型预测控制的方法,通过多参数二次规划来对状态空间进行凸划分,将原本大量的在线控制计算过程转移到离线阶段进行预计算。为降低其离线计算的复杂度,引入分离函数和误判点的概念,通过严格分离饱和分区的方法,减少需要预计算和划分的分区数量,也间接加快了在线计算时状态量搜索对应分区的速度。通过仿真分析验证了嵌入分离函数后,在负载突增和系统参数变化等环境下显式模型预测控制的控制性能。     

Nonlinear control for uncertain nonlinear systems with unknown control directions using less or no parameter estimates

For the parametric strict‐feedback nonlinear systems with unknown virtual control coefficients and unknown control directions, the control schemes presented in the existing literature have the disadvantage of overparametrization. In this paper, a novel systematic design procedure is developed to solve the overparametrization problem. Two nonlinear controllers are designed by combining the backstepping technique and the Nussbaum gain approach. A main advantage of the proposed controllers is that they contain less or no parameter estimates that need to be updated online. In the first scheme, the number of the estimated parameters is equal to the dimension of the controlled system. In the second scheme, no parameter estimates are required. In both of the control schemes, the boundedness of all the closed‐loop signal is guaranteed, and the asymptotic convergence of the system states is achieved. An example is provided to demonstrate the effectiveness of the proposed design approaches. Copyright © 2014 John Wiley & Sons, Ltd.     

Rejection of unknown periodic disturbances for continuous‐time MIMO systems with dynamic uncertainties

Rejection of unknown periodic disturbances in multi‐channel systems has several industrial applications that include aerospace, consumer electronics, and many other industries. This paper presents a design and analysis of an output‐feedback robust adaptive controller for multi‐input multi‐output continuous‐time systems in the presence of modeling errors and broadband output noise. The trade‐off between robust stability and performance improvement as well as practical design considerations for performance improvements are presented. It is demonstrated that proper shaping of the open‐loop plant singular values as well as over‐parameterizing the controller parametric model can significantly improve performance. Numerical simulations are performed to demonstrate the effectiveness of the proposed scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive function Q‐S synchronization of chaotic systems with unknown parameters

This work investigates the adaptive function Q‐S synchronization of non‐identical chaotic systems with unknown parameters. The sufficient conditions for achieving Q‐S synchronization with a desired scaling function of two different chaotic systems (including different dimensional systems) are derived based on the Lyapunov stability theory. By the adaptive control technique, the control laws and the corresponding parameter update laws are proposed such that the Q‐S synchronization of non‐identical chaotic systems is to be achieved. Finally, four illustrative numerical simulations are also given to demonstrate the effectiveness of the proposed scheme. Copyright © 2009 John Wiley & Sons, Ltd.     

一类非线性系统的自组织模糊神经网络控制

针对一类MIMO不确定非线性有干扰且控制增益符号未知的系统进行跟踪控制的问题,提出了一种在线自组织模糊神经网络的改进算法,用以克服参数选择困难的问题,并基于该算法给出了一种自适应鲁棒控制方法。首先基于主导输入的概念将MIMO系统分解为多个SISO系统构成的系统,然后结合自组织模糊神经网络在线对系统中的未知函数进行逼近,对网络结构和参数实现在线调节,再利用Nussbaum函数来克服控制增益符号未知,并且引入鲁棒项及复合误差的估计来补偿复合误差。最后基于Lyapunov稳定性理论证明了整个闭环系统半全局一致最终有界。理论和仿真结果表明提出方法的有效性。     

Identification of linear systems with time delay and unknown order

This paper proposes a system identification method for linear systems with time delay and unknown order. We hypothesize a number of candidate models, which have different order, because system order is unknown. In each model, we estimate the model parameters based on the maximum likelihood method by using nonlinear optimization technique. Then both local optimization technique and global search method are used because the estimated parameters may fall into a local minimum. After all candidate model's parameters are estimated, one model is selected among these models to estimate the system order by using a posteriori probability based on Bayes's theorem. Finally, the validity of the proposed method is demonstrated by numerical examples. © 2003 Wiley Periodicals, Inc. Electr Eng Jpn, 145(3): 61–68, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10166     

Accelerated neuroadaptive tracking control of strict‐feedback nonlinear systems without precise knowledge of target trajectory

The problem of tracking control under uncertain desired trajectory is interesting but nontrivial. The problem is even more challenging if the system under consideration involves modeling uncertainties. This paper investigates such problem for strict‐feedback nonlinear systems. By combining Fourier series with radial basis function neural networks (NNs), an analytical model is developed to reconstruct the unknown desired trajectory. Based on which, 2 neural adaptive control schemes are developed to maintain target tracking closely. The first control strategy is based on direct tuning of the NN weights, and the second strategy is built upon the concept of a virtual parameter related to NN weights, which substantially reduces the number of parameters to be online updated, rendering the strategy structurally simpler and computationally less expensive. The effectiveness of the proposed control strategy is confirmed by systematic stability analysis and numerical simulation.     

Adaptive variable universe of discourse fuzzy control for a class of nonlinear systems with unknown dead zones

In this paper, based on an adaptive nonbackstepping design algorithm, we proposed a novel variable universe of discourse fuzzy control (VUDFC) approach for a class of single‐input–single‐output strict‐feedback nonlinear systems with unknown dead‐zone inputs. Firstly, we convert the form of system into a normal form on the basis of some new state variables and coordinate transformation; at the same time, state‐feedback control is changed to output‐feedback control. Secondly, we design observers to estimate the new unmeasurable states. Then, different from considering the traditional backstepping‐based fuzzy control scheme, we introduce a direct VUDFC scheme, which is mainly based on changing of contraction‐expansion factors to modify the universe of discourse online, and fuzzy rules can automatically reproduce to develop the control performance; thus, the size of initial rule base is greatly reduced. This new algorithm can alleviate tracking error, improve the accuracy of the system, and strengthen robustness. Lastly, according to Lyapunov theorem analysis, we prove that all the signals in the closed‐loop system can be guaranteed to be stable, and the output can track the reference signal very well. Simulation results illustrated the effectiveness of the proposed VUDFC approach.     

The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input

This paper investigates the control of chaotic systems in the presence of unknown parameters, model uncertainties, and external disturbance. We first discuss the control of a class of chaotic systems and then investigate the control of general chaotic systems. Based on the adaptive control scheme, some novel criteria are proposed via a backstepping‐like procedure. As an example, the control of the Zhang hyperchaotic system is investigated via a single input. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Active fault tolerant control of piecewise affine systems with reference tracking and input constraints

An active fault tolerant control (AFTC) method is proposed for discrete‐time piecewise affine (PWA) systems. Only actuator faults are considered. The AFTC framework contains a supervisory scheme, which selects a suitable controller in a set of controllers such that the stability and an acceptable performance of the faulty system are held. The design of the supervisory scheme is not considered here. The set of controllers is composed of a normal controller for the fault‐free case, an active fault detection and isolation controller for isolation and identification of the faults, and a set of passive fault tolerant controllers (PFTCs) modules designed to be robust against a set of actuator faults. In this research, the piecewise nonlinear model is approximated by a PWA system. The PFTCs are state feedback laws. Each one is robust against a fixed set of actuator faults and is able to track the reference signal while the control inputs are bounded. The PFTC problem is transformed into a feasibility problem of a set of LMIs. The method is applied on a large‐scale live‐stock ventilation model. Copyright © 2013 John Wiley & Sons, Ltd.     

Model‐free fault‐tolerant control approach for uncertain state‐constrained linear systems with actuator faults

This paper investigates the robust adaptive fault‐tolerant control problem for state‐constrained continuous‐time linear systems with parameter uncertainties, external disturbances, and actuator faults including stuck, outage, and loss of effectiveness. It is assumed that the knowledge of the system matrices, as well as the upper bounds of the disturbances and faults, is unknown. By incorporating a barrier‐function like term into the Lyapunov function design, a novel model‐free fault‐tolerant control scheme is proposed in a parameter‐dependent form, and the state constraint requirements are guaranteed. The time‐varying parameters are adjusted online based on an adaptive method to prevent the states from violating the constraints and compensate automatically the uncertainties, disturbances, and actuator faults. The time‐invariant parameters solved by using data‐based policy iteration algorithm are introduced for helping to stabilize the system. Furthermore, it is shown that the states converge asymptotically to zero without transgression of the constraints and all signals in the resulting closed‐loop system are uniformly bounded. Finally, two simulation examples are provided to show the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust self‐tuning PI decoupling control of uncertain multivariable systems

In this paper, for a class of multivariable systems with strong couplings, a robust self‐tuning PI decoupling controller is developed by combining a self‐tuning PI controller with a feedforward decoupling compensator and a filter. To determine the gains and other parameters of the PI decoupling controller, we first introduced a reduced order model. The parameters of the reduced order model are identified by using a normalized projection algorithm with dead zone. The gains of the PI controller together with other parameters are tuned online according to the certainty equivalent principle. By resorting to time‐varying operation, we presented the bounded‐input bounded‐output stability conditions and convergence conditions of the closed‐loop system. Simulation results on a synthetic system and a twin‐tank level system show the effectiveness of the proposed method. Copyright © 2011 John Wiley & Sons, Ltd.     

A design of multivariable,self‐tuning PID controllers with an internal model structure

Self‐tuning control schemes (STC) are useful for systems with unknown or slowly time‐varying parameters. Some single‐input/single‐output PID control schemes based on STCs have been proposed for such systems. However, there are a lot of multivariable systems in real process industries. And these systems often have relatively large time delays. In this paper, a design scheme of self‐tuning PID control system is proposed for multivariable systems with unknown parameters and time delays. The controlled object is equipped with an internal model in order to compensate the time delay and also unstable zeros. Subsequently, a multivariable PID controller is designed for the augmented or compensated system. The PID parameters are calculated recursively based on the relationship between the minimum variance control law and the PID control law. A simulation example is presented to demonstrate the effectiveness of the proposed scheme. © 2004 Wiley Periodicals, Inc. Electr Eng Jpn, 146(4): 58–64, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10241     

Hybrid online learning control in networked multiagent systems: A survey

This survey paper studies deterministic control systems that integrate three of the most active research areas during the last years: (1) online learning control systems, (2) distributed control of networked multiagent systems, and (3) hybrid dynamical systems (HDSs). The interest for these types of systems has been motivated mainly by two reasons: First, the development of cheap massive computational power and advanced communication technologies, which allows to carry out large computations in complex networked systems, and second, the recent development of a comprehensive theory for HDSs that allows to integrate continuous‐time dynamical systems and discrete‐time dynamical systems in a unified manner, thus providing a unifying modeling language for complex learning‐based control systems. In this paper, we aim to give a comprehensive survey of the current state of the art in the area of online learning control in multiagent systems, presenting an overview of the different types of problems that can be addressed, as well as the most representative control architectures found in the literature. These control architectures are modeled as HDSs, which include as special subsets continuous‐time dynamical systems and discrete‐time dynamical systems. We highlight the different advantages and limitations of the existing results as well as some interesting potential future directions and open problems.     

A convex optimization approach to adaptive stabilization of discrete‐time LTI systems with polytopic uncertainties

This paper suggests a simple convex optimization approach to state‐feedback adaptive stabilization problem for a class of discrete‐time LTI systems subject to polytopic uncertainties. The proposed method relies on estimating the uncertain parameters by solving an online optimization at each time step, such as a linear or quadratic programming, and then, on tuning the control law with that information, which can be conceptually viewed as a kind of gain‐scheduling or indirect adaptive control. Specifically, an admissible domain of stabilizing state‐feedback gain matrices is designed offline by means of linear matrix inequality problems, and based on the online estimation of the uncertain parameters, the state‐feedback gain matrix is calculated over the set of stabilizing feedback gains. The proposed stabilization algorithm guarantees the asymptotic stability of the overall closed‐loop control system. An example is given to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Identification of time‐delay Markov jump autoregressive exogenous systems with expectation‐maximization algorithm

This paper is concerned with the identification problem of the Markov jump autoregressive exogenous system with an unknown time delay. The considered problem is solved using the expectation‐maximization algorithm, which estimates the parameters of local models, Markov transition probabilities, and time delay simultaneously. A numerical example and a simulated continuous fermentation reactor example are given to illustrate the capability of the proposed method. It shows that the influences of time delay during identification can be overcome by the proposed algorithm effectively.     

Global adaptive regulation control for a class of nonlinear systems with unknown control coefficients

This paper is concerned with the global asymptotic regulation control problem for a class of nonlinear uncertain systems with unknown control coefficients. The allowed class of uncertainties include unmeasured input‐to‐state stable (ISS) and/or weaker integral ISS (iISS) inverse dynamics, parametric uncertainties, and uncertain nonlinearities. By using the Nussbaum‐type gain technique and changing the ISS/integral ISS inverse dynamics supply rates, we design a dynamic output feedback controller which could guarantee that the system states are asymptotically regulated to the origin from any initial conditions, and the other signals are bounded in closed‐loop systems. The numerical example of a simple pendulum with all unknown parameters and without velocity measurement illustrates our theoretical results. The simulation results demonstrate its efficacy. Copyright © 2015 John Wiley & Sons, Ltd.     

A decentralized model following controllers for a class of large‐scale interconnected dynamical systems with uncertainties

The problem of decentralized robust tracking and model following is considered for a class of large‐scale interconnected systems with uncertainties. A class of linear decentralized state feedback controllers are proposed for robust tracking of dynamical signals in such a class of uncertain large‐scale systems. The proposed decentralized tracking controllers can guarantee that the tracking errors between each subsystem and local reference model are uniformly ultimately bounded. Moreover, we modify the linear controllers by introducing some nonlinear parts so that the tracking errors decrease asymptotically to zero in the presence of uncertain parameters and interconnection terms. Finally, an illustrative example is given to demonstrate the validity of our results. © 2002 Wiley Periodicals, Inc. Electr Eng Jpn, 142(2): 48–58, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/eej.10101