Analysis and design of control systems via parameter‐based approach

Abstract

Control laws can be constructed in systems design by introducing parameters to obtain good system performance or robustness. A typical example of such a class of design approaches is the high-gain design approach. In the design of high-gain controllers, an introduction of a parameter results in a family of feedback control laws. Such a feedback law is given by a parametrized gain matrix which approaches infinity as the introduced parameter approaches its extreme value. Such a class of design approach can be called a parameter-based approach. Another case of the parameter-based approach is to establish mathematical models by introducing some extra parameters. A typical example is to derive the mathematical model of a spacecraft by unit quaternions which are constructed by introducing three extra parameters i, j and k with the properties i 2 = j 2 = k 2 = − 1 ${i^2} = {j^2} = {k^2} = - 1$ , i j = k $ij\; = {\rm{\;}}k$ , j k = i $jk\; = {\rm{\;}}i$ and k i = j $ki\; = {\rm{\;}}j$ . This Special Issue aims to present the recent development of the parameter-based approach in analysing and designing control systems. The theme of this special issue can be divided into three parts: Model construction by introducing parameters, control law design by introducing parameters and parametric solutions to control-related matrix equations. This topic includes 6 papers. Qi et al., in their paper ‘Finite-time attitude consensus control for multiple rigid spacecraft based on distributed observers’, use unit quaternions, which are constructed by, to investigate attitude consensus control for multiple rigid spacecraft. Based on this model, a group of distributed finite-time observers is constructed for each follower, and then an attitude control protocol based on a fast nonsingular terminal sliding mode is proposed by using the observed information. In the papers ‘Adaptive dual model predictive control for linear systems with parametric uncertainties’ by Lin et al. and ‘Generalized predictive controller (GPC) design on single-phase full-bridge inverter with a novel identification method’ by Ghamari et al., regressive models including the unknown parameters are used, and the dual adaptive model predictive control (MPC) and the generalized MPC are respectively proposed by incorporating least squares identification algorithms. In the paper ‘A recursive identification algorithm for linear discrete periodic systems’ by Lv et al., a periodic autoregressive and moving average (ARMA) model of a linear discrete-time periodically time-varying system is transformed into a time-invariant ARMA model by adopting cyclic lifting techniques. With this model, the considered system is described by a regressive form with the unknown coefficients as parameters, and then the corresponding least squares identification algorithm is proposed. Cai et al., in their paper ‘Design of LPV controller for morphing aircraft using inexact scheduling parameters’, establish a linear parameter-varying model for a morphing aircraft by Jacobian linearization. In this model, there exist a group of scheduling parameters. With such a model, Cai et al. investigate the design problem of gain-scheduled output-feedback controllers by using inexact scheduling parameters for morphing aircraft during the wing transition process. Liu et al., in their paper ‘Event-triggered fuzzy output feedback fault-tolerant control for interval type-2 Takagi-Sugeno large-scale systems with time delays’, propose an observer-based event-triggered fault-tolerant control law for a class of T-S fuzzy systems. In order to obtain the desired control laws, the considered T-S fuzzy system is represented as a linearly-parameterized dynamical system by introducing a set of parameters related to the membership functions. This topic includes 6 papers. Jin et al., in their paper ‘Optimal control of nonlinear Markov jump systems by control parametrization technique’, investigate the optimal control problem for nonlinear Markov jump systems with continuous state inequality constraints. In this paper, the control parametrization technique is used to represent the control function by a piecewise constant function. In such a representation, the heights of the piecewise constant function on the subintervals are the introduced parameters, and can be taken as decision variables to be optimized. With such an efficient treatment, the original problem is converted into an approximate finite-dimensional optimization problem. Huang et al., in their paper ‘Fixed-time fault-tolerance attitude tracking control for spacecraft without unwinding’, propose a disturbance-observer-based fixed-time fault-tolerance control law for rigid spacecraft by adopting backstepping techniques. Some design parameters exist in the part of the observer and the part of the fixed-time control law. In addition, the singularity problem in traditional fixed-time controllers based on signal function is eliminated with the aid of the arctangent function in the proposed controller. Wu et al., in their paper ‘Fractional-order sliding mode attitude coordinated control for spacecraft formation flying with unreliable wireless communication’, present two types of fractional order sliding mode control protocols to solve the coordinated attitude control problem for spacecraft formation flying. The introduced design parameters in these protocols can be appropriately chosen to improve convergence speed. It should be pointed out that a set of weighting parameters are introduced in the first class control protocol such that some nonlinear functions can be approximated by Chebyshev neural network. In the paper ‘Asymptotic stabilization for nonlinear systems with time-varying delays’, Li et al. present a novel output feedback control law for a class of nonlinear systems with unknown time-varying delays by introducing the static gain functions as parameters. In addition, in the control law there also exists another positive parameter which can be adjusted to improve system performance. Bi, in his paper ‘Neural networks adaptive control for fractional-order nonlinear with unmodelled dynamics and actuator faults’, investigate the problem of fault-tolerant control for fractional-order nonlinear systems. Two groups of parameters are introduced to construct the control law. The first group of parameters are introduced in the neural networks to approximate unknown nonlinear functions in the system, and the second group of parameters are dynamic, and its evolution law is given by a fractional-order adaptation law. Hou et al., in their paper ‘Fuzzy linear extended states observer based iteration learning fault-tolerant control for autonomous underwater vehicle trajectory tracking system’, develops a fault-tolerant control law based on a linear extended state observer (LESO) for autonomous underwater vehicles. In this control law, the LESO includes some parameters to be adjusted. This topic includes two papers. In these two papers, two classes of matrix equations with their applications in systems control are investigated. Cao et al., in their paper ‘Output feedback based poles configuration for LDP systems with varying state and input dimension’, convert the problem of poles configuration via periodic output feedback for linear discrete periodic systems into the problem of solving a class of special Sylvester matrix equations. A parametric solution to this class of matrix equations is presented in this paper, and then the output feedback gains for the periodic system are provided based on this parametric solution. Lei Zhang et al., in their paper ‘On the solutions to Sylvester-conjugate periodic matrix equations via iteration’, develop an iterative algorithm to solve the so-called Sylvester-conjugate periodic matrix equations. In this algorithm, two scalar parameters are involved. When the gradient principle is applied to a quadratic index function related to the considered matrix equations, the explicit expressions for these two scalars are determined, and in this case the developed algorithm is finite-time convergent. All of the papers selected for this Special Issue show that the parameter-based approach plays an importantly instrumental role in the analysis and design of control systems. It can be observed from these papers and some existing results that many control problems can be cast into such a framework. It is expected that this parameter-based approach can be further applied in more aspects of control systems design. Ai-Guo Wu was born in Gong'an, Hubei, China, in 1980. He received the B.Eng. degree in automation, an M.Eng. degree in navigation, guidance and control, and the Ph.D. degree in control science and engineering from the Harbin Institute of Technology, in 2002, 2004, and 2008, respectively. In 2008, he joinedthe Shenzhen Graduate School, Harbin Institute of Technology as an Assistant Professor, where he was promoted to Professor in 2012. He was a Research Fellow with the Department of Manufacturing Engineering and Engineering Management, City University of Hong Kong, from 2009 to 2011. He was a Visiting Professor with the Department of Electrical, Electronic and Computer Engineering, The University of Western Australia, Australia, from 2013 to 2014. Since 2018, he has been a Professor at Harbin Institute of Technology (Shenzhen). His research interests include spacecraft control, time delay systems, fully actuated systems theory, and robust control. He has authored/co-authored one English monograph and over 100 SCI journal papers. He received the National Natural Science Award (Second Prize) from China in 2015, and the National Excellent Doctoral Dissertation Award from the Academic Degrees Committee of the State Council and the Ministry of Education of China in 2011. He was supported by the Program for New Century Excellent Talents in Universities in 2011, and by the National Natural Science Foundation of China for Excellent Young Scholars in 2018. He has been serving as a Regional Editor for Nonlinear Dynamics and Systems Theory since 2015, and an International Subject Editor for Applied Mathematical Modeling since 2017. Zheng-Guang Wu (Member, IEEE) was born in 1982. He received the B.S. and M.S. degrees in mathematics from Zhejiang Normal University, Jinhua, China, in 2004 and 2007, respectively, and the Ph.D. degree in control science and engineering from Zhejiang University, Hangzhou, China,in 2011. He has authored or co-authored over 100 papers in refereed international journals. His current research interests include hybrid systems, Markov jump systems, sampled-data systems, fuzzy systems, multi-agent systems, Boolean control networks, stochastic systems, and neural networks. Dr. Wu also serves as an Associate Editor/Editorial Board Member for some international journals, such as the IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS, the Journal of The Franklin Institute, Neurocomputing, the International Journal ofControl, Automation, and Systems, IEEE ACCESS, the International Journal of Sensors, Wireless Communications and Control, and IEEE Control Systems Society Conference Editorial Board. He was named a Highly Cited Researcher (Clarivate Analytics). He is also an Invited Reviewer of Mathematical Reviews of the American Mathematical Society. Victor Sreeram obtained Bachelor's degree in 1981 from Bangalore University, India, a Master's degree in 1983 from Madras University, India, and Ph.D. degree from the University of Victoria, British Columbia, Canada in 1990, all in Electrical Engineering. He worked as a Project Engineer in the Indian Space Research Organisation from 1983 to 1985. He joined the Department of Electrical, Electronic, and Computer Engineering, the University of Western Australia in 1990 as a lecturer and he is now a Professor and the Head of Department. He was a Graduate Research Coordinator from 2008 to 2017. He is an associated editor of IET Control Theory and Applications, and the Asian Journal of Control. He is currently the Vice President of the Asian Control Association for Technical Activities and the Chairman of the Australia New Zealand Control Conference Steering Committee Association Incorporated. He has authored over 250 publications including over 125 journal publications. He is a co-recipient of the 2012 Premium Award for Best Paper in IET Power Electronics, and the 2014 Premium Award for Best Paper in IET Generation, Transmission & Distribution. He is also a recipient of the 2013 Outstanding Reviewer for IEEE Transactions on Automatic Control Award. He is now a Fellow of the Institution of Engineers, Australia. He has successfully supervised over 25 PhD students and has examined over 50 PhD theses in his career. His teaching and research interests are Control Systems, Signal Processing, Communications, Power engineering and Smart Grid and Renewable Energy. Xiaofeng Wang is an associate professor in the Department of Electrical Engineering at the University of South Carolina, Columbia. He earned his B.S. degree in Applied Mathematics and M.S. in Operation Research and Control Theory from East China Normal University, China, in 2000 and2003, respectively, and obtained his PhD degree in Electrical Engineering from the University of Notre Dame in 2009. After that, he worked as postdoctoral research associate at the University of Illinois at Urbana and Champaign and then joined the University of South Carolina in 2012. His research interests include robotics and control, cyber-physical systems, networked control systems, robust adaptive control, and optimization. He is an associate editor of Journal of The Franklin Institute since 2015 and IEEE Transactions on Aerospace and Electronic Systems since 2021. He is also an associate editor of IEEE Control Systems Society Conference Editorial Board since 2018. He was the recipient of the best paper award in the Annual Conference of the Prognostics and Health Management Society in 2014. The authors declare no conflicts of interest.