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  • LJUNG Lennart
    Journal of Systems Science and Complexity. 2021, 34(5): 1598-1603.
    The paper contains a discussion of earlier work on Total Model Errors and Model Validation. It is maintained that the recent change of paradigm to kernel based system identification has also affected the basis for (and interest in) giving bounds for the total model error.
  • ANDERSON Brian D. O. · YE Mengbin
    Journal of Systems Science and Complexity. 2021, 34(5): 1604-1633.
    In social networks where individuals discuss opinions on a sequence of topics, the selfconfidence an individual exercises in relation to one topic, as measured by the weighting given to their own opinion as against the opinion of all others, can vary in the light of the self-appraisal by the individual of their contribution to the previous topic. This observation gives rise to a type of model termed a DeGroot-Friedkin model. This paper reviews a number of results concerning this model. These include the asymptotic behavior of the self-confidence (as the number of topics goes to infinity), the possible emergence of an autocrat or small cohort of leaders, the effect of changes in the weighting given to opinions of others (in the light for example of their perceived expertise in relation to a particular topic under discussion), and the inclusion in the model of individual behavioral characteristics such as humility, arrogance, etc. Such behavioral characteristics create new opportunities for autocrats to emerge.
  • BAS¸AR Tamer
    Journal of Systems Science and Complexity. 2021, 34(5): 1634-1665.
    This is an overview paper on the relationship between risk-averse designs based on exponential loss functions with or without an additional unknown (adversarial) term and some classes of stochastic games. In particular, the paper discusses the equivalences between risk-averse controller and filter designs and saddle-point solutions of some corresponding risk-neutral stochastic differential games with different information structures for the players. One of the by-products of these analyses is that risk-averse controllers and filters (or estimators) for control and signal-measurement models are robust, through stochastic dissipation inequalities, to unmodeled perturbations in controlled system dynamics as well as signal and the measurement processes. The paper also discusses equivalences between risk-sensitive stochastic zero-sum differential games and some corresponding risk-neutral three-player stochastic zero-sum differential games, as well as robustness issues in stochastic nonzero-sum differential games with finite and infinite populations of players, with the latter belonging to the domain of mean-field games.
  • CHENG Daizhan · WU Yuhu · ZHAO Guodong · FU Shihua
    Journal of Systems Science and Complexity. 2021, 34(5): 1666-1680.
    Nowadays the semi-tensor product (STP) approach to finite games has become a promising new direction. This paper provides a comprehensive survey on this prosperous field. After a brief introduction for STP and finite (networked) games, a description for the principle and fundamental technique of STP approach to finite games is presented. Then several problems and recent results about theory and applications of finite games via STP are presented. A brief comment about the potential use of STP to artificial intelligence is also proposed.
  • CHEN Shuhang · DEVRAJ Adithya · BERSTEIN Andrey · MEYN Sean
    Journal of Systems Science and Complexity. 2021, 34(5): 1681-1702.
    Several decades ago, Profs. Sean Meyn and Lei Guo were postdoctoral fellows at ANU, where they shared interest in recursive algorithms. It seems fitting to celebrate Lei Guo’s 60th birthday with a review of the ODE Method and its recent evolution, with focus on the following themes: • The method has been regarded as a technique for algorithm analysis. It is argued that this viewpoint is backwards: The original stochastic approximation method was surely motivated by an ODE, and tools for analysis came much later (based on establishing robustness of Euler approximations). The paper presents a brief survey of recent research in machine learning that shows the power of algorithm design in continuous time, following by careful approximation to obtain a practical recursive algorithm. • While these methods are usually presented in a stochastic setting, this is not a prerequisite. In fact, recent theory shows that rates of convergence can be dramatically accelerated by applying techniques inspired by quasi Monte-Carlo. • Subject to conditions, the optimal rate of convergence can be obtained by applying the averaging technique of Polyak and Ruppert. The conditions are not universal, but theory suggests alternatives to achieve acceleration. • The theory is illustrated with applications to gradient-free optimization, and policy gradient algorithms for reinforcement learning.
  • YIN George · WEN Zhexin · QIAN Hongjiang · NGUYEN Huy
    Journal of Systems Science and Complexity. 2021, 34(5): 1703-1722.
    This work is concerned with controlled stochastic Kolmogorov systems. Such systems have received much attention recently owing to the wide range of applications in biology and ecology. Starting with the basic premise that the underlying system has an optimal control, this paper is devoted to designing numerical methods for approximation. Different from the existing literature on numerical methods for stochastic controls, the Kolmogorov systems take values in the first quadrant. That is, each component of the state is nonnegative. The work is designing an appropriate discrete-time controlled Markov chain to be in line with (locally consistent) the controlled diffusion. The authors demonstrate that the Kushner and Dupuis Markov chain approximation method still works. Convergence of the numerical scheme is proved under suitable conditions.
  • XIAO Wei · CASSANDRAS G. Christos · BELTA Calin
    Journal of Systems Science and Complexity. 2021, 34(5): 1723-1742.
    This paper presents an overview of the state of the art for safety-critical optimal control of autonomous systems. Optimal control methods are well studied, but become computationally infeasible for real-time applications when there are multiple hard safety constraints involved. To guarantee such safety constraints, it has been shown that optimizing quadratic costs while stabilizing affine control systems to desired (sets of) states subject to state and control constraints can be reduced to a sequence of Quadratic Programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). The CBF method is computationally efficient, and can easily guarantee the satisfaction of nonlinear constraints for nonlinear systems, but its wide applicability still faces several challenges. First, safety is hard to guarantee for systems with high relative degree, and the above mentioned QPs can easily be infeasible if tight or time-varying control bounds are involved. The resulting solution is also sub-optimal due to its myopic solving approach. Finally, this method works conditioned on the system dynamics being accurately identified. The authors discuss recent solutions to these issues and then present a framework that combines Optimal Control with CBFs, hence termed OCBF, to obtain near-optimal solutions while guaranteeing safety constraints even in the presence of noisy dynamics. An application of the OCBF approach is included for autonomous vehicles in traffic networks.
  • LIU Wei · HUANG Jie
    Journal of Systems Science and Complexity. 2021, 34(5): 1743-1765.
    This paper investigates the semi-global robust output regulation problem for a class of uncertain nonlinear systems via a sampled-data output feedback control law. What makes the results interesting is that the nonlinearities of the proposed system do not have to satisfy linear growth condition and the uncertain parameters of our system are allowed to belong to some arbitrarily large prescribed compact subset. Two cases are considered. The first case is that the exogenous signal is constant. The second case is that the exogenous signal is time-varying and bounded. For the first case, the authors solve the problem exactly in the sense that the tracking error approaches zero asymptotically. For the second case, the authors solve the problem practically in the sense that the steady-state tracking error can be made arbitrarily small. Finally, an example is given to illustrate the effectiveness of our approach.
  • XIE Siyu · WANG Le Yi
    Journal of Systems Science and Complexity. 2021, 34(5): 1766-1781.
    Optimization methods in cyber-physical systems do not involve parameter uncertainties in most existing literature. This paper considers adaptive optimization problems in which searching for optimal solutions and identifying unknown parameters must be performed simultaneously. Due to the dual roles of the input signals on achieving optimization and providing persistent excitation for identification, a fundamental conflict arises. In this paper, a method of adding a small deterministic periodic dither signal to the input is deployed to resolve this conflict and provide sufficient excitation for estimating the unknown parameters. The designing principle of the dither is discussed. Under dithered inputs, the authors show that simultaneous convergence of parameter estimation and optimization can be achieved. Convergence properties and convergence rates of parameter estimation and optimization variable updates are presented under the scenarios of uncertainty-free observations and systems with noisy observation and unmodeled components. The fundamental relationships and tradeoff among updating step sizes, dither magnitudes, parameter estimation errors, optimization accuracy, and convergence rates are further investigated.
  • LI Wuquan · KRSTIC Miroslav
    Journal of Systems Science and Complexity. 2021, 34(5): 1782-1800.
    A new prescribed-time state-feedback design is presented for stochastic nonlinear strictfeedback systems. Different from the existing stochastic prescribed-time design where scaling-free quartic Lyapunov functions or scaled quadratic Lyapunov functions are used, the design is based on new scaled quartic Lyapunov functions. The designed controller can ensure that the plant has an almost surely unique strong solution and the equilibrium at the origin of the plant is prescribed-time mean-square stable. After that, the authors redesign the controller to solve the prescribed-time inverse optimal mean-square stabilization problem. The merit of the design is that the order of the scaling function in the controller is reduced dramatically, which effectively reduces the control effort. Two simulation examples are given to illustrate the designs.
  • LOURENC¸O Inˆes · MATTILA Robert · ROJAS Cristian R. · HU Xiaoming · WAHLBERG Bo
    Journal of Systems Science and Complexity. 2021, 34(5): 1801-1820.
    A hidden Markov model (HMM) comprises a state with Markovian dynamics that can only be observed via noisy sensors. This paper considers three problems connected to HMMs, namely, inverse filtering, belief estimation from actions, and privacy enforcement in such a context. First, the authors discuss how HMM parameters and sensor measurements can be reconstructed from posterior distributions of an HMM filter. Next, the authors consider a rational decision-maker that forms a private belief (posterior distribution) on the state of the world by filtering private information. The authors show how to estimate such posterior distributions from observed optimal actions taken by the agent. In the setting of adversarial systems, the authors finally show how the decision-maker can protect its private belief by confusing the adversary using slightly sub-optimal actions. Applications range from financial portfolio investments to life science decision systems.
  • QIU Li · CHEN Wei · WANG Dan
    Journal of Systems Science and Complexity. 2021, 34(5): 1821-1839.
    Year 2021 is special. It sees the renaissance of concept of phase and the birth of a phase theory for matters much beyond complex numbers and single-input single-output (SISO) linear timeinvariant (LTI) systems while we celebrate the 60th birthday of Lei Guo, an exemplary research leader of our times. Here we give a short tutorial of the newly developed phase theory, as a birthday present.
  • LI Yibei · WAHLBERG Bo · HU Xiaoming
    Journal of Systems Science and Complexity. 2021, 34(5): 1840-1857.
    In this paper, the inverse linear quadratic (LQ) problem over finite time-horizon is studied. Given the output observations of a dynamic process, the goal is to recover the corresponding LQ cost function. Firstly, by considering the inverse problem as an identification problem, its model structure is shown to be strictly globally identifiable under the assumption of system invertibility. Next, in the noiseless case a necessary and sufficient condition is proposed for the solvability of a positive semidefinite weighting matrix and its unique solution is obtained with two proposed algorithms under the condition of persistent excitation. Furthermore, a residual optimization problem is also formulated to solve a best-fit approximate cost function from sub-optimal observations. Finally, numerical simulations are used to demonstrate the effectiveness of the proposed methods.
  • QI Tian · CHEN Jie
    Journal of Systems Science and Complexity. 2021, 34(5): 1858-1878.
    This paper studies the stabilizability and stabilization of continuous-time systems in the presence of stochastic multiplicative uncertainties. The authors consider multi-input, multi-output (MIMO) linear time-invariant systems subject to multiple static, structured stochastic uncertainties, and seek to derive fundamental conditions to ensure that a system can be stabilized under a mean-square criterion. In the stochastic control framework, this problem can be considered as one of optimal control under state- or input-dependent random noises, while in the networked control setting, a problem of networked feedback stabilization over lossy communication channels. The authors adopt a mean-square small gain analysis approach, and obtain necessary and sufficient conditions for a system to be meansquare stabilizable via output feedback. For single-input, single-output (SISO) systems, the condition provides an analytical bound, demonstrating explicitly how plant unstable poles, nonminimum phase zeros, and time delay may impose a limit on the uncertainty variance required for mean-square stabilization. For MIMO minimum phase systems with possible delays, the condition amounts to solving a generalized eigenvalue problem, readily solvable using linear matrix inequality optimization techniques.
  • LI Jinggai · JI Ye · ZHU Chungang
    Journal of Systems Science and Complexity. 2021, 34(1): 21-46.

    De Casteljau algorithm and degree elevation of B´ezier and NURBS curves/surfaces are two important techniques in computer aided geometric design. This paper presents the de Casteljau algorithm and degree elevation of toric surface patches, which include tensor product and triangular rational B´ezier surfaces as special cases. Some representative examples of toric surface patches with common shapes are illustrated to verify these two algorithms. Moreover, the authors also apply the degree elevation of toric surface patches to isogeometric analysis. And two more examples show the effectiveness of proposed method.

  • NI Qian · DENG Jiansong · WANG Xuhui
    Journal of Systems Science and Complexity. 2021, 34(1): 47-67.

    This paper presents an adaptive collocation method with weighted extended PHT-splines. The authors modify the classification rules for basis functions based on the relation between the basis vertices and the computational domain. The Gaussian points are chosen to be collocation points since PHT-splines are C1 continuous. The authors also provide relocation techniques to resolve the mismatch problem between the number of basis functions and the number of interpolation conditions. Compared to the traditional Greville collocation method, the new approach has improved accuracy with fewer oscillations. Several numerical examples are also provided to test our the proposed approach.

  • WANG Guangyu · XU Gang · WU Qing · WU Xundong
    Journal of Systems Science and Complexity. 2021, 34(1): 68-82.

    This paper proposes a two-stage point cloud super resolution framework that combines local interpolation and deep neural network based readjustment. For the first stage, the authors apply a local interpolation method to increase the density and uniformity of the target point cloud. For the second stage, the authors employ an outer-product neural network to readjust the position of points that are inserted at the first stage. Comparison examples are given to demonstrate that the proposed framework achieves a better accuracy than existing state-of-art approaches, such as PU-Net, PointNet and DGCNN (Source code is available at

  • YUAN Chunming · MI Zhenpeng · JIA Xiaohong · LIN Fengming · SHEN Liyong
    Journal of Systems Science and Complexity. 2021, 34(1): 83-106.

    Tool path generation is a fundamental problem in 5-axis CNC machining, which consists of tool orientation planning and cutter-contact (CC) point planning. The planning strategy highly depends on the type of tool cutters. For ball-end cutters, the tool orientation and CC point location can be planned separately; while for flat end cutters, the two are highly dependent on each other. This paper generates a smooth tool path of workpiece surfaces for flat end mills from two stages: Computing smooth tool orientations on the surface without gouging and collisions and then designing the CC point path. By solving the tool posture optimization problem the authors achieve both the path smoothness and the machining efficiency. Experimental results are provided to show the effectiveness of the method.

  • WANG Rong-Hua
    Journal of Systems Science and Complexity. 2021, 34(1): 107-121.

    In 2014, Chen and Singer solved the summability problem of bivariate rational functions. Later an algorithmic proof was presented by Hou and the author. In this paper, the algorithm will be simplified and adapted to the q-case.

  • ZHANG Runfa · BILIGE Sudao · CHAOLU Temuer
    Journal of Systems Science and Complexity. 2021, 34(1): 122-139.

    This paper extends a method, called bilinear neural network method (BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this method. These test functions are composed of specific activation functions of single-layer model, specific activation functions of “2-2” model and arbitrary functions of “2-2-3” model. By means of the BNNM, nineteen sets of exact analytical solutions and twenty-four arbitrary function solutions of the dimensionally reduced p-gBKP equation are obtained via symbolic computation with the help of Maple. The fractal solitons waves are obtained by choosing appropriate values and the self-similar characteristics of these waves are observed by reducing the observation range and amplifying the partial picture. By giving a specific activation function in the single layer neural network model, exact periodic waves and breathers are obtained. Via various three-dimensional plots, contour plots and density plots, the evolution characteristic of these waves are exhibited.

  • ZHANG Yaqi · GUO Lei
    Journal of Systems Science and Complexity. 2021, 34(1): 236-250.

    In the classical theory of self-tuning regulators, it always requires that the conditional variances of the systems noises are bounded. However, such a requirement may not be satisfied when modeling many practical systems, and one significant example is the well-known ARCH (autoregressive conditional heteroscedasticity) model in econometrics. The aim of this paper is to consider self-tuning regulators of linear stochastic systems with both unknown parameters and conditional heteroscedastic noises, where the adaptive controller will be designed based on both the weighted least-squares algorithm and the certainty equivalence principle. The authors will show that under some natural conditions on the system structure and the noises with unbounded conditional variances, the closed-loop adaptive control system will be globally stable and the tracking error will be asymptotically optimal. Thus, this paper provides a significant extension of the classical theory on self-tuning regulators with expanded applicability.

  • GAO Yue · FAN Ying · DI Zengru
    Journal of Systems Science and Complexity. 2021, 34(1): 251-264.

    The formation of public opinion on the network is a hot issue in the field of complex network research, and some classical dynamic models are used to solve this problem. The signed network is a particular form of the complex network, which can adequately describe the amicable and hostile relationships in complex real-world systems. However, the methods for studying the dynamic process of public opinion propagation on signed networks still require to be further discussed. In this paper, the authors pay attention to the influence of negative edges in order to design a two-state public opinion propagation mechanism suitable for signed networks. The authors first set the interaction rules between nodes and the transition rules of node states and then apply the model to synthetic and real-world signed networks. The simulation results show that there is a critical value of the negative edge ratio. When the negative edge ratio exceeds this critical value, the evolutionary result of public opinion will change from a consistent state to a split state. This conclusion is also consistent with the distribution result of opinions within communities in the signed network. Besides, the research on the network structural balance shows that the model makes the network evolve in a more balanced direction.

  • WANG Zhao · SUN Jian · BAI Yongqiang
    Journal of Systems Science and Complexity. 2021, 34(1): 265-280.

    Networked control systems (NCSs) are facing a great challenge from the limitation of network communication resources. Event-triggered control (ETC) is often used to reduce the amount of communication while still keeping a satisfactory performance of the system, by transmitting the measurements only when an event-triggered condition is satisfied. However, some network-induced problems would happen inevitably, such as communication delay and packet loss, which can degrade the control performance significantly and can even lead to instability. In this paper, a periodic eventtriggered NCS considering both time-varying delay and packet loss is studied. The system is discretized into a piecewise linear system with uncertainty. Then the model is handled by a polytopic overapproximation method to be more suitable for stability analysis. Finally, stability conditions are obtained and presented in terms of linear matrix inequalities (LMIs). The result is illustrated by a numerical example.