In this paper, the problem of identifying autoregressive-moving-average systems under random threshold binary-valued output measurements is considered. With the help of stochastic approximation algorithms with expanding truncations, the authors give the recursive estimates for the parameters of both the linear system and the binary sensor. Under reasonable conditions, all constructed estimates are proved to be convergent to the true values with probability one, and the convergence rates are also established. A simulation example is provided to justify the theoretical results.

The scheduling problem in surgery is difficult because, in addition of the planning of the operating rooms which are the most expensive resources in hospitals, each surgery requires a combination of human and material resources. In this paper, the authors address a surgery scheduling problem which arises in operated health care facility. Moreover, the authors consider simultaneously materiel and human resources. This problem is a three-stages flow shop scheduling environment. The first stage (ward) contains a limited number of resources of the same type (beds); The second stage contains different resources with limited capacity (operating rooms, surgeons, nurses, anesthesiologists) and the third stage contains a limited number of recovery beds. There is also a limited number of transporters (porters) between the ward and the other stages. The objective of the problem is to minimize the completion time of the last patient (makespan). The authors formulate this NP-Hard problem in a mixed integer programming model and conduct computational experiments to evaluate the performance of the proposed model.

Curve interpolation with B-spline is widely used in various areas. This problem is classic and recently raised in application scenario with new requirements such as path planning following the tangential vector field under certified error in CNC machining. This paper proposes an algorithm framework to solve Hausdorff distance certified cubic B-spline interpolation problem with or without tangential direction constraints. The algorithm has two stages: The first stage is to find the initial cubic B-spine fitting curve which satisfies the Hausdorff distance constraint; the second stage is to set up and solve the optimization models with certain constraints. Especially, the sufficient conditions of the global Hausdorff distance control for any error bound are discussed, which can be expressed as a series of linear and quadratic constraints. A simple numerical algorithm to compute the Hausdorff distance between a polyline and its B-spline interpolation curve is proposed to reduce our computation. Experimental results are presented to show the advantages of the proposed algorithms.

The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger operator. The proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the problem. These improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded domains. The authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger operators. As an application, the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.

In this paper, the authors propose Neumann series neural operator (NSNO) to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions. Helmholtz equation is a crucial partial differential equation (PDE) with applications in various scientific and engineering fields. However, efficient solver of Helmholtz equation is still a big challenge especially in the case of high wavenumber. Recently, deep learning has shown great potential in solving PDEs especially in learning solution operators. Inspired by Neumann series in Helmholtz equation, the authors design a novel network architecture in which U-Net is embedded inside to capture the multiscale feature. Extensive experiments show that the proposed NSNO significantly outperforms the state-ofthe-art FNO with at least 60% lower relative L²-error, especially in the large wavenumber case, and has 50% lower computational cost and less data requirement. Moreover, NSNO can be used as the surrogate model in inverse scattering problems. Numerical tests show that NSNO is able to give comparable results with traditional finite difference forward solver while the computational cost is reduced tremendously.

This paper focuses on the disturbance suppression issue of hidden semi-Markov jump systems leveraging composite control. The system consists of a semi-Markov layer and an observed mode sequence layer, and it is subject to a matched disturbance generated by an exogenous system and a mismatched disturbance that is norm bounded. The proposal is to design a composite controller based on a disturbance observer to counteract and attenuate the disturbances effectively. By constructing a special Lyapunov function comparison point, the exponential stability is analyzed with the stability criterion in the form of linear matrix inequality is established. Two simulation examples are provided to demonstrate the practical merits of the composite controller relative to the single H_∞ control.

This paper investigates the networked evolutionary games (NEGs) with profile-dependent delays, including modeling and stability analysis. Profile-dependent delay, which varies with the game profiles, slows the information transmission between participants. Firstly, the dynamics model is proposed for the profile-dependent delayed NEG, then the algebraic formulation is established using the algebraic state space approach. Secondly, the dynamic behavior of the game is discussed, involving general stability and evolutionarily stable profile analysis. Necessary and sufficient criteria are derived using the matrices, which can be easily verified by mathematical software. Finally, a numerical example is carried out to demonstrate the validity of the theoretical results.

The cross-dimensional dynamical systems have received increasing research attention in recent years. This paper characterizes the structure features of the cross-dimensional vector space. Specifically, it is proved that the completion of cross-dimensional vector space is an infinite-dimensional separable Hilbert space. Hence, it means that one can isometrically and linearly embed the cross-dimensional vector space into the $\ell^{2}$, which is known as the space of square summable sequences. This result will be helpful in the modeling and analyzing the dynamics of cross-dimensional dynamical systems.

This paper studies the cluster consensus of multi-agent systems (MASs) with objective optimization on directed and detail balanced networks, in which the global optimization objective function is a linear combination of local objective functions of all agents. Firstly, a directed and detail balanced network is constructed that depends on the weights of the global objective function, and two kinds of novel continuous-time optimization algorithms are proposed based on time-invariant and timevarying objective functions. Secondly, by using fixed-time stability theory and convex optimization theory, some sufficient conditions are obtained to ensure that all agents’ states reach cluster consensus within a fixed-time, and asymptotically converge to the optimal solution of the global objective function. Finally, two examples are presented to show the efficacy of the theoretical results.

The tracking problem of uncertain nonstrict-feedback nonlinear systems (UNFNS) is examined to develop a novel adaptive neural control scheme to ensure fixed-time convergence. In particular, the challenge associated with the unknown nonlinear function can be overcome through neural network (NN) based estimation. Therefore, an NN-based adaptive fixed-time control scheme is established with only one parameter, using the property of the basis function vector to address the algebraic loop problem. Furthermore, the singularity problem can be solved by incorporating a smooth switching function. A rigorous theoretical analysis is performed to demonstrate that the output signal can track the reference signal within a fixed time and that the signals in the control systems are bounded. Finally, numerical simulations are performed to validate the feasibility of the proposed methodology.

This paper studies the output consensus problem of heterogeneous linear stochastic multiagent systems with multiplicative noises in system parameters and measurements, where the system noise in each agent is allowed to be different. By employing stochastic output regulation theory and the stochastic Lyapunov function approach, a composite controller embedded with stochastic output regulator equations (SOREs) and a stochastic dynamic compensator is designed to achieve the meansquare output consensus of the multi-agent systems. To implement the consensus algorithm, a sufficient condition for feasible solutions of the SOREs is first established in terms of Lyapunov and Selvester equations. Then the time-varying SOREs are approximated by the Euler-Maruyama method combined with an a-posteriori partial estimation of the increments of the Brownian motion. A numerical example illustrates the theoretical results.

This paper studies the formation control problem for the second-order heterogeneous nonlinear multi-agent systems (MASs) with switching topology and quantized control inputs. Compared with formation control under the fixed topology, under the switching topology inherent nonlinear dynamics of the agent and the connectivity change of the communication topology are considered. Moreover, to avoid the chattering phenomenon caused by unknown input disturbances, the hysteretic quantizers are incorporated to quantize the input signals. By using the Lyapunov stability theory and leader-follower formation approach, the proposed formation control scheme ensures that all signals of the MASs are semi-globally uniformly ultimately bounded (SGUUB). Finally, the efficiency of the theoretical results is proved by a simulation example.

In this paper, a new stochastic analysis tool on semi-global stability is constructed, for nonlinear systems disturbed by stochastic processes with strongly bounded in probability. The definition of semi-global noise to state practical stability in probability and its Lyapunov criterion for random systems are presented. As a major application of stability, the semi-global practical tracking of random nonlinear systems based on dynamic surface control technique is considered. The trajectory tracking of manipulator robot driven by direct current motors is carried out in simulation to illustrate the effectiveness and feasibility of the control scheme.

A cooperative game theoretical approach is taken to production and transportation coordinated scheduling problems of two-machine flow-shop (TFS-PTCS problems) with an interstage transporter. The authors assume that there is an initial scheduling order for processing jobs on the machines. The cooperative sequencing game models associated with TFS-PTCS problems are established with jobs as players and the maximal cost savings of a coalition as its value. The properties of cooperative games under two different types of admissible rearrangements are analysed. For TFS-PTCS problems with identical processing time, it is proved that, the corresponding games are σ₀-component additive and convex under one admissible rearrangement. The Shapley value gives a core allocation, and is provided in a computable form. Under the other admissible rearrangement, the games neither need to be σ₀-component additive nor convex, and an allocation rule of modified Shapley value is designed. The properties of the cooperative games are analysed by a counterexample for general problems.

In this paper, a theoretical model is developed on the basis of systems theory, which structures the livelihood system of low-income households in a European country characterized by a semi-peripheral economy. Based on the proposed model, the complex system of network connections and formal and informal financial transactions, which households use in their daily lives to cover their expenses, becomes graspable. The proposed theoretical model is analyzed through simulations based on agent-based modelling (ABM) centred on empirical network data. Through the simulations, the author explores the mechanisms of the market and asks what formal and informal credit transactions determine its operation, how these factors shape the local social structure and how resilient the market is to crises. The results show that this dynamic, complex risk-sharing system has an inherent logic and it can mitigate the small liquidity shocks but it is not resistant to bigger financial shocks or overconsumptions.

This paper adopts the DID approach to investigate the trade destruction effects and trade deflection effects of the US additional tariffs. The authors find that the US additional tariffs significantly reduce China’s exports of tariffed products to the US (i.e., trade destruction effect), especially intermediate and labor-intensive products. On the other hand, they significantly increase China’s exports of tariffed products to the third market (i.e., trade deflection effect). For the $50 billion list, both the trade destruction effect and trade deflection effect are concentrated on processing exports, and the US additional tariffs significantly increase China’s exports of tariffed products to ASEAN, Japan and Australia. For the $200 billion list, the US additional tariffs boost China’s exports of chemicals, textiles, wood, metal products, furniture and other products to the EU, Australia, Japan, South Africa and Hong Kong, China. Furthermore, most trade deflections are not realized by lowering export prices, indicating that the trade deflections could compensate for the profit losses caused by the US additional tariffs to a certain extent. The proposed results suggest that searching for substitutions of export markets and a more open trade policy is an important way to avoid profit losses and reduce risks for enterprises and economies suffering from trade frictions.

Influenced by the global economy, politics, energy and other factors, the price of carbon market fluctuates sharply. It is of great practical significance to explore a suitable measurement method of extreme risk of carbon market. Considering that the return series of carbon market has the characteristics of leptokurtosis, fat tail, skewness and multifractal, and there maybe many extreme risk values in the carbon market, this paper introduces the Skewed-$t$ distribution which can describe the characteristics of leptokurtosis, fat tail and skewness of return series into MSM model which can describe multifractal characteristic of return series to model volatility of carbon market. On the basis, based on the extreme value theory, this paper constructs Skewed-$t$-MSM-EVT model to measure extreme risk of carbon market. This paper chooses EUA market as the object to study extreme risk of carbon market, and draws the following conclusions: Skewed-$t$-MSM-EVT model has significantly higher prediction accuracy for carbon market's VaR than MSM-EVT models under other distributions (including normal distribution, $t$ distribution, GED distribution); Skewed-$t$-MSM-EVT model is superior to traditional Skewed-$t$-FIGARCH-EVT and Skewed-$t$-GARCH-EVT models in predicting carbon market's VaR. This research has important practical significance for accurately grasping the risk of carbon market and promoting energy conservation and emission reduction.

This paper studies the multi-period mean-variance (MV) asset-liability portfolio management problem (MVAL), in which the portfolio is constructed by risky assets and liability. It is worth mentioning that the impact of general correlation is considered, i.e., the random returns of risky assets and the liability are not only statistically correlated to each other but also correlated to themselves in different time periods. Such a model with a general correlation structure extends the classical multiperiod MVAL models with assumption of independent returns. The authors derive the explicit portfolio policy and the MV efficient frontier for this problem. Moreover, a numerical example is presented to illustrate the efficiency of the proposed solution scheme.

The authors consider an M/M/1 queue with two types of customers, where customers are classified into two categories according to their psychological feelings when facing uncertainty about queue information. In the unobservable queue, experienced customers could accurately calculate their expected utilities, while first-time customers are loss-averse and the psychological feelings could incur additional gain-loss utilities. By defining customers’ willingness to pay, the authors derive the equilibrium joining-balking behaviors for each type of customer and obtain the service provider’s optimal pricing decision. The authors also classify the implications of the obtained results.

Xinjiang’s agriculture is a typical irrigated agriculture for its agriculture water consumption accounts for 96% of the total water use. As a typical resource-deficient area, the key to Xinjiang’s agricultural development is saving water. This paper takes the high-efficient water-saving irrigation technology of 41 regions along the Tarim River from 2002 to 2013 as the research object, adopts spatial stochastic frontier model to measure the space efficiency of high-efficient water-saving irrigation technology, and analyzes the effect of water-saving irrigation technology on agricultural development. Results show that the water-saving irrigation technology has a spatial effect, if neglecting it, the error of missing variables will occur, and the average loss will be 6.98 percentage points. The spatial correlation effect promotes the improvement of the efficiency of water-saving irrigation technology. The spatial heterogeneity leads to the spatial imbalance of the efficiency of water-saving irrigation technology. The promotion of agricultural water-saving irrigation technology can increase production and the efficiency of agricultural development. Due to the technical heterogeneity of different types of water-saving irrigation technology, the contribution to the development of agriculture is also different. The study finds that water-saving irrigation technology of drip irrigation in the Tarim River contributes more to agricultural development.

This paper proposes a robust two-stage estimation procedure for a general spatial dynamic panel data model in light of the two-stage estimation procedure in Jin, et al. (2020). The authors replace the least squares estimation in the first stage of Jin, et al. (2020) by M-estimation. The authors also provide the justification for not making any change in its second stage when the number of time periods is large enough. The proposed methodology is robust and efficient, and it can be easily implemented. In addition, the authors study the limiting behavior of the parameter estimators, which are shown to be consistent and asymptotic normally distributed under some conditions. Extensive simulation studies are carried out to assess the proposed procedure and a COVID-19 data example is conducted for illustration.

This paper focuses on the support recovery of the Gaussian graphical model (GGM) with false discovery rate (FDR) control. The graceful symmetrized data aggregation (SDA) technique which involves sample splitting, data screening and information pooling is exploited via a node-based way. A matrix of test statistics with symmetry property is constructed and a data-driven threshold is chosen to control the FDR for the support recovery of GGM. The proposed method is shown to control the FDR asymptotically under some mild conditions. Extensive simulation studies and a real-data example demonstrate that it yields a better FDR control while offering reasonable power in most cases.

In many application fields of regression analysis, prior information about how explanatory variables affect response variable of interest is often available and can be formulated as constraints on regression coefficients. In this paper, the authors consider statistical inference of partially linear spatial autoregressive model under constraint conditions. By combining series approximation method, twostage least squares method and Lagrange multiplier method, the authors obtain constrained estimators of the parameters and function in the partially linear spatial autoregressive model and investigate their asymptotic properties. Furthermore, the authors propose a testing method to check whether the parameters in the parametric component of the partially linear spatial autoregressive model satisfy linear constraint conditions, and derive asymptotic distributions of the resulting test statistic under both null and alternative hypotheses. Simulation results show that the proposed constrained estimators have better finite sample performance than the unconstrained estimators and the proposed testing method performs well in finite samples. Furthermore, a real example is provided to illustrate the application of the proposed estimation and testing methods.

Triangular decomposition with different properties has been used for various types of problem solving. In this paper, the concepts of pure chains and square-free pure triangular decomposition (SFPTD) of zero-dimensional polynomial systems are defined. Because of its good properties, SFPTD may be a key way to many problems related to zero-dimensional polynomial systems. Inspired by the work of Wang (2016) and of Dong and Mou (2019), the authors propose an algorithm for computing SFPTD based on Gröbner bases computation. The novelty of the algorithm is that the authors make use of saturated ideals and separant to ensure that the zero sets of any two pure chains are disjoint and every pure chain is square-free, respectively. On one hand, the authors prove the arithmetic complexity of the new algorithm can be single exponential in the square of the number of variables, which seems to be among the rare complexity analysis results for triangular-decomposition methods. On the other hand, the authors show experimentally that, on a large number of examples in the literature, the new algorithm is far more efficient than a popular triangular-decomposition method based on pseudodivision, and the methods based on SFPTD for real solution isolation and for computing radicals of zero-dimensional ideals are very efficient.

Motivated by applications in advanced cryptographic protocols, research on arithmetizationoriented symmetric primitives has been rising in the field of symmetric cryptography in recent years. In this paper, the authors focus on on the collision attacks for a family of arithmetization-oriented symmetric ciphers GMiMCHash. The authors firstly enhance the algebraically controlled differential attacks proposed by introducing more variables. Then, combining algebraic attacks and differential attacks, the authors propose algebraic-differential attacks on GMiMCHash. This attack method is shown to be effective by experiments on toy versions of GMiMCHash. The authors further introduce some tricks to reduce the complexities of algebraic-differential attacks and improve the success probability of finding collisions.

In this paper, the notion of rational univariate representations with variables is introduced. Consequently, the ideals, created by given rational univariate representations with variables, are defined. One merit of these created ideals is that some of their algebraic properties can be easily decided. With the aid of the theory of valuations, some related results are established. Based on these results, a new approach is presented for decomposing the radical of a polynomial ideal into an intersection of prime ideals.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.