In the context of Internet of Things (IoT)-enabled wireless multi-sensor networks, efficient and reliable remote state estimation is often challenged by resource constraints and unreliable communication links. This paper investigates a coding-decoding-based state estimation problem for discrete-time dynamical systems subject to external disturbances and packet losses. Specifically, the influence of packet length, which is a critical design parameter constrained by practical IoT protocols, is studied in terms of its dual impact on quantization error and transmission reliability over lossy wireless channels. An ultimately bounded filtering approach is adopted to develop a packet-length-aware estimator, and a comprehensive analysis is conducted to quantify how packet length affects estimation accuracy under joint quantization and dropout effects. To optimize estimation performance, a co-design framework is proposed for selecting both the estimator gains and packet lengths, formulated as a mixed-integer nonlinear programming problem. This optimization is solved via a hybrid method combining particle swarm optimization and linear matrix inequality techniques. Simulation results validate the effectiveness and practicality of the proposed approach for real-world IoT monitoring and control scenarios.

This paper addresses the challenge of mismatched disturbance rejection in nonlinear discrete-time systems by proposing a novel model predictive control algorithm based on optimal control theory, which significantly enhances disturbance rejection performance. The algorithm constructs a concise yet effective performance index capable of handling both matched and mismatched disturbances by incorporating a disturbance observer, thereby simultaneously fulfilling the dual objectives of trajectory tracking and disturbance attenuation. To improve computational efficiency, a solution method grounded in optimal control theory is devised, enabling rapid online controller computation. This approach ensures superior real-time performance while delivering more efficient tracking and disturbance rejection. The effectiveness of the proposed algorithm is validated through simulations and experimental tests on an automated guided vehicle platform. Results show that the algorithm achieves outstanding performance in both disturbance rejection and computational efficiency, markedly surpassing conventional methods. It can effectively withstand unknown disturbances while meeting the real-time and reliability demands of practical engineering applications, demonstrating broad prospects for deployment in real-world systems.

Accurate parameter estimation is paramount for high-fidelity three-dimensional (3D) reconstruction in cryo-electron tomography (Cryo-ET), a pivotal technique for visualizing the intricate structures of biological macromolecules and cellular components in their near-native state. The alignment of the image sequence acquired at varying tilt angles constitutes a critical bottleneck in this process, directly governing reconstruction accuracy. While bundle adjustment (BA) serves as the computational cornerstone for parameter refinement, its conventional implementation via the Levenberg-Marquardt (L-M) algorithm exhibits critical limitations: sensitivity to initialization causes slow convergence and oscillatory behavior in noisy Cryo-ET datasets. To address this limitation and enhance parameter optimization robustness, this paper introduces a novel algorithm, leveraging principles from optimal control theory to directly optimize the nonlinear BA objective function. The optimal control principle (OCP) method demonstrates superior convergence characteristics compared to the L- M algorithm, effectively mitigating oscillations and achieving faster convergence rates. Extensive experiments on both synthetic and real-world Cryo-ET datasets validate the algorithm's performance. Results demonstrate that the OCP consistently achieves faster convergence than the L-M algorithm. Furthermore, incorporating a bisection-based update procedure for the OCP's control weight matrix significantly enhances its performance, particularly under conditions of poor initialization. These findings establish the OCP as a powerful tool that can substantially improve the efficiency and robustness of parameter optimization, thereby accelerating high-resolution 3D reconstructions in Cryo-ET.

The extended state observer (ESO) is widely used in disturbance rejection methods for its ability to achieve rapid convergence through high-gain design. However, this high-gain ESO often leads to significant noise amplification and increased sensitivity to disturbances, which adversely affects performance. To address this issue, we propose a novel method that integrates anH∞filter into the ESO framework. Unlike conventional methods, this approach does not assume Gaussian noise or require prior knowledge of noise statistics. Instead, it only assumes bounded noise, making it applicable to a broader range of scenarios. The method employs theH∞filter to attenuate noise within a predefined bound, after which the filtered signal is passed to the ESO for state and disturbance estimation. This significantly reduces the sensitivity of the high-gain ESO to noise. Finally, the proposed method is applied to the speed control of a permanent magnet synchronous motor servo system to verify its effectiveness. The results demonstrate that the method successfully suppresses noise, enhances control performance, and provides a parameter adjustment steps and recommendations its application.

This article investigates open-loop and feedback solutions to linear quadratic mean field (MF) games with a leader and many followers. The leader first gives its strategy and then all the followers cooperate to optimize the social cost as the sum of their costs. By variational analysis with MF approximations, we obtain a set of open-loop controls of players in terms of solutions to MF forward-backward stochastic differential equations (FBSDEs), which is further shown be to an asymptotic Stackelberg-team equilibrium. By applying the matrix maximum principle, a set of decentralized feedback strategies is constructed for all the players. For open-loop and feedback solutions, the corresponding costs of all players are explicitly given by virtue of the solutions to two Riccati equations, respectively. The performances of two solutions are compared by the numerical simulation.

Although techniques in optimal control theory often address unconstrained problems, many applications involve constraints. Despite attempts to address constrained linear-quadratic (LQ) control problems, these efforts primarily focus on delay-free systems. For constrained LQ control problems with delays, there is little theoretical understanding due to the significant complexity added by the inclusion of time delays. This article explores the stochastic LQ optimal control problem, which includes control-dependent multiplicative noise and delays, along with quadratic constraint. Through the application of duality theory, we streamline the optimal control problem is reduced to a parameterized, unconstrained stochastic LQ control problem incorporating delays. By solving the Riccati-ZXL equation, the optimal control and cost function are explicitly formulated. Notably, the optimal parameter is determined by solving a semi-definite programming (SDP) problem. The main contribution is presenting the optimal control as a nonlinear function of both the initial state and the state’s conditional expectation. Numerical examples illustrate the efficacy of the derived results.

In this article, we present a model-free output feedback (OPFB)Q-learning algorithm to find the optimal Nash equilibrium strategy for the decentralized control problem (DCP) of nonzero-sum games with asymmetric information. The main challenge lies in different historical information available to each controller, namely, the input information is shared while the measurement information is private. To overcome this difficulty, a novel optimal Nash strategy in the input/output form is derived without measurable system states. Then, the OPFBQ-learning iteration algorithm is developed to learn the optimal controllers online only by the knowledge of available input and measurement information, rather than the system dynamics and states. The key is solving the equilibrium equations under asymmetric information, which is achieved by reformulating them into a constrained minimization problem, yielding the numerical solution of the optimal controller pair. The presented idea is new to the best of authors’ knowledge. Numerical examples are shown to illustrate the effectiveness of the proposed algorithm.

As regards gas turbine engine control, how to achieve the optimal performance of engine within multiple control and physical constraints in real time is a sticky problem to be solved. A novel multivariable optimal control architecture is proposed to compensate engine into a pseudo-linear system by using the nonlinear dynamic inverse and the constrained optimization, and then linear feedback controller is used for control synthesis. At each sampling instant, a real-time linearized model of engine is applied to reduce computational complexity. The simulation results show the resultant control system of civil turbofan engine has good decoupling and tracking response.

This article focuses on solving a finite-horizon nonlinear optimal control problem by using the Pontryagin's maximum principle. In practical applications, linearization is a common approach for solving nonlinear dynamical systems. However, it is not universally applicable due to various reasons, such as instability and low accuracy. In contrast to linearization, the inherent challenge in directly solving the above nonlinear optimal control problem lies in addressing the highly coupled nonlinear forward and backward differential equations. In order to address this problem, an equivalent relationship is established between these equations and a new optimization problem. By exploiting the inherent relationship between supervised learning and an optimization problem from the view of a dynamical system, a deep neural network framework is constructed for describing the new optimization problem. Furthermore, a numerical algorithm for optimal control, which is very powerful for a large variety of nonlinear dynamical systems, is implemented by training a deep residual network. Finally, the effectiveness of the algorithm is demonstrated by solving a trajectory tracking control problem for automatic guided vehicle. The obtained results reveal that the proposed control scheme can achieve high-precision tracking.

This article studies the stabilization control of the Stackelberg game-based system (SGBS) which involves a leader and a follower under continuous time. There are two main contributions: first, the explicit Stackelberg strategy and the optimal performance index under finite horizon are derived based on Riccati equations (REs). Second, the equivalent condition for the SGBS to be stabilizable is obtained, meanwhile, the corresponding Stackelberg strategy and optimal index under this condition are given by REs. Different from the previous works, in the optimization process of the leader, we obtain the linear Stackelberg strategy based on state feedback by applying the matrix maximum principle. Our key technique is solving forward–backward differential equations obtained from the maximum principle.

Scanning transmission electron microscopy (STEM) is a powerful technique in high-resolution atomic imaging of materials. Decreasing scanning time and reducing electron beam exposure with an acceptable signal-to-noise ratio are two popular research aspects when applying STEM to beam-sensitive materials. Specifically, partially sampling with fixed electron doses is one of the most important solutions, and then the lost information is restored by computational methods. Following successful applications of deep learning in image in-painting, we have developed an encoder-decoder network to reconstruct STEM images in extremely sparse sampling cases. In our model, we combine both local pixel information from convolution operators and global texture features, by applying specific filter operations on the frequency domain to acquire initial reconstruction and global structure prior. Our method can effectively restore texture structures and be robust in different sampling ratios with Poisson noise. A comprehensive study demonstrates that our method gains about 50% performance enhancement in comparison with the state-of-art methods. Code is available at https://github.com/icthrm/Sparse-Sampling-Reconstruction.

The linear quadratic regulation (LQR) problem for discrete-time networked control systems (NCSs) is investigated in this article. The difference from most previous works is that input delay and packet losses occur simultaneously in the communication channel connecting the controller to the actuator. Moreover, the data packet dropout is modeled as a time-homogeneous Markov process which poses challenges due to the temporal correlation. The contributions of this article are twofold. First, by applying the maximum principle involving Markov jumps and delay, the linear quadratic optimal control problem in finite horizon is solved and the solution is given in terms of a forward and a backward stochastic difference equations (FBSDEs-M). Second, under a basic assumption, the infinite horizon optimal control problem is solved and the necessary and sufficient condition for mean square stabilization is given in terms of the solutions to coupled algebraic Riccati-type equations with Markov jumps. The presented results are new to the best of our knowledge since there is no existing work that tackles delay and Markovian packet dropouts simultaneously. It is a generalization of the previous work in which the packet dropouts is modeled as an independent identically distributed Bernoulli process.

This paper is concerned with the optimal control of rational expectations models in the general case of longer forward-looking time (d ≥ 2). The main contribution is the necessary and sufficient condition for the solvability of the finite-horizon problem. In particular, explicit characterizations of the optimal solution and the optimal cost are given in terms of difference equations. The key technique is to solve the forward and backward stochastic difference equations (FBSDEs) obtained by the stochastic maximum principle.

In this paper, we are concerned with a new class of mean field games which involve a finite number of agents. With help of conditional mathematical expectation, we obtain necessary and sufficient conditions for the existence of the decentralized open-loop Nash equilibrium for finite-population games. By decoupling a non-standard forward-backward stochastic differential equation, we design a set of decentralized strategies in term of two differential Riccati equations. Instead of the s-Nash equilibrium, the set of decentralized strategies is shown be a Nash equilibrium. Furthermore, we examine the infinite-horizon problem and give a neat condition for solvability of the related algebraic Riccati equation.

We investigate the optimal control problem for networked control systems consisting of a linear plant controlled by a remote controller and a local controller. By virtue of the maximum principle, we establish a non-homogeneous relationship between the state and the costate of this class of systems. Based on this relationship, the optimal controllers are derived in terms of the two Riccati equations.

This paper mainly focuses on the optimal output feedback control and stabilization problems for discrete-time multiplicative noise system with intermittent observations. The main contributions of this paper can be concluded as follows. First, different from the previous literatures, this paper overcomes the barrier of the celebrated separation principle for stochastic control problems of multiplicative noise systems. Based on the measurement process, the optimal estimation is presented, and by using dynamic programming principle, the optimal output feedback controller is designed with feedback gain based on the given coupled Riccati equations. Second, the necessary and sufficient stabilization conditions for multiplicative noise system with intermittent observation in the mean square sense are developed for the first time. Finally, the novel results developed in this paper can be applied to solve the output feedback control and stabilization problems for general networked control system of user datagram protocol network case. The range of packet losses rate and the allowable maximum packet losses rate are presented explicitly.

In this paper, a delay-dependent algebraic Riccati equation (DARE) approach is developed to study the meansquare stabilization problem for continuous-time networked control systems. Different from most previous studies that information transmission can be performed with zero delay and infinite precision, this paper presents a basic constraint that the designed control signal is transmitted over a delayed communication channel, where signal attenuation and transmission delay occur simultaneously. The innovative contributions of this paper are threefold. First, we propose a necessary and sufficient stabilizing condition in terms of a unique positive definite solution to a DARE with Q > 0 and R > 0. In accordance with this result, we derive the Lyapunov/spectrum stabilizing criterion. Second, we apply the operator spectrum theory to study the stabilizing solution to a more general DARE with Q ≥ 0 and R > 0. By defining a delay-dependent Lyapunov operator, we propose the existence theorem of the unique stabilizing solution. It is shown that the stabilizing solution, if it exists, is unique and coincides with a maximal solution. Third, as an application, we derive the explicit maximal allowable delay bound for a scalar system. To confirm the validity of our theoretic results, two illustrative examples are included in this paper.

This paper mainly considers the optimal measurement feedback control and stabilization for networked control systems (NCSs) with packet losses. The problems are involved with fundamental difficulties of separation principle and optimal estimation (conditional expectation) for multiplicative noise stochastic systems. First, the optimal estimator (conditional expectation) for NCSs with packet losses is derived and the optimal measurement feedback controller is obtained by using the maximum principle. The sufficient and necessary solvability condition of finite horizon measurement feedback control problem is first presented. Moreover, the asymptotic stability of the optimal estimator is studied. Finally, for the infinite horizon case, based on the introduction of a new Lyapunov function, which is defined with the optimal cost function, it is shown that the system is stabilizable in the mean square sense if and only if an algebraic Riccati equation admits a unique positive definite solution.

This paper is concerned with both difference and differential leader-follower games with time delay. The problem remains challenging although the leader-follower game for delay-free system has been well studied in the past decades. The main obstacle encountered is the noncausality of strategy design caused by the delay. The key technique developed to overcome the difficulty is the introduction of the new co-states which capture the future information of the control and the new state which contains the past effects. The novel contributions of this paper are as follows. First, the sufficient and necessary solvability condition is given to ensure the existence of a unique open-loop Stackelberg strategy for the difference game. Second, the open-loop strategy is explicitly obtained in terms of decoupled and symmetric Riccati equations. Last but not least, a unique strategy for continuous time systems is also given by applying the techniques developed in this paper.

A randomly deployed sensor network is typically not completely localizable using distance-based measurements only. Though a necessary and sufficient condition for testing whether a network is localizable has been given in the literature, how to find localizable nodes from a not fully localizable network is still open. In this paper, we try to address a connection between two well-known localization methods, the trilateration method and the WHEEL extension method, by using a graphical tool named Henneberg operations. We also study whether Henneberg operations always guarantee the localizability of a network. The localizability by a Henneberg operation-based algorithm is given. Simulation shows that the performance of this algorithm for finding localizable nodes is very close to a well-known necessary condition called 3-path condition.

In this paper, we consider the quantized quadratic performance control problem for a class of stochastic systems which are subject to multiplicative noises in the measurement, we look for a dynamic output feedback controller to guarantee certain level of performance. By using the sector bound approach to characterize the quantized error, we show that the existence of the solution of quantized quadratic guaranteed cost problem can be found by solving the so-called guaranteed cost control problem of the associated system with sector bound uncertainty. The main result of this paper show that this problem can be effectively solved using linear matrix inequalities (LMIs).

In this paper, we mainly study the Stackelberg strategy for the two-player game with time delay. A feedback-form open-loop strategy is obtained for the game with identical linear-quadratic cost function based on the maximum principle and the shifting method.

In this paper, we are concerned with the consensus problem for multi-agent systems with time delay. The consensus problem is taken as a root finding problem in stochastic approximation to deal with. Via choosing an appropriate regression function, the multi-agent system with a finite delay achieves asymptotic consensus. Furthermore, we establish a relationship between the convergence rate and the exponent of the step size of the algorithm. It is worth mentioning that the convergence rate only depends on the step size rather than the delay.

A common technical difficulty in target tracking in a wireless sensor network is that individual homogeneous sensors only measure their distances to the target whereas the state of the target composes of its position and velocity in the Cartesian coordinates. That is, the senor measurements are nonlinear in the target state. Extended Kalman filtering is a commonly used method to deal with the nonlinearity, but this often leads to unsatisfactory or even unstable tracking performances. In this paper, we present a new target tracking approach which avoids the instability problem and offers superior tracking performances. We first propose an improved noise model which incorporates both additive noises and multiplicative noises in distance sensing. We then use a maximum likelihood estimator for prelocalization to remove the sensing nonlinearity before applying a standard Kalman filter. The advantages of the proposed approach are demonstrated via experimental and simulation results.

This paper is concerned with estimation problem for discrete-time systems with packet dropping. A new optimal filter is derived by minimizing the mean squared estimation error. An optimal smoother is also derived in a similar way. Both estimators are designed by solving one deterministic Riccati equation. Both the convergence of the estimation error covariance and mean square stability of the estimator are proved under standard assumption. It is shown that the new estimator has smaller error covariance and has wider applications as compared with the MMSE estimator. One of the key techniques adopted in this paper is the introduction of the innovation sequence for the multiplicative noise systems.

This paper is concerned with the steady-state optimal filtering problem for continuous-time systems withldelayed measurements. The design of the filter involves in solving one spectral factorization with time-delays, which is the key problem to be solved. A novel approach for the spectral factorization is proposed based on reorganized innovation analysis. The calculation of spectral factor comes down to solvingl+1 standard Riccati equations with the same dimension as the original systems.

This paper proposes and analyzes a new distributed power-control algorithm based on the theory of stochastic approximation. The power-control problem is first converted into a stochastic approximation problem in which the zero point of a specific function is determined. A distributed power-control algorithm is then derived and its convergence properties are analyzed using standard techniques. In the distributed algorithm, each user iteratively updates its power level by using estimates of the inverse of the signal-to-interference ratio (SIR) of its channel. No knowledge of the channel gains or state information of other users is required. Moreover, the algorithm is robust in the sense that it can handle errors in the bit-error rate estimates, and hence, can be used in practical scenarios. Convergence of the algorithm is analyzed in the almost-sure sense

This paper is concerned with the finite horizon output feedback H2control problem for discrete time systems with multiple input delays. A separation principle is applied which converts the H2control problem into an associated linear quadratic regulation (LQR) problem in conjunction with a Kalman filter. The H2output feedback controller is constructed by solving two Riccati difference equations (RDEs) of the same dimension as the plant (ignoring the delays), similar to the solution of the standard H2control problem. The output feedback H2control result is then applied to ATM congestion control. Simulations show that the proposed control technique can achieve desired control performance effectively and is robust to the varying round trip delay of the ATM network to some extent

This paper deals with a class of power control problems where the system link gains are assumed to be time varying and SIR estimates are allowed to be corrupted with bounded noises. A simple distributed algorithm of fixed-step power control is devised and the feedback requires only local information. As a generalization of the power control algorithm proposed by Sung and Wong, we have obtained a more robust solution which can handle time varying link gains and measurement noises. Convergence of the new algorithm is analyzed and numerical studies show that it is effective.

The paper addresses the problem of channel estimation for DS-CDMA systems undergoing time-varying multipath fading channels. The multipath fading channels are modeled as AR models. Based on the minimum mean square error (MMSE) criterion, the linear optimal estimator is obtained by a spectral factorization and a Diophantine polynomial matrix equation. The uncertainty of the channel model is taken into consideration to improve the robustness of the estimator. Compared with the Kalman estimator, the proposed algorithm has O(K/sup 2/) computational complexity, where K is the number of users. The simulation results show that the proposed estimator provides good estimation performance and robustness for fast fading channels.

Transmitter power control has been proven to be an efficient method to solve co-channel interference in CDMA system, and to increase the capacity of systems. A novel distributed power control algorithm based on estimates of channel gains is presented in this paper. The proposed algorithm is robust and does not require the exact knowledge of channel gains. In the proposed scheme, power control problem is converted into the zero point problem of a certain function. It is proved that the algorithm converges to the average optimal solution by stochastic approximation approach.

This paper aims to give the efficient approach to the discrete-time systems with instantaneous and multiple time-delays measurements. Without resorting to the traditional augmentation and standard Kalman filtering formulation, a new approach termed as reorganized innovation analysis is developed in the paper. The improved performance is clearly demonstrated through analytical results and simulation experiments with multiple time-delayed measurements. More importantly, the approach presented in the paper forms the basis of solving the more complicated problems such as H/sub /spl infin// fixed-lag smoothing, multiple-step ahead prediction and H/sub /spl infin// control with control input multiple delays.

A class of discrete-time Kalman filtering problem for the descriptor time-varying systems with current and delayed measurements is considered. Using the known maximum likelihood (ML) estimation results and the method of measurements reorganization, the optimal Kalman filter and corresponding Riccati equations for descriptor systems involving current and delayed measurements are derived. Our solution does not require system augmentation or system transformation, and the estimator is given in terms of two Riccati equations of the same order as that of the system state. A simple algorithm is presented for the problem.