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This paper focuses on linear-quadratic (LQ) optimal control for a class of systems governed by first-order hyperbolic partial differential equations (PDEs). Different from most of the previous works, an approach of discretization-then-continuousization is proposed in this paper to cope with the infinite-dimensional nature of PDE systems. The contributions of this paper consist of the following aspects: 1) The differential Riccati equations and the solvability condition of the LQ optimal control problems are obtained via the discretization-then-continuousization method. 2) A numerical calculation way of the differential Riccati equations and a practical design way of the optimal controller are proposed. Meanwhile, the relationship between the optimal costate and the optimal state is established by solving a set of forward and backward partial difference equations (FBPDEs). 3) The correctness of the method used in this paper is verified by a complementary continuous method and the comparative analysis with the existing operator results is presented. It is shown that the proposed results not only contain the classic results of the standard LQ control problem of systems governed by ordinary differential equations as a special case, but also support the existing operator results and give a more convenient form of computation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal linear closed-loop Stackelberg strategy for stochastic system where the state is unknown but observed though linear stochastic measurement systems. Particularly, the information structure is asymmetric where the leader can obtain the follower's measurement information and its historical control inputs, while the follower can only obtain its own measurement information and historical inputs, which have led to major challenge since the 1970s. It is well known that the closed-loop Stackelberg optimal control in general is a hard problem and no explicit solution can be derived. Instead, this paper aims to present a linear closed-loop solution to the problem. However, how to give a rational definition for the linear closed-loop Stackelberg controller is a difficulty. By using innovation, this paper defines the linear closed-loop Stackelberg controller with specified given gain matrices. Then the analytical solutions for the leader and the follower are given, respectively, which are the feedback form of the Kalman filtering and the optimal gain matrices for the leader and follower are obtained by decoupled solving two Riccati equations. Finally, by using the forward iteration algorithm, the coupled forward and backward Riccati equations are solved in infinite horizon, which overcomes the obstacles that the separation principle becomes invalid. [ABSTRACT FROM AUTHOR]

A stabilization problem for stochastic systems with multiple input delays is investigated herein. A new method to construct an optimal control problem with input constraints is adopted. A sufficient stabilization condition is established via Riccati-type equations, whose verification is computationally simple because the variable dimension of the equations does not increase with regard to the delay. A stabilization controller is proposed, and it is a feedback of the state and a history input. This controller uses less history information than those with distributed terms. Two numerical examples illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the multiplicative-noise rational expectations (MRE) problem. By resorting to a linear quadratic optimal control (LQOC) problem, the approximate solution to the MRE problem can be obtained. It is worth highlighting that this approximate solution can be highly close to the exact solution by adjusting weighted matrices in the cost function of the LQOC problem. Since the conditional expectation of the state is involved in the cost function, the LQOC problem is an optimization control with an additional measurability restriction, which is very involved. The orthogonal decomposition technique is used to deal with this measurability restriction. The solvability condition and the optimal decision are given by developing generalized Riccati-type equations. Numerical experiments are provided to illustrate the effectiveness of the achieved results. [ABSTRACT FROM AUTHOR]

In this paper, we study the open-loop Stackelberg strategy of stochastic Stackelberg game with time delay. The main contribution is to give the explicit Stackelberg strategy in terms of Riccati equations. The key to solving the problem is the explicit solvability of the forward and backward stochastic difference equations (FBSDEs). Moreover, the optimal costs are indicated by using the initial value of the state. [ABSTRACT FROM AUTHOR]

This paper studies social optimal control problem for linear quadratic mean-field system with noisy output. For the output feedback control, each agent needs to estimate not only its own state but also the population average state, where both states are coupled with each other. Firstly, to deal with the noisy output, we give the optimal estimator of the state in the form of the sum of two Kalman filters. Then, by variational method, a set of forward-backward stochastic difference equations (FBSDEs) are presented, and output feedback-type centralized controllers are acquired from the backward iterative method by decoupling the FBSDEs. Finally, by mean field approximations, we further design a set of decentralized controllers, which is proved to have asymptotic social optimality. [ABSTRACT FROM AUTHOR]

Gas turbine engines must be operated by means of control, and how to achieve multivariable control decoupling with aero-engine control constraints is an open thorny issue attracting increasingly more attention. The paper considers the multivariable decoupling problems of aero-engines by using a compound controller, which originates from the fact that it is impossible to eliminate all the nonlinear dynamics of system to obtain desired constant linear closed-loop system by using full actuated control because of modeling errors and some physical constraints. Two controllers are involved in the compound controller. One is a fully actuated controller and the other is classical feedback controller. In order to use fully actuated control and maintain the accuracy of engine model, a full state scheduling linear parameter-varying (LPV) modeling method is proposed based on fuzzy neural network weights. For a general input matrix of the system, its generalized inverse is applied to design fully actuated controller to result in a pseudolinear system. Combined with a feedback controller and control limiter, the control synthesis is achieved. The simulation shows that the proposed method is possessed of a better decoupling and tracking effect compared with traditional control approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with the linear quadratic (LQ) control problem with multiple input channels and terminal state constraints. The problem can be solved by augmenting all the inputs into one. However, the calculation will be much more involved especially for the case with large scale of inputs. To overcome this complexity, we adopt a leader-follower game theory approach. The optimal controller is obtained in the feedback of the state in terms of Riccati equations. A numerical example is provided to demonstrate the effectiveness of the derived result. [ABSTRACT FROM AUTHOR]

The paper considers the linear quadratic regulation (LQR) and stabilization problems for Ito stochastic systems with two input channels of which one has input delay. The underlying problem actually falls into the field of asymmetric information control because of the nonidentical measurability induced by the input delay. In contrast with single-channel single-delay problems, the challenge of the problems under study lies in the interaction between the two channels which are measurable with respect to different filtrations. The key techniques conquering such difficulty are the stochastic maximum principle and the orthogonal decomposition and reorganization technique proposed in a companion paper. The authors provide a way to solve the delayed forward backward stochastic differential equation (D-FBSDE) arising from the maximum principle. The necessary and sufficient solvability condition and the optimal controller for the LQR problem are given in terms of a new Riccati differential equation established herein. Further, the necessary and sufficient stabilization condition in the mean square sense is provided and the optimal controller is given. The idea proposed in the paper can be extended to solve related control problems for stochastic systems with multiple input channels and multiple delays. [ABSTRACT FROM AUTHOR]

In this paper, the consensus problem is investigated for discrete-time multi-agent systems with additive process noises. Due to the presence of additive noises in the system dynamics, consensus cannot be achieved. The main contribution of this paper is to give the exact consensus error. In particular, control gain depending on the agent dynamics and network topology is designed based on the technique dealing with the simultaneous stabilization. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper studies the mixed H2/H∞ control for continuous-time linear dynamic systems. By applying Stackelberg game approach, the control input is treated as the leader and the disturbance is treated as the follower, respectively. Under standard assumptions and maximum principle, a necessary and sufficient existence condition which is based on three decoupled Riccati equations is obtained. Explicit expression of controllers and solutions to forward backward differential equations (FBDES) are obtained by homogeneous analysis of variables. A numerical example is finally given to verify the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper mainly discusses the stabilization problem for discrete-time Markov jump linear systems (MJLSs) involving multiplicative noise with an infinite horizon. The cost weighting matrices are generalized to be indefinite. To the best of our knowledge, this paper is novel and unlike most previous studies, it provides the necessary and sufficient conditions that stabilize the MJLSs in the mean square sense with indefinite weighting matrices. [ABSTRACT FROM AUTHOR]

In this paper, the stochastic H2/H∞ control problem for linear discrete-time systems with (x,u,v)-dependent noise is studied. By applying the leader-follower stochastic game approach, the disturbance is treated as the follower and the control input is treated as the leader, respectively. Necessary and sufficient conditions for the mixed control problem are presented which guarantee the existence and uniqueness of the optimal solution. By applying the stochastic maximum principle, the follower first solves a stochastic linear quadratic optimal control problem which is given in the form of H∞-norm with the aid of stochastic Riccati equations. Then the leader solves a stochastic linear quadratic problem with the aid of forward and backward equations. The main technique is to introduce two new co-states to capture the future information, the encountered difficulty is to establish a homogeneous relationship between the new co-states. [ABSTRACT FROM AUTHOR]

In this paper, the distributed control of the LQR problem for continuous-time multi-agent systems is considered. Based on the centralized optimal control, we prove that the solution of the algebraic Riccati equation is the maximal solution of the algebraic Riccati inequality. The algebraic relations of the solutions of the algebraic Riccati equations for different weighted matrices are shown and two distributed controllers are designed: the fully distributed one and the interconnected distributed one. They can provide an upper bounds and a lower bounds of the centralized optimal cost function. The optimal closed-loop feedback control systems for the two distributed controllers are also asymptotically stable. Some examples are given to show the correctness of the proposed results. [ABSTRACT FROM AUTHOR]

The stabilization with receding horizon control (RHC) of Itô stochastic time-varying systems is studied in this paper. Based on monotonically non-increasing of optimal cost and stochastic Lyapunov stability theory, a necessary and sufficient stabilization condition on the terminal weighting matrix is proposed, which guarantees the mean-square stability of the closed-loop system. The explicit receding horizon controller is obtained by employing stochastic maximum principle. Simulations demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, consensus problems for first-order multi-agent systems with unstable pole are investigated over undirected network, where the network is affected by communication delay. By jointly utilizing both the delayed distributed state information and agent's own historical input information in the protocol, sufficient condition related to agent dynamic, network topology and communication delay is obtained for consensus, which is also proven to be necessary in case of one step delay. Furthermore, the consensus problem is studied on condition that the delay is time-varying. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers the stochastic linear quadratic regulation (LQR) problem for Itô stochastic systems with multiple input controllers. The explicit controllers are given in terms of two Riccati equations by introducing one new costate and establishing the homogeneous relationship between the state and the new costate. More importantly, it is more computation saving for the derived Riccati equations than the one derived by augmentation technique. [ABSTRACT FROM AUTHOR]

A newly proposed distributed dynamic state estimation algorithm based on the maximum a posteriori (MAP) technique is generalised and studied for power systems. The system model involves linear time-varying load dynamics and nonlinear measurements. The main contribution of this paper is to compare the performance and feasibility of this distributed algorithm with several existing distributed state estimation algorithms in the literature. Simulations are tested on the IEEE 39-bus and 118-bus systems under various operating conditions. The results show that this distributed algorithm performs better than distributed quasi-steady state estimation algorithms which do not use the load dynamic model. The results also show that the performance of this distributed method is very close to that by the centralized state estimation method. The merits of this algorithm over the centralized method lie in its low computational complexity and low communication load. Hence, the analysis supports the efficiency and benefits of the distributed algorithm in applications to large-scale power systems. [ABSTRACT FROM AUTHOR]

This paper considers the distributed control of the LQR problem for discrete-time multiagent systems. Distributed controllers are designed based on the solutions of centralized optimal control and the topological structure of the systems. Under mild conditions, it is shown that the distributed controller can approximate to the centralized optimal controller. Then the states of the closed-loop systems of the distributed control exponentially converge to the states of the closed-loop systems of the centralized optimal control. Some examples are given to show effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, the distributed suboptimal LQR control problem for discrete-time multi-agent systems is considered. The distributed controllers that each subsystem can sense and/or exchange information with only a subset of its neighbors are designed, which are based on the topological structure of the system. Using the 'averaged' optimization approach, the suboptimal feedback gain matrices are presented and the distributed suboptimal controllers are obtained. Under mild conditions, the asymptotical convergence of the modified Riccati equation is proved. Accordingly, the infinite-time distributed suboptimal controllers are presented. Examples are given to show the efficiency of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the optimal control problem with multi-channel control. The main contribution is to treat the optimal control problem as a leader-follower problem with multi-hierarchy decision makers in game theory. According to the sequence of the decision makers, the optimal controller is derived by the maximum principle. It is worth mentioning that the optimal solution is in the feedback form related to two symmetric Riccati equations with same dimension as the original state. Furthermore, the obtained solution is sufficient and necessary. [ABSTRACT FROM AUTHOR]

This paper investigates a consensus design problem for continuous-time first-order multiagent systems with uniform constant communication delay. Provided that the agent dynamic is unstable and the diagraph is undirected, sufficient conditions are derived to guarantee consensus. The key technique is the adoption of historical input information in the protocol. Especially, when agent's own historical input information is used in the protocol design, the consensus condition is constructed in terms of agent dynamic, communication delay, and the eigenratio of the network topology. Simulation result is presented to validate the effectiveness of the theoretical result. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of modeling and controlling pursuer convoy in three-dimensional space. The guidance laws applied for convoy, the velocity pursuit, the deviated pursuit and the proportional navigation, steer the pursuer using the rate of line-of-sight (LOS) between successive pursuers. On the basis of the differential equations for the range, the pitch angle of LOS and the yaw angle of LOS between successive pursuers, the guidance laws are proposed to derive decentralized control strategy for pursuer convoy. The results concerning the pursuer convoy are rigorously proven. Simulations are conducted to demonstrate the feasibility and effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Target tracking using wireless sensor networks requires efficient collaboration among sensors to tradeoff between energy consumption and tracking accuracy. This paper presents a collaborative target tracking approach in wireless sensor networks using the combination of maximum likelihood estimation and the Kalman filter. The cluster leader converts the received nonlinear distance measurements into linear observation model and approximates the covariance of the converted measurement noise using maximum likelihood estimation, then applies Kalman filter to recursively update the target state estimate using the converted measurements. Finally, a measure based on the Fisher information matrix of maximum likelihood estimation is used by the leader to select the most informative sensors as a new tracking cluster for further tracking. The advantages of the proposed collaborative tracking approach are demonstrated via simulation results. [ABSTRACT FROM AUTHOR]

The problem of H filtering for continuous-time systems with pointwise time-varying delay is investigated in this paper. By applying an innovation analysis in Krein space, a necessary and sufficient condition for the existence of an H filter is derived in two methods: One is the partial differential equation approach, the other is the reorganized innovation analysis approach. The former gives a solution to the proposed H filtering problem in terms of the solution of a partial differential equation with boundary conditions. The later gives an analytical solution to the proposed H filtering problem in terms of the solutions of Riccati and matrix differential equations. [ABSTRACT FROM AUTHOR]

In this paper, optimal estimation for discrete-time linear time-varying systems with randomly state and measurement delays is considered. By introducing a set of binary random variables, the system is converted into the one with both multiplicative noises and constant delays. Then, an estimator which includes the cases of smoothing and filtering, is derived via the projection formula, and the solution is given in terms of a partial difference Riccati equation with boundary conditions. A predictor for such systems is also presented based on the proposed filter and smoother. The obtained estimators have the same dimension as the original state. Conditions for existence, uniqueness, and stability of the steady-state optimal estimators are studied for time-invariant cases. In this case, the obtained estimators are very easy to implement and all calculations can be performed off line, leading to a linear time-invariant estimator. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new target tracking approach for wireless sensor networks (WSNs) by using the extended H-infinity filter. First, the extended H-infinity filter for nonlinear discrete-time systems is deduced through the Krein space analysis scheme. Then, the proposed extended H-infinity filtering algorithm is applied to target tracking in wireless sensor networks. Finally, experiments are conducted through a small wireless sensor network test-bed. Both experimental and simulation results illustrate that the extended H-infinity filtering algorithm is more accurate to track a moving target in wireless sensor networks than using the extended Kalman filter in the case of having no knowledge of the statistics of the environment and the target to be tracked. [ABSTRACT FROM AUTHOR]

The problem of H filtering for discrete-time systems with time-varying delay in measurement is investigated in this paper. First, under the assumption that the time-varying delay is of a known upper bound, the delayed measurement is re-described as the one with multiple state delays. Then the proposed H filtering problem is transformed into one for systems with multiple measurement channels that contain the same state information as the original measurement and each channel has a single constant delay. Finally, based on the reorganized innovation analysis approach in Krein space, a necessary and sufficient condition for the existence of an H filter which guarantees a prescribed attenuation level is derived. The solution to the H filtering is given in terms of the solutions to Riccati and matrix difference equations. [ABSTRACT FROM AUTHOR]

The paper deals with the H∞ deconvolution fixed-lag smoothing problem for a linear timeinvariant discrete-time system with both known and unknown input series. The H∞ fixed-lag smoother is derived by proposing a new approach termed as re-organized innovation analysis in Krein space. Under the new approach, it is clearly shown that the central deconvolution smoother in an H∞ setting is the same as the one in an H2 setting associated with one self-constructed stochastic state-space model. This insight allows us to calculate the complicated H∞ deconvolution smoother in an intuitive and simple way. The deconvolution smoother is calculated by performing Riccati equation with the same order as the original system. [ABSTRACT FROM AUTHOR]

This paper is concerned with the linear quadratic regulation (LQR) problem for both linear discrete-time systems and linear continuous-time systems with multiple delays in a single input channel. Our solution is given in terms of the solution to a two-dimensional Riccati difference equation for the discrete-time case and a Riccati partial differential equation for the continuous-time case. The conditions for convergence and stability are provided. [ABSTRACT FROM AUTHOR]

This paper is concerned with the l2– l∞ filtering problem for a class of piecewise discrete-time linear systems. Attention is focused on the design of a stable filter guaranteeing a prescribed noise attenuation level in the l2– l∞ sense. By using the piecewise Lyapunov function, a sufficient condition for the solvability of this problem is obtained in terms of linear matrix inequalities (LMIs). It has been shown that the l2– l∞ filtering problem can be solved as an LMI optimization problem. Two numerical examples are presented to demonstrate the validity of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper is to investigate the linear minimum mean square error estimation for continuous-time Markovian jump linear systems with delayed measurements. The key technique applied for treating the measurement delay is the reorganization innovation analysis, by which the state estimation with delayed measurements is transformed into a standard linear mean square filter of an associated delay-free system. The optimal filter is derived based on the innovation analysis method together with geometric arguments in Hilbert space. An analytical solution to the filter is obtained in terms of two Riccati differential equations, and hence is very simple in computation. Computer simulations are carried out to evaluate the performance of the proposed algorithms. The problem of tracking a maneuvering target is addressed. [ABSTRACT FROM AUTHOR]

Optimal state estimation problem for discrete-time systems with delays in noise sequence is investigated. Predictor similar to the traditional Kalman ones is derived based on projection formula in Hilbert space. Filter and fixed-lag smoother are obtained at the same time. The estimators are presented by solving two coupled Riccati-type difference equations. One example shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper is concerned with robust model predictive control for linear continuous uncertain systems with state delay and control constraints. A piecewise constant control sequence is calculated by minimizing the upper-bound of the infinite horizon quadratic cost function. At each sampling time, the sufficient conditions for the existence of the model predictive control are derived, and expressed as a set of linear matrix inequalities. The robust stability of the closed-loop systems is guaranteed by the proposed design method. A numerical example is given to illustrate the main results. [ABSTRACT FROM AUTHOR]

The infinite-horizon linear quadratic regulation (LQR) problem is settled for discrete-time systems with input delay. With the help of an autoregressive moving average (ARMA) innovation model, solutions to the underlying problem are obtained. The design of the optimal control law involves in resolving one polynomial equation and one spectral factorization. The latter is the major obstacle of the present problem, and the reorganized innovation approach is used to clear it up. The calculation of spectral factorization finally comes down to solving two Riccati equations with the same dimension as the original systems. [ABSTRACT FROM AUTHOR]

In this paper, an uplink power control problem is considered for code division multiple access (CDMA) systems. A distributed algorithm is proposed based on linear quadratic optimal control theory. The proposed scheme minimizes the sum of the power and the error of signal-to-interference ratio (SIR). A power controller is designed by constructing an optimization problem of a stochastic linear quadratic type in Krein space and solving a Kalman filter problem. [ABSTRACT FROM AUTHOR]

H-infinity control problem for linear discrete-time systems with instantaneous and delayed measurements is studied. A necessary and sufficient condition for the existence of the H-infinity controller is derived by applying reorganized innovation analysis approach in Krein space. The measurement-feedback controller is designed by performing two Riccati equations. The presented approach does not require the state augmentation. [ABSTRACT FROM AUTHOR]

In this paper, a new approach to H-infinity fixed-lag smoothing is developed by applying the innovation analysis theory. The smoother is derived by resorting to the augmentation state. However, being completely different from the previous work, the augmented state here is considered as just a theoretical mathematical tool for deriving the estimator. A distributed algorithm for the Riccati equation of the augmented system is presented. The calculation of the estimator does not require any augmentation. The comparison of the computation costs between the new approach and previous work is made. The main technique applied in this paper is the re-organized innovation analysis in an indefinite space. [ABSTRACT FROM AUTHOR]