Stochastic H2 / H∞ Control for Poisson Jump-Diffusion Systems

This paper is concerned with stochastic H_2/H_∞ control problem for Poisson jump-diffusion systems with(x, u, v)-dependent noise, which are driven by Brownian motion and Poisson random jumps. A stochastic bounded real lemma(SBRL for short) for Poisson jump-diffusion systems is firstly established, which stands out on its own as a very interesting theoretical problem. Further, sufficient and necessary conditions for the existence of a state feedback H_2/H_∞ control are given based on four coupled matrix Riccati equations. Finally, a discrete approximation algorithm and an example are presented.     

A MAXIMUM PRINCIPLE APPROACH TO STOCHASTIC H_2/H_∞ CONTROL WITH RANDOM JUMPS

A necessary maximum principle is given for nonzero-sum stochastic differential games with random jumps.The result is applied to solve the H_2/H_∞ control problem of stochastic systems with random jumps.A necessary and sufficient condition for the existence of a unique solution to the H_2/H_∞ control problem is derived.The resulting solution is given by the solution of an uncontrolled forward backward stochastic differential equation with random jumps.     

Optimal variational principle for backward stochastic control systems associated with Lévy processes

The paper is concerned with optimal control of backward stochastic differential equation (BSDE) driven by Teugel’s martingales and an independent multi-dimensional Brownian motion,where Teugel’s martin- gales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see e.g.,Nualart and Schoutens’ paper in 2000).We derive the necessary and sufficient conditions for the existence of the op- timal control by means of convex variation methods and duality techniques.As an application,the optimal control problem of linear backward stochastic differential equation with a quadratic cost criteria (or backward linear-quadratic problem,or BLQ problem for short) is discussed and characterized by a stochastic Hamilton system.     

Output Feedback H∞ Control for a Class of Nonlinear Stochastic Systems

This paper deals with the output feedback H∞ control problem for a class of nonlinear stochastic systems. Based on the latest developed theory of stochastic dissipation, a notable result about the nonlinear H∞ output feedback control of deterministic system is generalized to the stochastic case. Finally, in the cases of state feedback and output feedback, two families of controllers are provided respectively.     

Stochastic maximum principle for mean-field forward-backward stochastic control system with terminal state constraints

In this paper,we consider an optimal control problem with state constraints,where the control system is described by a mean-field forward-backward stochastic differential equation(MFFBSDE,for short)and the admissible control is mean-field type.Making full use of the backward stochastic differential equation theory,we transform the original control system into an equivalent backward form,i.e.,the equations in the control system are all backward.In addition,Ekeland’s variational principle helps us deal with the state constraints so that we get a stochastic maximum principle which characterizes the necessary condition of the optimal control.We also study a stochastic linear quadratic control problem with state constraints.     

The spectrum of (gv, g, 3, λ)-DF in Z_(gv)

In this paper, the necessary and sufficient conditions for the existence of a (gv, g, 3, λ)- difference family in Zgv are established. As a consequence, the existence spectrum of a cyclic (3, λ)-GDD of type gv without short orbits is determined.     

GUARANTEED COST CONTROL OF CONTINUOUS-TIME UNCERTAIN SINGULAR SYSTEM WITH BOTH STATE AND INPUT DELAYS

The guaranteed cost control problem for a continuous-time uncertain singular system with state and control delays, and a given quadratic cost function is studied in this paper. Sufficient conditions for the existence of the guaranteed cost controller are derived based on the linear inequality (LMI) approach. A parameterized characterization of the guaranteed cost laws is given in terms of the feasible solutions to a certain LMI, and the cost function of guaranteed cost controller exists an upper bound.     

Optimal investment consumption model with a higher interest rate for borrowing

This paper considers a consumption and investment decision problem with a higher interest rate for borrowing as well as the dividend rate. Wealth is divided into a riskless asset and risky asset with logrithmic Erownian motion price fluctuations. The stochastic control problem of maximizating expected utility from terminal wealth and consumption is studied. Equivalent conditions for optimality are obtained. By using duality methods ,the existence of optimal portfolio consumption is proved,and the explicit solutions leading to feedback formulae are derived for deteministic coefficients.     

Backward Doubly Stochastic Differential Equations with Jumps and Stochastic Partial Differential-Integral Equations

Backward doubly stochastic differential equations driven by Brownian motions and Poisson process(BDSDEP) with non-Lipschitz coeffcients on random time interval are studied.The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations(SPDIEs) is treated with BDSDEP.Under non-Lipschitz conditions,the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique.Then,the continuous dependence for solutions to BDSDEP is derived.Finally,the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.     

EMBEDDINGS OF SIMPLE TWO-FOLD BALANCED INCOMPLETE BLOCK DESIGNS WITH BLOCK SIZE FOUR

The necessary and sufficient conditions for the existence of simple incomplete block design (v, w; 4,2)-IPBDs are determined. As a consequence, the necessary and sufficient conditions for the embeddings of simple two-fold balanced incomplete block designs with block size 4 are also determined.     

Robust reliable H∞ control for neural networks with mixed time delays

This paper considers the problem of robust reliable H_∞ control for neural networks. The system has time-varying delays, parametric uncertainties and faulty actuators. The faulty actuators are considered as a disturbance signal to the system which is augmented with system disturbance input. Based on the LMI technique and the Lyapunov stability theory, a new set of sufficient conditions is obtained for the existence of the robust reliable H_∞ controller. An example is also presented illustrate the results.     

Resilient and robust finite-time H∞ control for uncertain discrete-time jump nonlinear systems

This paper studies the robust and resilient finite-time H_∞ control problem for uncertain discrete-time nonlinear systems with Markovian jump parameters. With the help of linear matrix inequalities and stochastic analysis techniques, the criteria concerning stochastic finite-time boundedness and stochastic H_∞ finite-time boundedness are initially established for the nonlinear stochastic model. We then turn to stochastic finite-time controller analysis and design to guarantee that the stochastic model is stochastically H_∞ finite-time bounded by employing matrix decomposition method. Applying resilient control schemes, the resilient and robust finite-time controllers are further designed to ensure stochastic H_∞ finite-time boundedness of the derived stochastic nonlinear systems. Moreover, the results concerning stochastic finite-time stability and stochastic finite-time boundedness are addressed. All derived criteria are expressed in terms of linear matrix inequalities, which can be solved by utilizing the available convex optimal method. Finally, the validity of obtained methods is illustrated by numerical examples.     

Multiplicative stochastic systems: Optimization and analysis

We consider the H ₂/H _∞-optimal control problem for a dynamical system defined by a linear stochastic Itô equation whose drift and diffusion coefficients linearly depend on the state vector, the control signal, and the external disturbance. The optimization is carried out under the a priori requirement of maximum possible damping of the harmful influence of external disturbances on the system operation. We present theorems on the solvability of matrix Riccati differential equations to which the original optimization problem is reduced.     

Robust H∞ control for linear Markovian jump systems with unknown nonlinearities

This paper studies the problem of stochastic stability and disturbance attenuation for a class of linear continuous-time uncertain systems with Markovian jumping parameters. The uncertainties are assumed to be nonlinear and state, control and external disturbance dependent. A sufficient condition is provided to solve the above problem. An H_∞ controller is designed such that the resulting closed-loop system is stochastically stable and has a disturbance attenuation γ for all admissible uncertainties. It is shown that the control law is in terms of the solutions of a set of coupled Riccati inequalities. A numerical example is included to demonstrate the potential of the proposed technique.     

General Linear Quadratic Optimal Stochastic Control Problem Driven by a Brownian Motion and a Poisson Random Martingale Measure with Random Coefficients

In this article, we consider a linear-quadratic optimal control problem (LQ problem) for a controlled linear stochastic differential equation driven by a multidimensional Browinan motion and a Poisson random martingale measure in the general case, where the coefficients are allowed to be predictable processes or random matrices. By the duality technique, the dual characterization of the optimal control is derived by the optimality system (so-called stochastic Hamilton system), which turns out to be a linear fully coupled forward-backward stochastic differential equation with jumps. Using a decoupling technique, the connection between the stochastic Hamilton system and the associated Riccati equation is established. As a result, the state feedback representation is obtained for the optimal control. As the coefficients for the LQ problem are random, here, the associated Riccati equation is a highly nonlinear backward stochastic differential equation (BSDE) with jumps, where the generator depends on the unknown variables K, L, and H in a quadratic way (see (5.9) herein). For the case where the generator is bounded and is linearly dependent on the unknown martingale terms L and H, the existence and uniqueness of the solution for the associated Riccati equation are established by Bellman's principle of quasi-linearization.     

Dissipative sampled‐data control of uncertain nonlinear systems with time‐varying delays

This article investigates the delay‐dependent robust dissipative sampled‐data control problem for a class of uncertain nonlinear systems with both differentiable and non‐differentiable time‐varying delays. The main purpose of this article is to design a retarded robust control law such that the resulting closed‐loop system is strictly (Q, S, R)‐dissipative. By introducing a suitable Lyapunov–Krasovskii functional and using free weighting matrix approach, some sufficient conditions for the solvability of the addressed problem are derived in terms of linear matrix inequalities. From the obtained dissipative result, we deduce four cases namely, H_∞ performance, passivity performance, mixed H_∞, and passivity performance and sector bounded performance of the considered system. From the obtained result, it is concluded that based on the passivity performance it is possible to obtain the controller with less control effort, and also the minimum H_∞ performance and the maximum allowable delay for achieving stabilization conditions can be obtained via the mixed H_∞ and passivity control law. Finally, simulation studies based on aircraft control system are performed to verify the effectiveness of the proposed strategy. © 2015 Wiley Periodicals, Inc. Complexity 21: 142–154, 2016     

Finite-time H∞ control for a class of discrete-time switched time-delay systems with quantized feedback

This paper is concerned with the finite-time quantized H_∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H_∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.     

L\''evy过程驱动的正倒向随机系统的随机最大值原理

研究了由Teugels鞅和与之独立的多维Brown运动共同驱动的正倒向随机控制系统的最优控制问题. 这里Teugels鞅是一列与L\'{e}vy 过程相关的两两强正交的正态鞅 (见Nualart, Schoutens 在2000年的结果). 在允许控制值域为一非空凸闭集假设下, 采用凸变分法和对偶技术获得了最优控制存在所满足的充分和必要条件. 作为应用, 系统研究了线性正倒向随机系统的二次最优控制问题(简记为FBLQ问题), 通过相应的随机哈密顿系统对最优控制 进行了对偶刻画. 这里的随机哈密顿系统是由Teugels鞅和多维Brown运动共同驱动的线性正倒向随机微分方程, 其由状态方程、伴随方程和最优控制的对偶表示共同来构成.     

Discrete-time Indefinite LQ Control with State and Control Dependent Noises

This paper deals with the discrete-time stochastic LQ problem involving state and control dependent noises, whereas the weighting matrices in the cost function are allowed to be indefinite. In this general setting, it is shown that the well-posedness and the attainability of the LQ problem are equivalent. Moreover, a generalized difference Riccati equation is introduced and it is proved that its solvability is necessary and sufficient for the existence of an optimal control which can be either of state feedback or open-loop form. Furthermore, the set of all optimal controls is identified in terms of the solution to the proposed difference Riccati equation.