27 results on '"Zhang, Huanshui"'
Search Results
2. Optimal Control and Stabilization for Itô Systems with Input Delay
- Author
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Wang, Hongxia, Zhang, Huanshui, and Xie, Lihua
- Published
- 2021
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3. Optimal Linear Closed-Loop Stackelberg Strategy with Asymmetric Information.
- Author
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Sun, Yue, Li, Hongdan, Xu, Juanjuan, and Zhang, Huanshui
- Subjects
INFORMATION asymmetry ,RICCATI equation ,STOCHASTIC systems ,KALMAN filtering ,INFORMATION measurement ,NONHOLONOMIC dynamical systems - Abstract
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]
- Published
- 2023
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4. Linear quadratic optimal control for time-delay stochastic system with partial information.
- Author
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Wang, Wenjing, Xu, Liang, Xu, Juanjuan, Li, Xun, and Zhang, Huanshui
- Subjects
STOCHASTIC control theory ,STOCHASTIC systems ,STOCHASTIC difference equations ,INFORMATION storage & retrieval systems ,RICCATI equation - Abstract
This paper is concerned with the linear quadratic optimal control problem for the time-delay stochastic system with partial information. The main contribution is to derive the equivalent solvability condition and give the explicitly optimal controller under partial information in terms of the Riccati equations. The key is to explicitly solve the forward and backward stochastic difference equations with partial information, which is derived from the stochastic maximum principle. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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- View/download PDF
5. Stabilization of Discrete-Time Multiplicative-Noise System Under Decentralized Controllers.
- Author
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Xu, Juanjuan, Wang, Wei, and Zhang, Huanshui
- Subjects
DISCRETE-time systems ,RICCATI equation ,ALGEBRAIC equations ,STOCHASTIC systems ,DIFFERENCE equations - Abstract
In this article, we study the mean-square stabilization of discrete-time multiplicative-noise stochastic systems under decentralized controllers. Two controllers are involved in the system where each controller has access to different information and one information set is contained by another one. The adopted information structure is adapted open-loop. The main contribution of the article is twofold. On one hand, we give the unique explicit solution of the finite-horizon optimization problem in terms of difference Riccati equations. On the other hand, we characterize the equivalent condition for the mean-square stabilization under the decentralized controllers via the corresponding algebraic Riccati equations. Moreover, we derive the optimal and stabilizing solution for the infinite-horizon optimization problem. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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6. LQ control of forward and backward stochastic difference system.
- Author
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Zhang, Shen, Xu, Juanjuan, Wang, Guangchen, and Zhang, Huanshui
- Subjects
STOCHASTIC systems ,STOCHASTIC difference equations ,RICCATI equation ,STOCHASTIC differential equations ,ANALYTICAL solutions - Abstract
This paper studies linear quadratic (LQ) control of forward and backward stochastic difference system (FBSDS). There are two main contributions: first, the equivalent condition is obtained for the solvability of optimal control of FBSDS with multi-multiplicative noises under complete information and the analytic solution is also stated by the proposed Riccati equation. Second, the result of complete information is deduced to the situation of incomplete information, that is, the equivalent conditions of solvability and analytical solution are obtained based on Riccati equation. The main technique we use is to solve the forward–backward stochastic difference equations (FBSDEs) originated from maximum principle (MP). [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
7. Stabilization control for Itô stochastic system with indefinite state and control weight costs.
- Author
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Li, Hongdan, Qi, Qingyuan, and Zhang, Huanshui
- Subjects
STOCHASTIC systems ,RICCATI equation ,ALGEBRAIC equations ,COST control ,MATRIX inequalities ,DIFFERENTIAL equations ,LINEAR matrix inequalities - Abstract
In standard linear-quadratic (LQ) control, the first step in investigating infinite-horizon optimal control is to derive the stabilisation condition with the optimal LQ controller. This paper focuses on the stabilisation of an Itô stochastic system with indefinite control and state-weighting matrices in the cost functional. A generalised algebraic Riccati equation (GARE) is obtained via the convergence of the generalised differential Riccati equation (GDRE) in the finite-horizon case. More importantly, the necessary and sufficient stabilisation conditions for indefinite stochastic control are obtained. One of the key techniques is that the solution of the GARE is decomposed into a positive semi-definite matrix that satisfies the singular algebraic Riccati equation (SARE) and a constant matrix that is an element of the set satisfying certain linear matrix inequality conditions. Using the equivalence between the GARE and SARE, we reduce the stabilisation of the general indefinite case to that of the definite case, in which the stabilisation is studied using a Lyapunov functional defined by the optimal cost functional subject to the SARE. [ABSTRACT FROM AUTHOR]
- Published
- 2022
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8. The difference and unity of irregular LQ control and standard LQ control and its solution.
- Author
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Zhang, Huanshui and Xu, Juanjuan
- Subjects
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RICCATI equation , *STOCHASTIC systems , *CONCORD - Abstract
Irregular linear quadratic control (LQ, was called Singular LQ) has been a long-standing problem since 1970s. This paper will show that an irregular LQ control (deterministic) is solvable (for arbitrary initial value) if and only if the quadratic cost functional can be rewritten as a regular one by changing the terminal cost x′(T)Hx(T) to x′(T)[H + P1(T)]x(T), while the optimal controller can achieve P1(T)x(T) = 0 at the same time. In other words, the irregular controller (if exists) needs to do two things at the same time, one thing is to minimize the cost and the other is to achieve the terminal constraint P1(T)x(T) = 0, which clarifies the essential difference of irregular LQ from the standard LQ control where the controller is to minimize the cost only. With this breakthrough, we further study the irregular LQ control for stochastic systems with multiplicative noise. A sufficient solving condition and the optimal controller is presented based on Riccati equations. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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9. Optimal Control for Stochastic Systems With Multiple Controllers of Different Information Structures.
- Author
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Qi, Qingyuan, Xie, Lihua, and Zhang, Huanshui
- Subjects
STOCHASTIC systems ,STOCHASTIC control theory ,DIFFERENCE equations ,RICCATI equation ,SYMMETRIC matrices - Abstract
In this article, we investigate the optimal linear quadratic control problem for stochastic systems with multiple controllers, where each controller has its own information structure, which differs from each other. More specifically, we consider the optimal control problem for systems with multiple controllers of different delayed state information. First, the necessary and sufficient solvability conditions are given in terms of forward and backward difference equations (FBSDEs). Further, an innovation method is proposed to decouple the FBSDEs, and the optimal control strategies are derived based on a given nonsymmetric Riccati equation. Finally, a numerical example is provided to show the effectiveness of the main results. It is stressed that the proposed methods and results can be seen as an important addition to the optimal control theory with asymmetric-information-structure controllers. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
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10. Integrated stabilisation policy over multipath routing‐enabled network.
- Author
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Tan, Cheng, Wong, Wing Shing, Zhang, Huanshui, and Zhang, Zhengqiang
- Abstract
In this study, a sampled‐data networked control system over a multipath routing‐enabled network is investigated, where each delivered signal in a path suffers a random delay. For such a system, the mean square stabilisation problem is considered under the joint design of the event‐driven strategy on the actuator side and the control policy on the decision‐maker side. The contributions of this study are twofold. First, by pre‐defining an application time as an event‐triggering parameter, the sampled‐data system is transformed into a stochastic form with input delay and packet dropout. When the probability distribution F(⋅) of random delay is known a priori, the close form of packet dropout rate is proposed and a set of necessary and sufficient stabilisation conditions are developed simultaneously. When F(⋅) is unknown, the reduced system is an uncertain dynamic system. Utilising matrix polynomials, a verifiable criterion is derived for stabilising the uncertain system, which is also necessary and sufficient. Second, for the scalar system, the close form of allowable sampling period bound is developed in terms of F(⋅) and system parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2020
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11. Optimal control of a class of semi‐linear stochastic evolution equations with applications.
- Author
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Li, Zhipeng, Cai, Qianqian, Ren, Zhigang, Zhang, Huanshui, Fu, Minyue, and Wu, Zongze
- Abstract
In this study, the authors derive a new type of maximum principle for both stochastic evolution and parabolic type stochastic partial differential systems. The systems only require the Hamiltonian functional to be concave in the state variable rather than in both state and control variables. They also show a connection between these two types of systems. Finally, examples are given to illustrate the authors' theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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12. Stabilization Control for Linear Continuous-Time Mean-Field Systems.
- Author
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Qi, Qingyuan, Zhang, Huanshui, and Wu, Zhen
- Subjects
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RICCATI equation , *STOCHASTIC systems , *CONTINUOUS time systems , *ALGEBRAIC equations , *MEAN field theory , *SYMMETRIC matrices , *COST functions - Abstract
This paper investigates the stabilization and control problems for linear continuous-time mean-field systems. Under standard assumptions, the necessary and sufficient conditions to stabilize the mean-field systems in the mean-square sense are explored for the first time. It is shown that, under the assumption of exact detectability (exact observability), the mean-field system is stabilizable if and only if a coupled algebraic Riccati equation admits a unique positive-semidefinite solution (positive-definite solution), which coincides with the classical stabilization results for standard deterministic systems and stochastic systems. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
13. Optimal Stabilization Control for Discrete-Time Mean-Field Stochastic Systems.
- Author
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Zhang, Huanshui, Qi, Qingyuan, and Fu, Minyue
- Subjects
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DISCRETE time filters , *RICCATI equation , *H2 control , *MATHEMATICAL analysis , *CRYSTAL structure - Abstract
This paper will investigate the stabilization and optimal linear quadratic (LQ) control problems for infinite horizon discrete-time mean-field systems. Unlike the previous works, for the first time, the necessary and sufficient stabilization conditions are explored under mild conditions, and the optimal LQ controller for infinite horizon is designed with a coupled algebraic Riccati equation (ARE). More specifically, we show that under the exact detectability (exact observability) assumption, the mean-field system is stabilizable in the mean square sense with the optimal controller if and only if a coupled ARE has a unique positive semidefinite (positive definite) solution. The presented results are parallel to the classical results for the standard LQ control. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
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14. Control for Itô Stochastic Systems With Input Delay.
- Author
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Zhang, Huanshui and Xu, Juanjuan
- Subjects
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STOCHASTIC systems , *CONTROL theory (Engineering) , *MATHEMATICAL models , *COMMAND & control systems , *INDUSTRIAL controls manufacturing , *PROGRAMMABLE controllers - Abstract
This paper examines the long-standing problem of linear quadratic regulation and stabilization for Itô stochastic systems with input delay. This problem remains a primary challenge because the separation principle does not hold for Itô stochastic systems. This paper presents a complete solution to the problem: 1) The (sufficient and necessary) solvability condition of the optimal control and the analytical controller are given based on the modified Riccati differential equation defined herein. 2) The sufficient and necessary stabilization condition in mean square sense is explored. We show that the Itô stochastic system with input delay is stabilized if and only if the modified algebraic Riccati equation developed in this paper has a unique positive-definite solution. The essential obstacle encountered in this paper concerns a Delayed Forward-Backward Stochastic Differential Equation (D-FBSDE), which is mathematical challenging. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
- Full Text
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15. Quantized output feedback control with multiplicative measurement noises.
- Author
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Wei, Li, Fu, Minyue, and Zhang, Huanshui
- Subjects
ELECTRONIC feedback ,FEEDBACK control systems ,STOCHASTIC systems ,STOCHASTIC processes ,SOUND measurement - Abstract
In this paper, we consider the problem of quantized quadratic performance control for a class of stochastic systems, which are subject to multiplicative noises in the measurement. A dynamic output feedback controller is designed to guarantee a given level of performance. By using the sector bound approach to characterize the quantization error, the existence of a solution for the quantized quadratic performance control problem is found by solving the so-called guaranteed cost control problem of the associated system with a sector bounded uncertainty. We show that the latter problem can be solved using LMIs. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
16. Adapted and casual maximum principle and analytical solution to optimal control for stochastic multiplicative-noise systems with multiple input-delays.
- Author
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Zhang, Huanshui, Wang, Hongxia, and Li, Lin
- Abstract
The main purpose of the paper is to provide the adapted and casual solution to the stochastic linear quadratic control problem for systems with multiple input-delays (SLQD). We introduce a special stochastic discrete-time maximum principle (SDMP) where instead of the admissible set consisting of the Fk−1-measurable control variable uk for any k, the admissible set is restricted to compose of the Fk−s−1-measurable with s ≥ 0 uk for any k. The introduced SDMP plays an important part in obtaining the adapted and casual controller. It should be noted that our derivation avoids the augmented argument, mainly establishes and takes advantage of the link between the optimal state and auxiliary variable. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
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17. Optimal control for stochastic discrete-time systems with multiple input-delays.
- Author
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Wang, Hongxia, Zhang, Huanshui, and Wang, Xuan
- Abstract
The main purpose of the paper is to settle the stochastic linear quadratic control problem for systems with multiple input-delays (SDLQ) which is very intractable and remains to be solved. We introduce a different version of stochastic discrete-time maximum principle (SDMP) where it is shown that the auxiliary variable depends on the optimal system state through a stochastic matrix and the expectation of the relationship matrix happens to be the solution to the standard generalized Riccati equation with the same dimension as the origin system. The relationship explores the key difference of stochastic LQ from the deterministic one. It enables us to obtain the kernel of the optimal cost function for stochastic control and further the analytical and explicit solution to the stochastic LQ control problem with multiple input-delays. [ABSTRACT FROM PUBLISHER]
- Published
- 2012
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18. Linear Quadratic Regulation and Stabilization of Discrete-Time Systems With Delay and Multiplicative Noise.
- Author
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Zhang, Huanshui, Li, Lin, Xu, Juanjuan, and Fu, Minyue
- Subjects
- *
DISCRETE-time system stability , *RICCATI equation , *STOCHASTIC systems , *COST functions , *WHITE noise - Abstract
This paper is concerned with the long-standing problems of linear quadratic regulation (LQR) control and stabilization for a class of discrete-time stochastic systems involving multiplicative noises and input delay. These fundamental problems have attracted resurgent interests due to development of networked control systems. An explicit analytical expression is given for the optimal LQR controller. More specifically, the optimal LQR controller is shown to be a linear function of the conditional expectation of the state, with the feedback gain based on a Riccati-ZXL difference equation. It is also shown that the system is stabilizable in the mean-square sense if and only if an algebraic Riccati-ZXL equation has a particular solution. These results are based on a new technical tool, which establishes a non-homogeneous relationship between the state and the costate of this class of systems, and the introduction of a new Lyapunov function for the finite-horizon optimal control design. [ABSTRACT FROM PUBLISHER]
- Published
- 2015
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19. Linear estimation for random delay systems
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Zhang, Huanshui, Feng, Gang, and Han, Chunyan
- Subjects
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ESTIMATION theory , *LINEAR systems , *STOCHASTIC systems , *DISCRETE-time systems , *KALMAN filtering , *STOCHASTIC convergence , *PERFORMANCE evaluation , *ANALYSIS of covariance - Abstract
Abstract: This paper is concerned with the linear estimation problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time-stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal linear filter is presented based on the Kalman filtering technique. However, the optimal filter is time-varying, stochastic, and does not converge to a steady state in general. Then an alternative suboptimal filter with deterministic gains is developed under a new criteria. The estimator performance in terms of their error covariances is provided, and its mean square stability is established. Finally, a numerical example is presented to illustrate the efficiency of proposed estimators. [Copyright &y& Elsevier]
- Published
- 2011
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20. Linear quadratic regulation for linear time-varying systems with multiple input delays
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Zhang, Huanshui, Duan, Guangren, and Xie, Lihua
- Subjects
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DISCRETE-time systems , *DIGITAL control systems , *DIFFERENTIAL equations , *STOCHASTIC systems - Abstract
Abstract: This paper studies the classic linear quadratic regulation (LQR) problem for both continuous-time and discrete-time systems with multiple input delays. For discrete-time systems, the LQR problem for systems with single input delay has been studied in existing literature, whereas a solution to the multiple input delay case is not known to our knowledge. For continuous-time systems with multiple input delays, the LQR problem has been tackled via an infinite dimensional system theory approach and a frequency/time domain approach. The objective of the present paper is to give an explicit solution to the LQR problem via a simple and intuitive approach. The main contributions of the paper include a fundamental result of duality between the LQR problem for systems with multiple input delays and a smoothing problem for an associated backward stochastic system. The duality allows us to obtain a solution to the LQR problem via standard projection in linear space. The LQR controller is simply constructed by the solution of one backward Riccati difference (for the discrete-time case) or differential (for the continuous-time case) equation of the same order as the plant (ignoring the delays). [Copyright &y& Elsevier]
- Published
- 2006
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21. Stabilization and optimal control of discrete-time systems with multiplicative noise and multiple input delays.
- Author
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Li, Lin, Zhang, Huanshui, and Wang, Yu
- Subjects
- *
DISCRETE-time systems , *ALGEBRAIC equations , *NOISE , *COST control , *STOCHASTIC systems - Abstract
This paper is concerned with the stabilization and optimal control of discrete-time systems with multiplicative noise and multiple input delays. First, it is shown that the systems are stabilizable if and only if some algebraic Riccati-type equations have a solution which satisfies a given condition. To the best of our knowledge, this is the first time to propose a necessary and sufficient stabilizing condition for general multiple-input delay systems with multiplicative noise. The method constructs a Lyapunov–Krasovskii function based on the optimal cost of a finite-horizon LQR problem. Next, under the assumption that the system is stabilizable, an infinite-horizon LQR problem is investigated. The optimal control and the optimal cost are given by the above algebraic Riccati-type equations. Finally, based on the above stabilizing condition, an exact delay range for the stabilization of the system is derived in a special case. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
22. Decentralized control of forward and backward stochastic difference system with nested asymmetric information.
- Author
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Zhang, Shen, Xu, Juanjuan, and Zhang, Huanshui
- Subjects
- *
STOCHASTIC systems , *STOCHASTIC difference equations , *INFORMATION asymmetry , *RICCATI equation , *MAXIMUM principles (Mathematics) , *STOCHASTIC differential equations - Abstract
This paper is concerned with the linear quadratic decentralized control of forward and backward stochastic difference system (FBSDS) with multiplicative noises and nested asymmetric information. The main contribution is to give the equivalent condition for the solvability of the problem and the explicit decentralized optimal controllers in terms of Riccati equations. The key technology is solving the forward and backward stochastic difference equations with partial information derived from stochastic maximum principle. • LQ decentralized control of forward and backward stochastic difference system with nested asymmetric information. • Forward and backward stochastic difference equations with partial information. • Present solvability condition and explicitly decentralized optimal controllers of the problem. • Propose novel Riccati equations to solve forward and backward stochastic difference equations. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
23. Bounded consensus control for stochastic multi-agent systems with additive noises.
- Author
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Wang, Zhongmei, Sun, Huifang, Zhang, Huanshui, and Liu, Xiyu
- Subjects
- *
MULTIAGENT systems , *STOCHASTIC systems , *KALMAN filtering , *TELECOMMUNICATION systems , *NOISE , *STOCHASTIC resonance - Abstract
This paper considers bounded consensus problem of continuous-time linear multi-agent systems with both additive system and communication noises under an undirected communication topology. Owning to the coexistence of the additive system and communication noises, the exact consensus cannot reach. Hence, the distributed controller is to be designed such that all the agents can reach to a collection behavior to some degree. It is supposed that each agent can obtain full state of itself and receive its neighbors' state with additive noises. For each agent, the consensus protocol is designed based on the error between the estimated state of its neighbors' and full state of itself. By means of Kalman filtering and matrix analysis, the bound of consensus is given via the solution of a Lyapunov equation. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
24. Exact controllability of forward and backward stochastic difference system.
- Author
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Wang, Wenjing, Xu, Juanjuan, and Zhang, Huanshui
- Subjects
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STOCHASTIC difference equations , *STOCHASTIC systems , *CONTROLLABILITY in systems engineering - Abstract
In this paper, we study the exact controllability of forward and backward stochastic difference system (FBSDS) with multiplicative noise. Different from the standard system governed by forward stochastic difference equation (FSDE), the inclusion of both initial and terminal conditions in FBSDS complicates the solvability which also leads to the challenge of exact controllability. To overcome the difficulty, we transform the FBSDS into an equivalent backward stochastic difference equation. Accordingly, we derive both the necessary and sufficient Gramian matrix criterion and the Rank criterion for the exact controllability of FBSDS, which is the main contribution of the paper. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
25. Solution to stochastic LQ control problem for Itô systems with state delay or input delay.
- Author
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Liang, Xiao, Xu, Juanjuan, and Zhang, Huanshui
- Subjects
- *
H2 control , *STOCHASTIC systems , *LINEAR systems , *TECHNOLOGY , *DIFFERENTIAL equations - Abstract
This paper is concerned with the linear quadratic (LQ) control problem for Itô stochastic systems with state delay or input delay. The main contribution is to give the explicit optimal LQ controllers for Itô stochastic systems with input delay and with state delay respectively. For the case of state delay, the optimal LQ controller is a linear function of the state at the current time and the past time. For the case of input delay, the optimal LQ controller is a linear function of the state and the past inputs. The key technology is to define the value function and complete the square based on the coupled differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
26. Mixed optimal control for discrete-time stochastic systems with random coefficients.
- Author
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Sun, Yawen, Li, Hongdan, and Zhang, Huanshui
- Subjects
- *
STOCHASTIC difference equations , *STOCHASTIC systems , *DISCRETE-time systems , *STOCHASTIC control theory , *DATA structures , *DIFFERENCE equations , *PROBLEM solving - Abstract
This paper is concerned with the problem of mixed optimal control for discrete-time systems with random coefficients where "mixed" means that there are two controllers: the deterministic controller and the random controller. Different from previous works, random coefficients and controllers with different information structures arise simultaneously in the optimal control problem, which lead to large difficulty. Using decoupling technique to solve the forward and backward stochastic difference equations, the necessary and sufficient conditions for the solvability of optimal control problem are given. An explicit expression of the optimal control strategies is derived based on a stochastic Riccati-type equation, which is new to the best of knowledge. Finally, a pension management problem is solved with the obtained theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
27. Linear quadratic regulation for discrete-time systems with input delay and colored multiplicative noise.
- Author
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Li, Hongdan, Xu, Juanjuan, and Zhang, Huanshui
- Subjects
- *
DISCRETE-time systems , *STOCHASTIC difference equations , *DIFFERENCE equations , *NOISE , *STOCHASTIC systems - Abstract
This paper is concerned with the linear quadratic regulation (LQR) problem for discrete-time systems involving input delay and colored multiplicative noise. Due to the correlation of the adjoining state, this problem will be more complicated than the case of white noise. In this paper, the necessary and sufficient condition for the solvability of optimal control problem is presented by solving the forward and backward stochastic difference equations (FBSDEs). Moreover, the optimal LQR controller is given in terms of the coupled difference equations developed in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
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