Linear quadratic regulation for Itô system with state delays

This paper is concerned with the linear quadratic (LQ) control problem for Itô stochastic system with state delays. An explicit and analytical expression is given for the optimal LQ controller in terms of several coupled Riccati equations. The key technology is to define the value function and complete the square.

[1]  H. Banks,et al.  Optimal control of linear time-delay systems , 1969 .

[2]  H. Sendaula.  Optimal control of linear systems with time-varying lags , 1972 .

[3]  D. Williams.  STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[4]  M. Athans,et al.  Further results on the uncertainty threshold principle , 1977 .

[5]  R. Vinter,et al.  The Infinite Time Quadratic Control Problem for Linear Systems with State and Control Delays: An Evolution Equation Approach , 1981 .

[6]  A. Olbrot.  A sufficiently large time delay in feedback loop must destroy exponential stability of any decay rate , 1984 .

[7]  S. Peng.  A general stochastic maximum principle for optimal control problems , 1990 .

[8]  K. Morris,et al.  Solving the linear quadratic optimal control problem for infinite-dimensional systems , 1996 .

[9]  Kolmanovskii,et al.  Introduction to the Theory and Applications of Functional Differential Equations , 1999 .

[10]  D. Hinrichsen,et al.  H∞-type control for discrete-time stochastic systems , 1999 .

[11]  X. Zhou,et al.  Stochastic Controls: Hamiltonian Systems and HJB Equations , 1999 .

[12]  X. Chen,et al.  Discrete-time Indefinite LQ Control with State and Control Dependent Noises , 2002, J. Glob. Optim..

[13]  Wook Hyun Kwon,et al.  Delay-dependent robust Hinfinity control for uncertain systems with a state-delay , 2004, Autom..

[14]  Huijun Gao,et al.  New Results on Stability of Discrete-Time Systems With Time-Varying State Delay , 2007, IEEE Transactions on Automatic Control.

[15]  Zhen Wu,et al.  The quadratic problem for stochastic linear control systems with delay , 2011, Proceedings of the 30th Chinese Control Conference.

[16]  Kemao Ma,et al.  Global output feedback stabilization of upper-triangular nonlinear time-delay systems , 2012 .

[17]  Ishak Hashim,et al.  Adaptive pseudospectral methods for solving constrained linear and nonlinear time-delay optimal control problems , 2014, J. Frankl. Inst..

[18]  Minyue Fu,et al.  Linear Quadratic Regulation and Stabilization of Discrete-Time Systems With Delay and Multiplicative Noise , 2015, IEEE Transactions on Automatic Control.

[19]  Huanshui Zhang,et al.  Optimal Control and Stabilization for Networked Control Systems With Packet Dropout and Input Delay , 2017, IEEE Transactions on Circuits and Systems II: Express Briefs.