TY - GEN

T1 - Optimal control of the state statistics for a linear stochastic system

AU - Chen, Yongxin

AU - Georgiou, Tryphon

AU - Pavon, Michele

N1 - Publisher Copyright:
© 2015 IEEE.

PY - 2015/2/8

Y1 - 2015/2/8

N2 - We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from LQG as well as from formulations that bound the probability of violating state constraints. We develop results for optimal state-feedback control in the two cases where i) steering of the state distribution is to take place over a finite window of time with minimum energy, and ii) the goal is to maintain the state at a stationary distribution over an infinite horizon with minimum power. For both problems the distribution of noise and state are Gaussian. In the first case, we show that provided the system is controllable, the state can be steered to any terminal Gaussian distribution over any specified finite time-interval. In the second case, we characterize explicitly the covariance of admissible stationary state distributions that can be maintained with constant state-feedback control. The conditions for optimality are expressed in terms of a system of dynamically coupled Riccati equations in the finite horizon case and in terms of algebraic conditions for the stationary case. In the case where the noise and control share identical input channels, the Riccati equations for finite-horizon steering become homogeneous and can be solved in closed form. The present paper is largely based on our recent work in [1], [2] and presents an overview of certain key results.

AB - We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from LQG as well as from formulations that bound the probability of violating state constraints. We develop results for optimal state-feedback control in the two cases where i) steering of the state distribution is to take place over a finite window of time with minimum energy, and ii) the goal is to maintain the state at a stationary distribution over an infinite horizon with minimum power. For both problems the distribution of noise and state are Gaussian. In the first case, we show that provided the system is controllable, the state can be steered to any terminal Gaussian distribution over any specified finite time-interval. In the second case, we characterize explicitly the covariance of admissible stationary state distributions that can be maintained with constant state-feedback control. The conditions for optimality are expressed in terms of a system of dynamically coupled Riccati equations in the finite horizon case and in terms of algebraic conditions for the stationary case. In the case where the noise and control share identical input channels, the Riccati equations for finite-horizon steering become homogeneous and can be solved in closed form. The present paper is largely based on our recent work in [1], [2] and presents an overview of certain key results.

KW - covariance control

KW - Linear stochastic systems

KW - stationary distributions

KW - stochastic optimal control

UR - http://www.scopus.com/inward/record.url?scp=84961987964&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84961987964&partnerID=8YFLogxK

U2 - 10.1109/CDC.2015.7403245

DO - 10.1109/CDC.2015.7403245

M3 - Conference contribution

AN - SCOPUS:84961987964

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 6508

EP - 6515

BT - 54rd IEEE Conference on Decision and Control,CDC 2015

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 54th IEEE Conference on Decision and Control, CDC 2015

Y2 - 15 December 2015 through 18 December 2015

ER -