Covariance Control of Discrete-Time Gaussian Linear Systems Using Affine Disturbance Feedback Control Policies

Balci, Isin M.; Bakolas, Efstathios

doi:10.1109/cdc45484.2021.9683236

Cited by 8 publications

(15 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In our previous work, we have addressed covariance steering and minimum variance steering problems for discrete-time stochastic linear systems under both full state and partial state information based on convex optimization techniques. 10,11,14,16,30,31 In these references, the reduction of the stochastic optimal control problems to convex programs relied on the utilization of the so-called state feedback control parametrization. 32 According to this parametrization, the control input at each stage corresponds to an affine function of the states (or outputs) visited up to the present stage.…”

Section: Literature Reviewmentioning

confidence: 99%

“…This section shows that different affine control policy parametrizations are equivalent, meaning their corresponding optimization problems yield the same optimal solution in terms of control input sequences, concatenated state and input vectors, and resulting cost given the same initial state and disturbance sequence. We mentioned three other policy parametrizations that are used to solve covariance steering problems in the literature, namely the state feedback, 20 state history feedback, 31 and auxiliary variable feedback 44 policies. It is shown that the optimal policy parametrization for the covariance steering problem is the state feedback policy parametrization, 20,45 and optimal policy parameters for an instance of the covariance steering problem can be efficiently found by the associated SDP.…”

Section: Control Policy Comparison With Existing Approachesmentioning

confidence: 99%

“…Furthermore, the matrix  is constrained to have block lower-triangular structure to preserve the causality of the control policy. However, this parametrization does not yield a convex optimization problem for the covariance steering (or even more standard stochastic optimal control problems, such as the Linear Quadratic Gaussian problem) since the covariance of the concatenated state vector x is given by 31 :…”

Section: State History Feedback Policymentioning

confidence: 99%

See 2 more Smart Citations

Constrained minimum variance and covariance steering based on affine disturbance feedback control parameterization

Balci,

Bakolas

2024

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

This paper deals with finite‐horizon minimum‐variance and covariance steering problems subject to constraints. The goal of the minimum variance problem is to steer the state mean of an uncertain system to a prescribed vector while minimizing the trace of its terminal state covariance whereas the goal in the covariance steering problem is to steer the covariance matrix of the terminal state to a prescribed positive definite matrix. The paper proposes a solution approach that relies on a stochastic version of the affine disturbance feedback control parametrization. In this control policy parametrization, the control input at each stage is expressed as an affine function of the history of disturbances that have acted upon the system. It is shown that this particular parametrization reduces the stochastic optimal control problems considered in this paper into tractable convex programs or difference of convex functions programs with essentially the same decision variables. In addition, the paper proposes a variation of this control parametrization that relies on truncated histories of past disturbances, which allows for sub‐optimal controllers to be designed that strike a balance between performance and computational cost. The suboptimality of the truncated policies is formally analyzed and closed form expressions are provided for the performance loss due to the use of the truncation scheme. Finally, the paper concludes with a comparative analysis of the truncated versions of the proposed policy parametrization and other standard policy parametrizations through numerical simulations.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Control Policy Comparison With Existing Approachesmentioning

confidence: 99%

Section: State History Feedback Policymentioning

confidence: 99%

See 1 more Smart Citation

Constrained minimum variance and covariance steering based on affine disturbance feedback control parameterization

Balci,

Bakolas

2024

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…Figures 2a and 2c show comparison results between the randomized state feedback policy in (11), the truncated affine disturbance feedback policy [15] and the truncated state history feedback policy [22]. In the utilized truncated affine disturbance feedback policy, only the last disturbance term w k−1 from the history of disturbances is used for the computation of the control input u k at time step k (in contrast with the standard or non-truncated affine disturbance feedback policy in which the whole history of disturbances {w 0 , .…”

Section: Numerical Experimentsmentioning

confidence: 99%

Exact SDP Formulation for Discrete-Time Covariance Steering with Wasserstein Terminal Cost

Balci¹,

Bakolas²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

In this paper, we present new results on the covariance steering problem with Wasserstein distance terminal cost. We show that the state history feedback control policy parametrization, which has been used before to solve this class of problems, requires an unnecessarily large number of variables and can be replaced by a randomized state feedback policy which leads to more tractable problem formulations without any performance loss. In particular, we show that under the latter policy, the problem can be equivalently formulated as a semidefinite program (SDP) which is in sharp contrast with our previous results that could only guarantee that the stochastic optimal control problem can be reduced to a difference of convex functions program. Then, we show that the optimal policy that is found by solving the associated SDP corresponds to a deterministic state feedback policy. Finally, we present nontrivial numerical simulations which show the benefits of our proposed randomized state feedback policy derived from the SDP formulation of the problem over existing approaches in the field in terms of computational efficacy and controller performance.

show abstract

“…Most terminal constraint control problems for stochastic systems concentrate on the optimal covariance control problem, which is concerned with how to optimally steer the terminal state of an additive system to a given probability distribution with minimum energy [9–12]. The optimal steering problem remains to be studied because its solvability heavily depends on a nonlinear Schr

\ddot{o}

dinger system, whose solution is quite challenging [13, 14].…”

Section: Introductionmentioning

confidence: 99%

Stochastic linear quadratic optimal control problem with terminal state constraints

Wang,

Hu,

Liu

et al. 2023

Asian Journal of Control

View full text Add to dashboard Cite

This paper addresses the stochastic linear quadratic (LQ) control problem with first‐ and second‐order moment constraints on the terminal state. The problem is a modified version of the optimal covariance control problem, where the terminal state is steered to a given probability distribution. Studying a multiplicative‐noise stochastic system rather than an additive‐noise system is a salient feature. Unlike the existing ideas in the optimal steering, by using the Lagrange multipliers method and establishing the stochastic maximum principle, our problem is converted into solving forward–backward stochastic difference equations (FBSDEs), which is a special stochastic two‐point boundary‐value problem (TPBVP). We provide the optimal closed‐loop controller and necessary and sufficient solvability conditions by developing a nonhomogeneous relationship between the optimal state and costate in FBSDEs. Finally, numerical examples are given to demonstrate our results.

show abstract

Covariance Control of Discrete-Time Gaussian Linear Systems Using Affine Disturbance Feedback Control Policies

Cited by 8 publications

References 20 publications

Constrained minimum variance and covariance steering based on affine disturbance feedback control parameterization

Constrained minimum variance and covariance steering based on affine disturbance feedback control parameterization

Exact SDP Formulation for Discrete-Time Covariance Steering with Wasserstein Terminal Cost

Stochastic linear quadratic optimal control problem with terminal state constraints

Contact Info

Product

Resources

About