Discrete-time Optimal Covariance Steering via Semidefinite Programming

Rapakoulias, George; Tsiotras, Panagiotis

doi:10.48550/arxiv.2302.14296

Cited by 3 publications

(5 citation statements)

References 22 publications

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“…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. However, the presence of chance-constraints, defined as in (13), violates the convexity of the optimization-based formulation of the covariance steering problem as a SDP.…”

Section: Control Policy Comparison With Existing Approachesmentioning

confidence: 99%

“…This policy parametrization is optimal for unconstrained covariance steering problems in both continuous-time 7 and discrete-time. 20,45,46 While Reference 20 suggests a randomized version of the latter policy, it is proven that at optimality, the randomized component is zero, making the optimal policy a deterministic state feedback policy. 20 Under the state feedback policy parametrization, the dynamics of the state mean and the state covariance are given as follows:…”

Section: State Feedback Policymentioning

confidence: 99%

“…Comparisons with the state feedback policy will also be omitted since the latter policy does not yield a convex optimization problem when chance constraints are considered. To address the latter optimization problem one may resort to, for instance, successive convexification methods 45 ; however, it should be noted that the convexified sub-problems obtained by such methods are usually ill-conditioned, and commercial solvers such as MOSEK often fail to return a solution. 51…”

Section: Numerical Experimentsmentioning

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

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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.

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Section: Control Policy Comparison With Existing Approachesmentioning

confidence: 99%

Section: State Feedback Policymentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

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

Balci,

Bakolas

2024

Intl J Robust & Nonlinear

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“…In the sequel, and similar to [38], we treat the moments of the intermediate states {Σ k , µ k } N −1 k=1 in the steering horizon as decision variables in the resulting optimization problem.…”

Section: Problem Reformulationmentioning

confidence: 99%

Covariance Steering With Optimal Risk Allocation

Pilipovsky¹,

Tsiotras²

2021

IEEE Trans. Aerosp. Electron. Syst.

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This paper studies the problem of steering the distribution of a linear time-invariant system from an initial normal distribution to a terminal normal distribution under no knowledge of the system dynamics. This data-driven control framework uses data collected from the input and the state and utilizes the seminal work by Willems et al. to construct a databased parametrization of the mean and the covariance control problems. These problems are then solved to optimality as convex programs using standard techniques from the covariance control literature. We also discuss the equivalence of indirect and direct data-driven covariance steering designs, as well as a regularized version of the problem that provides a balance between the two. We illustrate the proposed framework through a set of randomized trials on a double integrator system and show that the results match up almost exactly with the corresponding model-based method in the noiseless case. We then analyze the robustness properties of the data-free and data-driven covariance steering methods and demonstrate the trade-offs between performance and optimality among these methods in the presence of data corrupted with exogenous noise.

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“…As safety requirements in robotics and control are of great significance, covariance steering (CS) theory has recently emerged as a promising approach for guiding the state distribution of a system to prescribed targets while providing probabilistic safety guarantees [3,4,10,20]. Successful robotics applications can be found in trajectory optimization [5,34], path planning [23], flight control [7,17,27], multi-robot systems [31,33] and robotic manipulation [18], to name a few. While the main barrier for applying CS methods for multi-agent stochastic control was due to their significant computational requirements, recent distributed optimization based approaches [31,33] have shown that CS is a viable option for multi-agent systems.…”

Section: Introductionmentioning

confidence: 99%

Distributed Hierarchical Distribution Control for Very-Large-Scale Clustered Multi-Agent Systems

D.¹,

Li²,

Theodorou³

2023

Robotics: Science and Systems XIX

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As the scale and complexity of multi-agent robotic systems are subject to a continuous increase, this paper considers a class of systems labeled as Very-Large-Scale Multi-Agent Systems (VLMAS) with dimensionality that can scale up to the order of millions of agents. In particular, we consider the problem of steering the state distributions of all agents of a VLMAS to prescribed target distributions while satisfying probabilistic safety guarantees. Based on the key assumption that such systems often admit a multi-level hierarchical clustered structure -where the agents are organized into cliques of different levels -we associate the control of such cliques with the control of distributions, and introduce the Distributed Hierarchical Distribution Control (DHDC) framework. The proposed approach consists of two subframeworks. The first one, Distributed Hierarchical Distribution Estimation (DHDE), is a bottom-up hierarchical decentralized algorithm which links the initial and target configurations of the cliques of all levels with suitable Gaussian distributions. The second part, Distributed Hierarchical Distribution Steering (DHDS), is a top-down hierarchical distributed method that steers the distributions of all cliques and agents from the initial to the targets ones assigned by DHDE. Simulation results that scale up to two million agents demonstrate the effectiveness and scalability of the proposed framework. The increased computational efficiency and safety performance of DHDC against related methods is also illustrated. The results of this work indicate the importance of hierarchical distribution control approaches towards achieving safe and scalable solutions for the control of VLMAS.

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Discrete-time Optimal Covariance Steering via Semidefinite Programming

Cited by 3 publications

References 22 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

Covariance Steering With Optimal Risk Allocation

Distributed Hierarchical Distribution Control for Very-Large-Scale Clustered Multi-Agent Systems

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