Chance Constrained Covariance Control for Linear Stochastic Systems With Output Feedback

Ridderhof, Jack; Okamoto, K.; Tsiotras, Panagiotis

doi:10.1109/cdc42340.2020.9303731

Cited by 14 publications

(8 citation statements)

References 27 publications

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“…Previous works have shown that state history feedback laws result in a convex formulation of the chance constrained covariance steering problem [4,[19][20][21]. For the present problem, we may therefore jointly optimize updates to the nominal control and the feedback gains, while considering the local effect of the GRF-induced disturbances, and while enforcing chance constraints.…”

Section: Introductionmentioning

confidence: 99%

Chance-Constrained Covariance Steering in a Gaussian Random Field via Successive Convex Programming

Ridderhof¹,

Tsiotras²

2021

Preprint

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The problem of optimizing affine feedback laws that explicitly steer the mean and covariance of an uncertain system state in the presence of a Gaussian random field is considered. Spatiallydependent disturbances are successively approximated with respect to a nominal trajectory by a sequence of jointly Gaussian random vectors. Sequential updates to the nominal control inputs are computed via convex optimization that includes the effect of affine state feedback, the perturbing effects of spatial disturbances, and chance constraints on the closed-loop state and control. The developed method is applied to solve for an affine feedback law to minimize the 99 th percentile of Δ𝑣 required to complete an aerocapture mission around a planet with a randomly disturbed atmosphere.

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Section: Introductionmentioning

confidence: 99%

Chance-Constrained Covariance Steering in a Gaussian Random Field via Successive Convex Programming

Ridderhof¹,

Tsiotras²

2021

Preprint

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“…In contrast with standard LQG control where the final state covariance is indirectly controlled, covariance steering [17] aims at driving the final state mean and covariance to specific prescribed targets. While the first contributions [15,17,33] in the area focused on the steady-state (infinite-horizon) covariance control problem, recently, covariance steering has also been formulated in a finite-horizon control setting, under continuous [2,10,11,12,16] and discrete-time [3,4,7,8] linear dynamics, as well as for systems with partial state information [5,18,27] and nonlinear dynamics [26,31,34].…”

Section: Introductionmentioning

confidence: 99%

Distributed Covariance Steering with Consensus ADMM for Stochastic Multi-Agent Systems

D.¹,

Tsolovikos²,

Bakolas³

et al. 2021

Robotics: Science and Systems XVII

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In this paper, we address the problem of steering a team of agents under stochastic linear dynamics to prescribed final state means and covariances. The agents operate in a common environment where inter-agent constraints may also be present. In order for our method to be scalable to largescale systems and computationally efficient, we approach the problem in a distributed control framework using the Alternating Direction Method of Multipliers (ADMM). Each agent solves its own covariance steering problem in parallel, while additional copy variables for its closest neighbors are introduced to ensure that the inter-agent constraints will be satisfied. The inclusion of these additional variables creates a requirement for consensus between original and copy variables that involve the same agent. For this reason, we employ a variation of ADMM for consensus optimization. Simulation results on multi-vehicle systems under uncertainty with collision avoidance constraints illustrate the effectiveness of our algorithm. The substantially improved scalability of our distributed approach with respect to the number of agents is also demonstrated, in comparison with an equivalent centralized scheme.

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“…The solutions to all of the above problems assume full knowledge of the state at every time step, which is often a limiting assumption on physical systems. Reference [27] solves the CC-CS problem for the case when the state is only indirectly accessible via noise measurements, by adding a Kalman filter in the control loop. By filtering the state and using output feedback, the control problem may be reformulated in terms of the estimated state, and subsequently solved as a convex program.…”

Section: Introductionmentioning

confidence: 99%

“…The contribution of this paper is two-fold. First, we solve the output feedback CC-CS (OFCC-CS) problem in a computationally efficient manner as a non-trivial extension to [27], using the techniques employed in [22]. Second, we introduce a novel approach to make the state and control chance constraints tractable by reformulating them as difference of convex (DC) constraints, as opposed to linearizing the constraints about some reference values as in [22].…”

Section: Introductionmentioning

confidence: 99%

Chance-Constrained Optimal Covariance Steering with Iterative Risk Allocation

Pilipovsky

Tsiotras

2021

2021 American Control Conference (ACC)

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This paper extends the optimal covariance steering problem for linear stochastic systems subject to chance constraints to account for optimal risk allocation. Previous works have assumed a uniform risk allocation to cast the optimal control problem as a semi-definite program (SDP), which can be solved efficiently using standard SDP solvers. We adopt the Iterative Risk Allocation (IRA) formalism from [1], which uses a twostage approach to solve the optimal risk allocation problem for covariance steering. The upper-stage of IRA optimizes the risk, which is proved to be a convex problem, while the lowerstage optimizes the controller with the new constraints. This is done iteratively so as to find the optimal risk allocation that achieves the lowest total cost. The proposed framework results in solutions that tend to maximize the terminal covariance, while still satisfying the chance constraints, thus leading to less conservative solutions than previous methodologies. We also introduce two novel convex relaxation methods to approximate quadratic chance constraints as second-order cone constraints. We finally demonstrate the approach to a spacecraft rendezvous problem and compare the results.

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Chance Constrained Covariance Control for Linear Stochastic Systems With Output Feedback

Cited by 14 publications

References 27 publications

Chance-Constrained Covariance Steering in a Gaussian Random Field via Successive Convex Programming

Chance-Constrained Covariance Steering in a Gaussian Random Field via Successive Convex Programming

Distributed Covariance Steering with Consensus ADMM for Stochastic Multi-Agent Systems

Chance-Constrained Optimal Covariance Steering with Iterative Risk Allocation

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