Nonlinear Uncertainty Control with Iterative Covariance Steering

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

doi:10.48550/arxiv.1903.10919

Cited by 4 publications

(9 citation statements)

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“…Note that both of the previously described linearized models are different from the one obtained after linearizing a nonlinear system around a given pair of reference state and input sequences z0:N := {z(t) : t ∈ [0, N ] d } and ū0:N−1 := {ū(t) : t ∈ [0, N − 1] d }, respectively, as is proposed, for instance, in [16]. In the latter case, one would consider a single time-varying linearized system described by the following equation:…”

Section: Collection Of Finite-horizon Linearized Covariance Steering ...mentioning

confidence: 99%

“…Nonlinear density steering problems for feedback linearizable nonlinear systems were recently studied in [15]. An iterative covariance steering algorithm for nonlinear systems based on a simple linearization of the system dynamics along reference state and input trajectories can be found in [16]. Stochastic nonlinear model predictive control with probabilistic constraints can be found in [17]- [20].…”

Section: Introductionmentioning

confidence: 99%

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Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform

Bakolas¹,

Tsolovikos²

2020

Preprint

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In this work, we consider the problem of steering the first two moments of the uncertain state of a discretetime nonlinear stochastic system to prescribed goal quantities at a given final time. In principle, the latter problem can be formulated as a density tracking problem, which seeks for a feedback policy that will keep the probability density function of the state of the system close, in terms of an appropriate metric, to the goal density. The solution to the latter infinite-dimensional problem can be, however, a complex and computationally expensive task. Instead, we propose a more tractable and intuitive approach which relies on a greedy control policy. The latter control policy is comprised of the first elements of the control policies that solve a sequence of corresponding linearized covariance steering problems. Each of these covariance steering problems relies only on information available about the state mean and state covariance at the current stage and can be formulated as a tractable (finitedimensional) convex program. At each stage, the information on the state statistics is updated by computing approximations of the predicted state mean and covariance of the resulting closedloop nonlinear system at the next stage by utilizing the (scaled) unscented transform. Numerical simulations that illustrate the key ideas of our approach are also presented.

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Section: Collection Of Finite-horizon Linearized Covariance Steering ...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform

Bakolas¹,

Tsolovikos²

2020

Preprint

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“…Recently, the covariance control theory was extended to a finite horizon control setting [5]- [10] where the goal was to steer the state covariance of a continuous-time linear dynamic system from an initial value to a terminal one. This finite-horizon perspective was further extended to cases with discretetime dynamics [11], [12], nonlinear dynamics [13], multiple systems [14] etc. The basic idea of covariance control is to relax the hard constraints in classical optimal control with soft probabilistic constraints; the former is usually unrealistically strong due to the stochastic disturbance.…”

Section: Introductionmentioning

confidence: 99%

“…The nonlinear covariance control problem was recently studied in [13] under different assumptions with a different method. In particular, the cost function used in [13] is quadratic.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Covariance Control via Differential Dynamic Programming

Cao

Theodorou

et al. 2020

2020 American Control Conference (ACC)

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We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This problem is considerably more complicated than previous studies on covariance control for linear systems. We leverage a widely used technique -differential dynamic programming -in nonlinear optimal control to achieve our goal. In particular, we adopt the stochastic differential dynamic programming framework to handle the stochastic dynamics. Additionally, to enforce the terminal statistical constraints, we construct a Lagrangian and apply a primal-dual type algorithm. Several examples are presented to demonstrate the effectiveness of our framework.

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“…The authors in [9] introduced the first covariance steering controller that simultaneously deals with the mean and the covariance dynamics such that the resulting trajectories satisfy the state chance constraints. The approach was further modified to be computationally more efficient in [15], which was eventually extended to deal with input hard constraints [16] and nonlinear dynamics [17]. Furthermore, covariance control theory was applied to autonomous vehicle control in [18] and spacecraft control in [19], [20].…”

Section: Introductionmentioning

confidence: 99%

Chance Constrained Covariance Control for Linear Stochastic Systems With Output Feedback

Ridderhof¹,

Okamoto²,

Tsiotras³

2020

Preprint

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We consider the problem of steering, via output feedback, the state distribution of a discrete-time linear stochastic system from an initial Gaussian distribution to a terminal Gaussian distribution with prescribed mean and maximum covariance, subject to probabilistic path constraints on the state. The filtered state is obtained by a Kalman filter, and the problem is formulated as a deterministic convex program in terms of the distribution of the filtered state. We observe that in the presence of constraints on the state covariance, and in contrast to classical LQG control, the optimal feedback control depends on both the process noise and the observation model. The effectiveness of the proposed approach is verified using a simple numerical example.

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Nonlinear Uncertainty Control with Iterative Covariance Steering

Cited by 4 publications

References 0 publications

Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform

Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform

Nonlinear Covariance Control via Differential Dynamic Programming

Chance Constrained Covariance Control for Linear Stochastic Systems With Output Feedback

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