Sparse optimal stochastic control

Ito, Kaito; Ikeda, Takeshi; Kashima, Kenji

doi:10.1016/j.automatica.2020.109438

Cited by 13 publications

(12 citation statements)

References 20 publications

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“…In [3], it was shown that sparse signals can be more effectively compressed than densely represented signals. Motivated by these various applications, the maximum hands-off control has been proposed for discrete-time systems [4]- [6], uncertain systems [7], stochastic systems [8], [9], and infinite-dimensional systems [10]. A good survey of the maximum hands-off control is given in [11].…”

Section: Introductionmentioning

confidence: 99%

Risk-Aware Maximum Hands-Off Control Using Worst-Case Conditional Value-at-Risk

Kishida

Nagahara

2023

IEEE Trans. Automat. Contr.

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Section: Introductionmentioning

confidence: 99%

Risk-Aware Maximum Hands-Off Control Using Worst-Case Conditional Value-at-Risk

Kishida

Nagahara

2023

IEEE Trans. Automat. Contr.

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“…For example, a number of results have been established for linear systems, 1-3 nonlinear systems, 4 and stochastic systems. 5 In this study, we focus on a type of sparse control problem called the maximum turn-off control problem, described as follows. Consider a discrete-time linear system with multiple inputs.…”

Section: Introductionmentioning

confidence: 99%

“…If the system has a single input, this problem is exactly the same as the conventional sparse control problem. However, if this is not the case, the problem is somewhat different from the conventional problems, [1][2][3][4][5] in which sparsity is maximized in the elementwise sense.…”

Section: Introductionmentioning

confidence: 99%

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Maximum turn‐off control for discrete‐time linear systems

Iwata

Azuma

Ariizumi

et al. 2022

Intl J Robust & Nonlinear

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We aim to address the problem of finding a control input maximizing the time instants when all control channels take a zero‐value (are turned off) while stabilizing the system to zero over a given horizon length. This problem is called the maximum turn‐off control problem. To solve it, we reduce the problem into a block‐sparse optimization problem with respect to the control input sequence, where the ℓ2false/ℓ0$$ {\ell}_2/{\ell}_0 $$ norm of the control input sequence is the objective function that must be minimized. Because the problem is not convex, we introduce a relaxed problem based on the ℓ2false/ℓ1$$ {\ell}_2/{\ell}_1 $$ norm, which is a convex function, and characterize the equivalence relation between the original and relaxed problems using the so‐called block restricted isometry property (block‐RIP). Based on the equivalence, the solution can be obtained by solving the convex relaxed problem. However, the block‐RIP is not easy to interpret and verify. Thus, we propose the notion of sparse controllability Gramians, which is an extension of the controllability Gramians, and show that the block‐RIP can be interpreted by the eigenvalues of the sparse controllability Gramian. This study presents an easy‐to‐check condition of the block‐RIP. Moreover, the above control framework is extended to a model predictive control scheme. These results are demonstrated using numerical examples.

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“…Optimal control theory is a powerful mathematical tool for achieving control objectives while considering, for example, energy efficiency and sparsity of control [1,2]. Optimal control problems arise in a variety of physical, biological, and economic systems, to name a few.…”

Section: Introductionmentioning

confidence: 99%

Kullback-Leibler control for discrete-time nonlinear systems on continuous spaces

Ito¹,

Kashima²

2022

Preprint

Self Cite

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Kullback-Leibler (KL) control enables efficient numerical methods for nonlinear optimal control problems. The crucial assumption of KL control is the full controllability of the transition distribution. However, this assumption is often violated when the dynamics evolves in a continuous space. Consequently, applying KL control to problems with continuous spaces requires some approximation, which leads to the lost of the optimality. To avoid such approximation, in this paper, we reformulate the KL control problem for continuous spaces so that it does not require unrealistic assumptions. The key difference between the original and reformulated KL control is that the former measures the control effort by KL divergence between controlled and uncontrolled transition distributions while the latter replaces the uncontrolled transition by a noise-driven transition. We show that the reformulated KL control admits efficient numerical algorithms like the original one without unreasonable assumptions. Specifically, the associated value function can be computed by using a Monte Carlo method based on its path integral representation.

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Sparse optimal stochastic control

Cited by 13 publications

References 20 publications

Risk-Aware Maximum Hands-Off Control Using Worst-Case Conditional Value-at-Risk

Risk-Aware Maximum Hands-Off Control Using Worst-Case Conditional Value-at-Risk

Maximum turn‐off control for discrete‐time linear systems

Kullback-Leibler control for discrete-time nonlinear systems on continuous spaces

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