Computation of Time Optimal Feedback Control Using Groebner Basis

Patil, Deepak U.; Chakraborty, Debraj

doi:10.1109/tac.2014.2303239

Cited by 22 publications

(8 citation statements)

References 11 publications

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“…These state-feedback strategies involve finding switching surface in terms of state variables that govern the switching the signs of input. Computation of the switching surface for particular case of system (1) was presented in [32], [33] and for general LTI systems in [29], [30].…”

Section: Min-max Time Control Strategy For Two Agentsmentioning

confidence: 99%

“…In the framework of the difference system (3) define the following functions [13], [30] characterizing the states that can be driven to origin using bang-bang input (with u *…”

Section: Min-max Time Control Strategy For Two Agentsmentioning

confidence: 99%

“…Further it was shown in [30] that M 1 ⊂ M 2 and M 1 divides M 2 in two symmetric parts M + 2 and M − 2 . These sets are shown in Figure 2.…”

Section: Min-max Time Control Strategy For Two Agentsmentioning

confidence: 99%

“…This article is an extension of this notion under finite sensing radius constraint. The communication preserving min-max time feedback control strategy [13] proposed in this article utilizes the methods for time optimal feedback computation developed recently in [29], [30].…”

Section: Introductionmentioning

confidence: 99%

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Communication preserving min-max time consensus tracking

Mulla

Chakraborty

2015

2015 European Control Conference (ECC)

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A collection of double integrator agents is considered, where each agent has bounded input and a limited range for receiving information from other agents. One autonomous node (the Root) generates an unknown reference trajectory to which other agents are required to converge in minimum possible time, using only locally available information. A distributed algorithm is proposed to identify a directed spanning tree rooted at the Root agent. The child agent of each edge of this selected tree uses min-max time control strategies to converge to the states of the parent node. Necessary and sufficient conditions are derived for limiting the inter-agent distance so as to preserve the tree communication structure chosen. Under these conditions, the proposed control strategy turns out to be the global communication preserving min-max strategy for the entire collection.

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Section: Min-max Time Control Strategy For Two Agentsmentioning

confidence: 99%

“…In the framework of the difference system (3) define the following functions [13], [30] characterizing the states that can be driven to origin using bang-bang input (with u *…”

Section: Min-max Time Control Strategy For Two Agentsmentioning

confidence: 99%

“…Further it was shown in [30] that M 1 ⊂ M 2 and M 1 divides M 2 in two symmetric parts M + 2 and M − 2 . These sets are shown in Figure 2.…”

Section: Min-max Time Control Strategy For Two Agentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Communication preserving min-max time consensus tracking

Mulla

Chakraborty

2015

2015 European Control Conference (ECC)

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“…In early methods, feasible control paths were exhaustively explored, especially in the analysis of discrete systems. Then, later, results for linear systems were developed by invoking algebraic or convexity properties or via time‐optimal synthesis as early as the 1960s. In the nonlinear setting, Lyapunov‐based approaches are most often employed; however, with this method, typically, only subsets of the NCR can be identified .…”

Section: Introductionmentioning

confidence: 99%

A trajectory‐based method for constructing null controllable regions

Homer

Mahmood

Mhaskar

2019

Intl J Robust & Nonlinear

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Summary The problem of determining a system's set of stabilizable states, the null controllable region (NCR), is intricately related to the problem of determining control Lyapunov functions. In this paper, we address the problem of construction of the NCR for control‐affine nonlinear systems with input constraints. To this end, we explain how the boundary of the NCR is covered by time‐optimal trajectories. To construct the NCR, we employ an algorithm based on Pontryagin's minimum principle, which integrates optimal trajectories of a special smooth system in reverse time from the boundary of an initial NCR estimate. We illustrate this algorithm with linear and nonlinear system examples.

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Time Optimal Feedback Control using Chebyshev Polynomials and Gröbner Basis∗∗This paper is partially supported by Department of Science and Technology Grant SB/S3/EECE/051/2013 and Tata Centre for Technology and Design, IIT Bombay India.

Patil

Chakraborty

2015

IFAC-PapersOnLine

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Computation of Time Optimal Feedback Control Using Groebner Basis

Cited by 22 publications

References 11 publications

Communication preserving min-max time consensus tracking

Communication preserving min-max time consensus tracking

A trajectory‐based method for constructing null controllable regions

Time Optimal Feedback Control using Chebyshev Polynomials and Gröbner Basis∗∗This paper is partially supported by Department of Science and Technology Grant SB/S3/EECE/051/2013 and Tata Centre for Technology and Design, IIT Bombay India.

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