Multitime Controllability, Observability and Bang-Bang Principle

Udrişte, Constantin

doi:10.1007/s10957-008-9430-2

Cited by 28 publications

(24 citation statements)

References 6 publications

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“…The basic problem in multitime nonlinear control theory [21]- [28] is to construct q-sheets x(t), t = (t α ) ∈ Ω t0t1 ⊂ R q + , α = 1, q, connecting two points x 0 , x 1 of a manifold M , subject to sheet constraints of the form x(t) ∈ V (x(t)), where V (x) ∈ T x M are subsets varying with the point x. The sets V (x) are represented as images of a map u → F (x, u) = (F α (x, u)), where the control u varies over some auxiliary set, usually a subset of a Euclidean space.…”

Section: Udrişte and V Cianciomentioning

confidence: 99%

“…We apply the Pontryagin minimum principle (for multitime minimum principle, see [21][22][23][24][25][26][27][28]). In general notation, we have x = (x i ), u = (u a ), p = (p i ), a = 1, 4; i = 1, 5,…”

Section: Solutionmentioning

confidence: 99%

“…To solve such a multitime optimum problem we use the techniques from our papers [21][22][23][24][25][26][27][28]. To simplify, let us show that the foregoing problem can be solved via controls of gradient type, i.e.…”

Section: Two-time Optimal Control On Black Hole Systemmentioning

confidence: 99%

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Controllability of Nonholonomic Black Holes Systems

Udrişte

Ciancio

2012

Int. J. Geom. Methods Mod. Phys.

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This paper studies the sub-Lorentz-Vrȃnceanu geometry and the optimal control of nonholonomic black hole systems. This is strongly connected to the possibility of describing a nonholonomic black hole system as kernel of a Gibbs-Pfaff form or by the span of four appropriate vector fields. Joining techniques from sub-Riemannian geometry, optimal control and thermodynamics, we bring into attention new models of black holes systems. These are reflected by the original results: a Lorentz-Vrȃnceanu geometry on the total space, a new sub-Lorentz-Vrȃnceanu geometry, a new stress-energy-momentum tensor, original solutions to Einstein field equations, and the controllability of nonholonomic black holes systems by uni-temporal or bi-temporal controls.

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Section: Udrişte and V Cianciomentioning

confidence: 99%

Section: Solutionmentioning

confidence: 99%

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Controllability of Nonholonomic Black Holes Systems

Udrişte

Ciancio

2012

Int. J. Geom. Methods Mod. Phys.

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“…The term multitime was initially introduced in physics by Dirac in 1932 and was later used in mathematics (see, for example, [18,21]). Multitime control theory is related to the partial derivatives of dynamical systems * Correspondence: jhashalini.rash89@gmail.com 2010 AMS Mathematics Subject Classification: 49J20, 65K10, 93C35 The research of the first author was financially supported by CSIR, New Delhi, India, through Grant No.…”

Section: Introductionmentioning

confidence: 99%

Modi ed objective function approach for multitime variational problems

2018

Turk J Math

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The present paper is devoted to studying the modified objective function approach used for solving the considered multitime variational problem. In this method, a new multitime variational problem is constructed by modifying the objective function in the original considered multitime variational problem. Further, the equivalence between an optimal solution to the original multitime variational problem and its associated modified problem is established under both hypotheses of invexity and generalized invexity defined for a multitime functional. Thereafter, using the modified objective function method, we derive the saddle-point results for the considered multitime variational problem. Moreover, we provide some examples to illustrate the results established in the paper.

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“…In Udrişte (2008), it is studied the controllability, observability and bang-bang properties of multi-time completely integrable autonomous linear systems described by partial differential equations (PDE). In O'Brien (2006), it is described a bang-bang control algorithm developed for a double integrator plant that can be extended to higher order plants with two integrators.…”

Section: Introductionmentioning

confidence: 99%

Rate control system algorithm developed in state space for models with parameter uncertainties

Teixeira¹

2011

JATM

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researching in weightlessness above the atmosphere needs a payload to carry the experiments. To achieve the weightlessness, the payload uses a rate control system (RCS) in order to reduce the centripetal acceleration within the payload. The rate control system normally has actuators that supply a constant force when they are turned on. The development of an algorithm control for this rate control system will be based on the minimum-time problem method in the state space to overcome the payload and actuators dynamics uncertainties of the parameters. This control algorithm uses the initial conditions of optimal trajectories to create intermediate points or to adjust existing points of a switching function. It associated with inequality constraint will form a decision function to turn on or off the actuators. This decision function, for linear time-invariant systems in state space, needs only to test the payload state variables instead of spent effort in solving differential equations and it will be tuned in real time to the payload dynamic. It will be shown, through simulations, the results obtained for some cases of parameters uncertainties that the rate control system algorithm reduced the payload centripetal acceleration below µg level and keep this way with no limit cycle.

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Multitime Controllability, Observability and Bang-Bang Principle

Cited by 28 publications

References 6 publications

Controllability of Nonholonomic Black Holes Systems

Controllability of Nonholonomic Black Holes Systems

Modi ed objective function approach for multitime variational problems

Rate control system algorithm developed in state space for models with parameter uncertainties

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