An iterative procedure for computing time-optimal controls

Knudsen, H.

doi:10.1109/tac.1964.1105637

Cited by 24 publications

(4 citation statements)

References 10 publications

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“…For linear systems, methods of solution to the minimumtime control problems are well known (See, for example, Neustadt, 1960;Eaton, 1962;Knudsen, 1964;Athans and Falb, 1966. ) In most linear systems, the minimum-time control is of the bang-bang type, in which the control functions are at their upper or lower bounds.…”

Section: Methods Of Solutionmentioning

confidence: 99%

A coordinate‐transformation method for the numerical solution of nonlinear minimum‐time control problems

Kwon

Evans

1975

AIChE Journal

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A new method is presented for the numerical solution of nonlinear minimum‐time control problems where at least one of the state variables is monotone. A coordinate transformation converts the problem with fixed end point and free end time to one of free end point and fixed end time. The transformed problem can be solved efficiently by the use of the gradient method with penalty functions to force the system to achieve target values of state variables. Application of the method is illustrated by the synthesis of a minimum‐time temperature path for the thermally initiated bulk polymerization of styrene.

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Section: Methods Of Solutionmentioning

confidence: 99%

A coordinate‐transformation method for the numerical solution of nonlinear minimum‐time control problems

Kwon

Evans

1975

AIChE Journal

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“…This is impossible to do directly since G is not square. Knudsen (15) overcomes thi-difficulty at by augmenting G with an (a + 1) row which is independent of the others. However, for the control problem considered in this report and, in general, for systems to which the algorithm applies, the problem associated with G being non-square can be solved in a number of ways…”

Section: A4andi4 Evaluating G "mentioning

confidence: 99%

“…Second, providing the initial (terminal) state point does not lie on a switching hypersurface which contains optimal trajectories (i.e., h1 + h 2 3) then the previously described difficulties will not occur if (g, tf) is close enough to (9, tf). In general, this means that in the region where Iyk 0.2 and T:yI.10 the derived and optimal steering functions must have the same shape [15]. This condition will not be satisfied if the "guess" for the optimal control corresponding to states which lie within this region is "bad" or if during the flooding process (1f)i+l ((1o)i+l) is separated from (vf), ((1o),) by a switchin& hypersarface.…”

Section: Selection Of the Iterative Scale Factormentioning

confidence: 99%

Time-Optimal Attitude Control of an Axially Symmetric Spinning Spacecraft

Does¹,

Dirk²

1969

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This report considers the problem of controlling both the attitudc and angular velocities of an axially symmetric spacecraft while minimizing the maneuver duration. In particular, various combinations of thrust limited reaction jets are employed to properly orient a spinning space body with respect to specified reference directions starting from known initial conditions of the vehicleva attitude and angular rates. Five control jet configurations are considered: two gimballed systems where torques can be applied about, In cases where the total angular momentum vector and the spin axis are aligned at the initiation and termination of control three modes of operation which characterize optimal steering are defined.These include the two limiting cases where, for example, the control magnitude is very large (small) compared to the angular momentum due to spin. The third mode is characterized by the transition region iii between the "short" and ".long" time solutions. In the latter case, the maneuver duration may be from one to ten revolutions of the spacecraft about its axis of symmetry. Finally, for certain values of the dimensionless physical parameters the response of the non-linear system is typified by that of the linear plant. Hence the results of this report are useful in determining the minimum time required for arbitrarily large reorientations of a vehicle's spin axis.iv r ACKNOWLEDGMENTS

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“…However, optimal controllers n-hich directly implement the maximum principle are impractical for most systems because of their complexity. Such controllers must always have available a computer capable of rapidly solving the differential equations of the system and then computing the control input as a function of time for every initial condition [2], [ 3 ] . They u-ill usually require an on-line digital computer.…”

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confidence: 99%

Design of quasi-optimal minimum-time controllers

Smith

1966

IEEE Trans. Automat. Contr.

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Absfroct-This paper presents and evaluates a heuristic method for designing easily implemented quasi-optimal, minimum-time controllers for high-order dynamic systems. The high-performance, or quasi-optimal, controller is obtained by least-squares fitting points on the optimal switching surface with an easily implemented, linear-segment switching surface. This method is attractive because least-squares approximation is an analytic procedure which is readily applicable to high-order dynamic systems since it requires no visualization of the surface for its application. The method is applicable to linear dynamic systems with real characteristic f r e quencies as well as many other dynamic systems.For evaluation, the method has been used to design the switching surface for a triple-integrator dynamic system (Le., l/s3 plant).A third-order system has been used, instead of a more easily portrayed second-order system, since it more typically illustrates the problems encountered in the approximation of higher-order switching surfaces. Typical response times for the q-Jasi-optimal switching surface in this example are 1.5 to 2 times those of the minimum-time optimal switching surface and roughly one-half those of the best linear switching surface.

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An iterative procedure for computing time-optimal controls

Cited by 24 publications

References 10 publications

A coordinate‐transformation method for the numerical solution of nonlinear minimum‐time control problems

A coordinate‐transformation method for the numerical solution of nonlinear minimum‐time control problems

Time-Optimal Attitude Control of an Axially Symmetric Spinning Spacecraft

Design of quasi-optimal minimum-time controllers

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