Differential dynamic programming methods for solving bang-bang control problems

Jacobson, D. H.

doi:10.1109/tac.1968.1099026

Cited by 49 publications

(17 citation statements)

References 13 publications

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“…The singular arc is given by us = xi = xz = 0 (5. The predicted behavior at the junction is useful knowledge for numerical computational schemes, e. g. , Jacobson [9] was able to successfully compute bang-bang solutions for this problem with T sufficiently small so that the singular arc did not occur. However, for large T the nonanalytic junction came into play After computing about ten switches, the method became unstable [10].…”

Section: A(t) Is A(tx(t)x(t)) (42) P(t) a B(tx(t)%(t)) (43)mentioning

confidence: 99%

Necessary Conditions Joining Optimal Singular and Nonsingular Subarcs

Mcdanell¹,

Powers²

1971

SIAM Journal on Control

137

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Section: A(t) Is A(tx(t)x(t)) (42) P(t) a B(tx(t)%(t)) (43)mentioning

confidence: 99%

Necessary Conditions Joining Optimal Singular and Nonsingular Subarcs

Mcdanell¹,

Powers²

1971

SIAM Journal on Control

137

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“…However, their approach required a kinematic plan to be given and only optimized the timing of the motion. Several authors have developed risk-sensitive optimal control methods [10,36] for nonlinear stochastic systems with known models [6] or datadriven control-learning approaches [35,4,15].…”

Section: Related Workmentioning

confidence: 99%

DIRTREL: Robust Trajectory Optimization with Ellipsoidal Disturbances and LQR Feedback

Manchester

Kuindersma

2017

Robotics: Science and Systems XIII

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Abstract-Many critical robotics applications require robustness to disturbances arising from unplanned forces, state uncertainty, and model errors. Motion planning algorithms that explicitly reason about robustness require a coupling of trajectory optimization and feedback design, where the system's closedloop response to bounded disturbances is optimized. Due to the often-heavy computational demands of solving such problems, the practical application of robust trajectory optimization in robotics has so far been limited. We derive a tractable robust optimization algorithm that combines direct transcription with linear-quadratic control design to reason about closed-loop responses to disturbances. In the case of ellipsoidal disturbance sets, the state and input deviations along a nominal trajectory can be computed locally in closed form, thus allowing for fast evaluations of robust cost and constraint functions. The resulting algorithm, called DIRTREL, is an extension of classical direct transcription that demonstrably improves tracking performance over non-robust formulations while incurring only a modest increase in computational cost. We evaluate the algorithm in several simulated robot control tasks.

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“…The underlying idea is that a rough initial approximation is determined from sufficient conditions via global optimization and then iteratively refined using local optimality conditions, i.e., stationarity (U = R m ), or the maximum principle (U ⊂ R m ). Let us find the conditions under which minimization (7) of the Bellman equation [6] ∂S(t,…”

Section: Formulation Of the Degenerate Design Problemmentioning

confidence: 99%

Nonlinear Controller Design: An Iterative Relaxation Method

Сизых

2005

Autom Remote Control

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Analytical design of optimal controllers for nonlinear systems is studied. To refine the method related to minimization of the general work functional, the initial control problem is transformed to a degenerate problem and solved with a suitable strategy. The joint control design strategy is the construction of minimizing sequences, which converge in intervals by stationarity to the optimal process of the initial problem. An illustrative example is given.

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Differential dynamic programming methods for solving bang-bang control problems

Cited by 49 publications

References 13 publications

Necessary Conditions Joining Optimal Singular and Nonsingular Subarcs

Necessary Conditions Joining Optimal Singular and Nonsingular Subarcs

DIRTREL: Robust Trajectory Optimization with Ellipsoidal Disturbances and LQR Feedback

Nonlinear Controller Design: An Iterative Relaxation Method

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