Practical Methods for Optimal Control Using Nonlinear Programming

By John T. Betts, I. Kolmanovsky. 1987

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Citations in the corpus

Reinforcement learning in robotics: A survey (2013, methodology): “…stochastic optimization methods (such as Nelder–Mead (Bagnell and Schneider, 2001), cross-entropy (Rubinstein and Kroese, 2004) and population-based methods (Goldberg, 1989)) to approaches coming from optimal control such as DDP (Atkeson, 1998) and multiple shooting approaches (Betts, 2001).”
Rate of convergence for the Legendre pseudospectral optimal control of feedback linearizable systems (2010, methodology): “ent discretizations of the problem: Euler, Hermite-Simpson [8] and PS. Part of the reason for choosing the Hermite-Simpson discretization scheme for comparison is because it is a widely-used method that forms the basis of wellknown commercial optimal control software packages such as OTIS [8] and SO”
Optimal trajectory planning for trains – A pseudospectral method and a mixed integer linear programming approach (2013, methodology): “In a direct method, the continuous-time optimal control problem is transformed into a nonlinear programming problem (Bettes, 2001).”
On semi-convergence of parameterized Uzawa methods for singular saddle point problems☆ (2009, background): “1) arises in a wide variety of scientific and engineering applications such as computational fluid dynamics, mixed finite element approximation of elliptic partial differential equations, optimization, optimal control, weighted least-squares problems, electronic networks, computer graphics andothers”
Modeling and optimization with Optimica and JModelica.org - Languages and tools for solving large-scale dynamic optimization problems (2010, methodology): “A detailed treatment of direct collocation methods is given in [25].”
Homotopic approach and pseudospectral method applied jointly to low thrust trajectory optimization (2012, background): “Some focus on advanced evolving algorithms [13–16] in parameter optimization and most of them try to transcribe the trajectory optimization problem into a NLP [10–12].”
Fast Model Predictive Control Using Online Optimization (2010, methodology): “For dynamic trajectory optimization using optimization methods, see [26].”
Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control (2009, background): “Details on these methods and how they relate to one another can be found, e.g., in [5] [2].”
On Discrete-Time Optimality Conditions for Pseudospectral Methods (2006, unknown): “36,37 This implies that a practitioner may treat the outcome of the LGL/PS method in terms of a rigorous application of the Pontryagin Minimum Principle and accept or reject solutions based on the optimality conditions.”
Whole-body motion planning with centroidal dynamics and full kinematics (2014, methodology): “This technique is widely used in trajectory optimization [1], [9], [25].”
Efficient Numerical Methods for Nonlinear MPC and Moving Horizon Estimation (2009, methodology): “While several excellent numerical optimization textbooks exist [25, 28, 44], in the field of numerical optimal control there are only a few [2, 11], and when it comes to real-time optimal control algorithms there is even less overview material [5].”