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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 14:09:29 +0000Nonlinear Games: examples and counterexamples
https://resolver.caltech.edu/CaltechAUTHORS:20140527-071022483
Authors: {'items': [{'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John'}, 'orcid': '0000-0002-1828-2486'}, {'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}, {'id': 'Shapiro-B', 'name': {'family': 'Shapiro', 'given': 'Benjamin'}}, {'id': 'Nevistić-V', 'name': {'family': 'Nevistić', 'given': 'Vesna'}}]}
Year: 1996
DOI: 10.1109/CDC.1996.577292
Popular nonlinear control methodologies are compared using benchmark examples generated with a "converse Hamilton-Jacobi-Bellman" method (CoHJB). Starting with the cost and optimal value function V, CoHJB solves HJB PDEs "backwards" algebraically to produce nonlinear dynamics and optimal controllers and disturbances. Although useless for design, it is great for generating benchmark examples. It is easy to use, computationally tractable, and can generate essentially all possible nonlinear optimal control problems. The optimal control and disturbance are then known and can be used to study actual design methods, which must start with the cost and dynamics without knowledge of V. This paper gives a brief introduction to the CoHJB method and some of the ground rules for comparing various methods. Some very simple examples are given to illustrate the main ideas. Both Jacobian linearization and feedback linearization combined with linear optimal control are used as "strawmen" design methods.https://authors.library.caltech.edu/records/xg6y0-9gr72On receding horizon extensions and control Lyapunov functions
https://resolver.caltech.edu/CaltechAUTHORS:20190315-104922109
Authors: {'items': [{'id': 'Primbs-J-A', 'name': {'family': 'Primbs', 'given': 'James A.'}}, {'id': 'Nevistić-V', 'name': {'family': 'Nevistić', 'given': 'Vesna'}}, {'id': 'Doyle-J-C', 'name': {'family': 'Doyle', 'given': 'John C.'}, 'orcid': '0000-0002-1828-2486'}]}
Year: 1998
DOI: 10.1109/ACC.1998.703180
Control Lyapunov functions (CLFs) are used in conjunction with receding horizon control (RHC) to develop a new class of control schemes. In the process, strong connections between the seemingly disparate approaches are revealed, leading to a unified picture that ties together the notions of pointwise min-norm, receding horizon, and optimal control. This framework is used to develop a control Lyapunov function based receding horizon scheme, of which a special case provides an appropriate extension of a variation on Sontag's formula. These schemes are shown to possess a number of desirable theoretical and implementation properties. An example is provided, demonstrating their application to a nonlinear control problem.https://authors.library.caltech.edu/records/mcwtt-mmb40