Suboptimal Stabilizing Controllers for Linearly Solvable System
| Autor: | Leong, Yoke Peng, Horowitz, Matanya B., Burdick, Joel W. |
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| Rok vydání: | 2015 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1109/CDC.2015.7403348 |
| Popis: | This paper presents a novel method to synthesize stochastic control Lyapunov functions for a class of nonlinear, stochastic control systems. In this work, the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation is transformed into a linear partial differential equation for a class of systems with a particular constraint on the stochastic disturbance. It is shown that this linear partial differential equation can be relaxed to a linear differential inclusion, allowing for approximating polynomial solutions to be generated using sum of squares programming. It is shown that the resulting solutions are stochastic control Lyapunov functions with a number of compelling properties. In particular, a-priori bounds on trajectory suboptimality are shown for these approximate value functions. The result is a technique whereby approximate solutions may be computed with non-increasing error via a hierarchy of semidefinite optimization problems. Comment: Accepted in IEEE Conference on Decision and Control (CDC) 2015 |
| Databáze: | arXiv |
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