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arXiv · 1509.07922

Suboptimal Stabilizing Controllers for Linearly Solvable System

Yoke Peng Leong·Matanya B. Horowitz·Joel W. Burdick
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Abstract

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.

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Yoke Peng Leong, Matanya B. Horowitz, Joel W. Burdick. 2015-09-25. Suboptimal Stabilizing Controllers for Linearly Solvable System. https://doi.org/10.1109/cdc.2015.7403348

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