Name
Abstract | ||
|---|---|---|
This paper presents a new method for synthesizing stochastic control Lyapunov functions for a class of nonlinear stochastic control systems. The technique relies on a transformation of the classical nonlinear Hamilton-Jacobi-Bellman partial differential equation to a linear partial differential equation for a class of problems with a particular constraint on the stochastic forcing. This linear partial differential equation can then be relaxed to a linear differential inclusion, allowing for relaxed solutions to be generated using sum of squares programming. The resulting relaxed solutions are in fact viscosity super-/subsolutions, and by the maximum principle are pointwise upper and lower bounds to the underlying value function, even for coarse polynomial approximations. Furthermore, the pointwise upper bound is shown to be a stochastic control Lyapunov function, yielding a method for generating nonlinear controllers with pointwise bounded distance from the optimal cost when using the optimal controller. These approximate solutions may be computed with nonincreasing error via a hierarchy of semidefinite optimization problems. Finally, this paper develops a priori bounds on trajectory suboptimality when using these approximate value functions and demonstrates that these methods, and bounds, can be applied to a more general class of nonlinear systems not obeying the constraint on stochastic forcing. Simulated examples illustrate the methodology. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1137/16M105767X | SIAM JOURNAL ON CONTROL AND OPTIMIZATION |
Keywords | Field | DocType |
stochastic control Lyapunov function,sum of squares programming,Hamilton-Jacobi-Bellman equation,nonlinear systems,optimal control | Lyapunov function,Lyapunov equation,Mathematical optimization,Nonlinear system,Mathematical analysis,Stochastic differential equation,Stochastic partial differential equation,Partial differential equation,Mathematics,Stochastic control,Pointwise | Journal |
Volume | Issue | ISSN |
54 | 6 | 0363-0129 |
Citations | PageRank | References |
2 | 0.42 | 13 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yoke Peng Leong | 1 | 3 | 2.51 |
| Matanya B. Horowitz | 2 | 46 | 4.79 |
| Burdick, J.W. | 3 | 2988 | 516.87 |