Nonlinear robust stochastic control for unmanned aerial vehicles

Almost all dynamical systems experience inherent uncertainties such as environmental disturbance and sensor noise. This paper describes a new robust stochastic control methodology, which is capable of controlling the statistical nature of state variables of a nonlinear system to designed (attainable) statistical properties. First, an asymptotically stable and robust output tracking controller is designed in which discontinuous functions are not involved. Second, undetermined control parameters in the closed-loop system are optimized through nonlinear programming. In this constrained optimization, the error between the desired and actual moments of state variables is minimized subject to constraints on statistical moments. As the key point to overcome the difficulties in solving the associated Fokker-Planck equation, a direct quadrature method of moments is proposed. The advantages of the proposed method are: (1) ability to control any specified stationary moments of the states or output probability density function; (2) no need for the state process to be a Gaussian; (3) robustness with respect to parametric and functional uncertainties.

I. Introduction

VIEWING system behaviors within a stochastic framework allows for the inclusion of random disturbances and calculation of expected long term system trends. Normally Monte Carlo simulation approaches are used to find proper control parameters such that a desired statistical distribution of system performance can be achieved. However, this approach has a polynomial complexity in computation [1]. It will become intractable when the system is large, which results in a prohibitive number of control design iterations and CPU and labor time. To reduce the computational cost, extensive research efforts were spent for both linear and nonlinear stochastic systems, as discussed below.