Nonlinear Robust Stochastic Control for Unmanned Aerial Vehicles

• Published in: Journal of guidance, control, and dynamics control, and dynamics, 2009-07, Vol.32 (4), p.1308-1319
• Main Author: Xu, Yunjun
• Format: Article
• Language: English
• Subjects: Applied sciences; Closed loop systems; Computer science; control theory; systems; Control system analysis; Control system synthesis; Control theory. Systems; Controllers; Design; Exact sciences and technology; Monte Carlo simulation; Robotics; Unmanned aerial vehicles; Variables; Vehicles
• ISSN: 0731-5090; 1533-3884
• DOI: 10.2514/1.40753

Almost all dynamical systems experience inherent uncertainties such as environmental disturbance, sensor noise, and modeling error due to approximations. In safety-critical applications, such as control of unmanned aerial vehicles, characterizing and controlling the statistical performance of the system become important tasks. This paper describes a new robust stochastic control methodology that is capable of controlling the statistical nature of state or output variables of a nonlinear system to desired (attainable) statistical properties (e.g., moments). First, as the online step, an asymptotically stable and robust output trackting controller is designed in which discontinuous functions are not involved. Second, as the offline step, 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 or output 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. In this approach, the state probability density function is expressed in terms of a finite collection of Dirac delta functions, with the associated weights and locations determined by moment equations. The advantages of the proposed method are 1) the 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, and 3) robustness with respect to parametric and functional uncertainties. An unmanned aerial vehicle command-tracking control is used to demonstrate the capability of the proposed nonlinear stochastic control method and the results are successfully validated by Monte Carlo simulations.