Probabilistic Control of Nonlinear Uncertain Systems

Abstract

Robust controllers for nonlinear systems with uncertain parameters can be reliably designed using probabilistic methods. In this chapter, a design approach based on the combination of stochastic robustness and dynamic inversion is presented for general systems that have a feedback-linearizable nominal system. The efficacy of this control approach is illustrated through the design of flight control systems for a hypersonic aircraft and a highly nonlinear, complex aircraft model. The proposed stochastic robust nonlinear control explores the direct design of nonlinear flight control logic; therefore the final design accounts for all significant nonlinearities in the aircraft's high-fidelity simulation model. Monte Carlo simulation is used to estimate the likelihood of closed-loop system instability and violation of performance requirements subject to variations of the probabilistic system parameters. The stochastic robustness cost function is defined in terms of the probabilities that design criteria will not be satisfied. We use randomized algorithms, in particular genetic algorithms, to search the design parameters of the parameterized controller with feedback linearization structure. The design approach is an extension of earlier methods for probabilistic robust control of linear systems. Prior results are reviewed, and the nonlinear approach is presented.

Robust and Randomized Control Design of Mini-UAVs: The MH1000 Platform

“…In this and several subsequent papers, see e.g. [9], [10], [11] and references therein, various techniques, mainly based on Monte Carlo simulations, have been successfully utilized for the computation of the socalled probability of instability, and related performance indices. The application area providing motivations for the development of these methods was indeed aerospace control.…”

Non-intrusive generalized polynomial chaos approach to the stability analysis of uncertain nonlinear dynamic systems

“…For uncertain linear systems, if the parameters are linear functions of the random variables modelling uncertainties, then it is only necessary to test the stability corresponding to the extreme value of the uncertain parameters [2]. For general cases, Monte Carlo methods based on sampling processes are the most useful [3][4][5]. These methods try to approximate probability densities by using a great number of points.…”