Probabilistic Control of Nonlinear Uncertain Systems

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.