Optimisation-based worst-case analysis and anti-windup synthesis for uncertain nonlinear systems
This thesis describes the development and application of optimisation-based methods for worst-case analysis and anti-windup synthesis for uncertain nonlinear systems. The worst-case analysis methods developed in the thesis are applied to the problem of nonlinear flight control law clearance for highly augmented aircraft. Local, global and hybrid optimisation algorithms are employed to evaluate worst-case violations of a nonlinear response clearance criterion, for a highly realistic aircraft simulation model and flight control law. The reliability and computational overheads associated with different opti misation algorithms are compared, and the capability of optimisation-based approaches to clear flight control laws over continuous regions of the flight envelope is demonstrated. An optimisation-based method for computing worst-case pilot inputs is also developed, and compared with current industrial approaches for this problem. The importance of explicitly considering uncertainty in aircraft parameters when computing worst-case pilot demands is clearly demonstrated. Preliminary results on extending the proposed framework to the problems of limit-cycle analysis and robustness analysis in the pres ence of time-varying uncertainties are also included. A new method for the design of anti-windup compensators for nonlinear constrained systems controlled using nonlinear dynamics inversion control schemes is presented and successfully applied to some simple examples. An algorithm based on the use of global optimisation is proposed to design the anti-windup compensator. Some conclusions are drawn from the results of the research presented in the thesis, and directions for future work are identified.