Set-Valued Methods for Robust Nonlinear Control

摘要

The proposed research is to develop set-valued methods for robust nonlinear control, where 'nonlinear control' refers to nonlinear controllers for both linear and nonlinear systems. Set-valued methods represent a natural framework for incorporating uncertainty into control system analysis and design. Uncertainty may come from unknown parameters, bounded disturbances, neglected dynamics, or uncertain state values. In a set-valued setting, system dynamics become set-valued, state estimates are set-valued, and feedback controls become set-valued. The proposed research is to explore the utility of set-valued methods in the specific areas of (1) output feedback control of systems with saturation, (2) decentralize control, (3) nonlinear gain-scheduled control design, (4) adaptive control, and (5) control of hybrid dynamical systems. A primary objective throughout is the explicit computational construction of control laws which guarantee achievable optimal performance. The set-valued approach is sufficiently diverse to accommodate the formulation of a variety of control problems. The computational burden associated with set-valued methods can be significant, involving the solution of relatively small linear programs many times over. The spirit of the project has been to exploit computational power so that the design and implementation of set-valued methods can be a reality.