Johannes Gerhard, Martin Mönnigmann, Wolfgang Marquardt:
Constructive nonlinear dynamics –foundations and application to robust nonlinear control
In: T. Meurer, K. Graichen, E. Gilles (Eds.): Control and observer design for nonlinear finite- and infinite-dimensional systems, Springer Verlag, 2005, 165-182
This paper summarizes two recently presented strategies based on bifurcation theory and nonlinear dynamics that address robust control design of nonlinear systems. The first strategy applies numerical bifurcation analysis to the robust controller tuning of uncertain nonlinear systems. Continuation in the controller and system parameters is used to compute stability boundaries for the controller tuning parameters. Restrictions on the controller tuning are determined that must hold to guarantee stability for the complete operating range of the closed loop system. The second strategy, the recently presented optimization-based Constructive Nonlinear Dynamics (CNLD) extends ideas from nonlinear dynamics and bifurcation theory to address the synthesis rather than analysis problems. CNLD is based on constraints that enforce a minimal back off from critical manifolds. Critical manifolds are boundaries in the space of system and controller parameters that separate regions with qualitatively different system behavior, e. g. a region with stable operating points from a region with unstable system behavior. The generality of the concept of critical manifolds permits to address feasibility, stability and performance of a nonlinear (closed-loop) system. The back off from the critical manifolds admits to robustly account for parametric uncertainty during the design step and to guarantee the operability of the optimal solution. For closed-loop systems the approach admits simultaneous plant and control system design. This work summarizes the background and the basic ideas of both approaches. The application to robust nonlinear control design is illustrated by several case studies.
Robust control, nonlinear dynamics, parametric uncertainty, stability