A Mixed Control Approach to Nonlinear Coupled Burgers' PDE-ODE Systems with Sensor Nonlinearities

Abstract

This paper studies the stability analysis and control design problems for a class of nonlinear coupled complex systems with sensor nonlinearities via a mixed control approach. The nonlinear coupled complex systems are modelled as a nonlinear finite-dimensional ordinary differential equation coupled with an infinite-dimensional viscid burgers' equation. Due to the existence of both time and space dimensional nonlinearities and based on the Lyapunov stability theory, a mixed control approach is proposed to produce a fuzzy-model-based controller tackling the time dimensional nonlinearity and a boundary controller eliminating the space dimensional nonlinearity, such that the addressed coupled complex systems achieve asymptotic stability. Sufficient conditions are obtained via the convex optimization. Different from the existing results on control of coupled PDE-ODE systems, a mixed control approach is firstly developed by combining the boundary control approach and the fuzzy-model-based control approach. Finally, the proposed mixed control approach is applied to a nonlinear hypersonic rocket car to testify its validity.