Nonlinear Controller Design based on Piecewise Linear Approximations

ANDRES GARCIA; JOSE LUIS FIGUEROA; LILIANA RAQUEL CASTRO; SILVINA INES BIAGIOLA; OSVALDO ENRIQUE AGAMENNONI

San Francisco

Conferencia; SIAM Conference on Control and its Applications; 2007

SIAM

In this paper a general approach to the design of controllers for Nonlinear Control systems is presented. The methodology uses a Piecewise Linear (PWL) approximation of the Ordinary Differential Equations (ODEs) vector field which describes the dynamics of a system parameterized by the control inputs in order to exploit the linear properties of the PWL vector field facilitating the design of an stabilizing controller. The controller design can be carried out into the PWL approximation and with mild assumptions is possible to ensure the same asymptotic properties for real and approximate vector fields. A measure of the dynamics approximation error is used to estimate upper and lower bounds for the error between the actual and the approximated trajectories once the control vector calculated with the PWL system is replaced into the real one. A case study is presented in order to contrast the theoretical results along the paper.