Normal forms for x-flat two-input control-affine systems in dimension five

Two Normal Forms for Rewriting P Systems

Hopf bifurcations in normal forms of third order nonlinear affine control systems

The paper investigates Hopf bifurcations in a class of simple nonlinear systems, i.e., third order affine control systems described in terms of “quadratic plus cubic” normal forms and subject to linear state feedback control laws. By employing Harmonic Balance (HB) tools, the set of system parameters corresponding to supercritical and subcritical bifurcations is analytically determined. Also, a...

Normal Forms of Nonlinear Control Systems

Numerous papers were published during the last decade on the normal forms of nonlinear control systems with applications in bifurcation and its control. The approach is motivated by Poincaré’s theory of normal forms for classical dynamical systems using homogeneous transformations. In this paper, we summarize a variety of control system normal forms published in the literature so that the norma...

Multi-input sliding mode control of nonlinear uncertain affine systems

In this paper the multi-input sliding mode methodology for uncertain nonlinear system affine in the control is generalized to the case in which the matrix pre-multiplying the control in the state equation is uncertain, non constant and state-dependent. This property is inherited by the matrix multiplying the control in the sliding output dynamics, which is the nonlinear version of the well know...

Approximate Finite-Horizon Optimal Control for Input-Affine Nonlinear Systems with Input Constraints

The finite-horizon optimal control problem with input constraints consists in controlling the state of a dynamical system over a finite time interval (possibly unknown) minimizing a cost functional, while satisfying hard constraints on the input. For linear systems the solution of the problem often relies upon the use of bang-bang control signals. For nonlinear systems the “shape” of the optima...