**Keywords:** Nonlinear

control, Passivity-based

control, Port-Hamiltonian

systems
**Abstract:**Power-shaping control is a control

design method which can be seen as an extension of energy-balancing

passivity-based control. This control scheme is characterized by the

fact that stabilization is achieved by shaping a function that is

related to power instead of energy. One of the most difficult parts in

achieving such a control design is the derivation of a specific form of

the dynamics, namely the Brayton-Moser form, on which Power-shaping

control is based. More specifically the latter involves the solution of

a partial differential equation (PDE) system together with an

additional sign constraint.

This talk will include a

*brief tutorial* on the Brayton-Moser

Form for Power Shaping Control, a short survey of the literature and

some examples illustrating the wide applicability of this control

design method. In addition, a general methodology will be described for

solving the PDE system that is needed for getting the Brayton-Moser

form. The solution set of this PDE system can be characterized in terms

of the solutions of a related system of algebraic linear equations. A

necessary condition will also be reported that guarantees the existence

of a solution to the algebraic linear system which satisfies the sign

condition. The methodology will be illustrated by an example of a

chemical reactor where the physical knowledge of the system is used to

find a suitable solution.