  This paper presents a new concept of controlled dissipativity as an extension
of the standard dissipativity property to systems with parameter-varying
storage functions under the framework of economic model predictive control
(EMPC). Based on this concept, two EMPC controllers, integrated with the
dissipation inequality constraints rendering the storage function parameters as
decision variables, are formulated and the associated recursive feasibility is
ensured. Then, the asymptotic convergence to an optimal equilibrium in
closed-loop, without requiring the standard dissipativity assumption, is
enforced by trading it off with asymptotic performance. The upper bound of
asymptotic average closed-loop performance is also evaluated. Finally, an
illustrative example by using the EMPC controllers with terminal equilibrium or
terminal region conditions is provided to show the effectiveness of our
methods.
