On linear quadratic regulation of linear port-Hamiltonian systems

The linear quadratic regulator is a widely used and studied optimal control technique for the control of linear dynamical systems. It consists in minimizing a quadratic cost functional of the states and the control inputs by the means of solving a linear Riccati equation. The effectiveness of the linear quadratic regulator relies on the cost function parameters hence, an appropriate selection of these parameters is of mayor importance in the control design. Port-Hamiltonian system modelling arise from balance equations, interconnection laws and the conservation of energy. These systems encode the physical properties in their structure matrices, energy function and definition of input and output ports. This paper establishes a relation between two classical passivity based control tools for port-Hamiltonian systems, namely control by interconnection and damping injection, with the linear quadratic regulator. These relations allow then to select the weights of the quadratic cost functional on the base of physical considerations. A simple RLC circuit has been used to illustrate the approach.