Optimal control problem in bond graph formalism

Abstract

This paper presents a new way to derive an optimal control system for a specific optimisation problem, based on bond graph formalism. The procedure proposed concerns the optimal control of linear time invariant MIMO systems and can deal with both cases of the integral performance index, these correspond to dissipative energy minimization and output error minimization. An augmented bond graph model is obtained starting from the bond graph model of the system associated with the optimal control problem. This augmented bond graph, consisting of the original model representation coupled to an optimizing bond graph, supplies, by its bicausal exploitation, the set of differential-algebraic equations that analytically give the solution to the optimal control problem without the need to develop the analytical steps of Pontryagin's method. The proof uses the Pontryagin Maximum Principle applied to the port-Hamiltonian formulation of the system.

Structural analysis of hybrid electro-hydraulic power steering system - a bond graph approach

“…Formulating the design problem in the form of an inverse problem implies reformulating the specifications in terms of temporal functions, which can be tricky or even irrelevant in terms of technical specifications. To address this issue, several approaches can be exploited, such as expressing the specifications as a function of the system's power variables (Mechin, 2003) or coupling them with an optimisation problem (Mouhib et al, 2009).…”

Optimal Control of Port-Hamiltonian Systems: A Time-Continuous Learning Approach

“…In [16,17,18], the necessary conditions which follow from Pontryagin's Maximum Principle are used to derive an explicit expression for the optimal feedback controller, provided the Hamiltonian of the system is quadratic. The authors in [19] provide full-and reduced-order LQR controllers for linear ISO-PHSs.…”