Lyapunov/Passivity-Based Adaptive Control of Relative Degree Two MIMO Systems With an Application to Visual Servoing

This note presents a Lyapunov-based design of model-reference adaptive control (MRAC) for multiple-input-multiple-output (MIMO) systems of uniform relative degree two. It consists of an extension of a well known MRAC Lyapunov-based scheme for single-input-single-output (SISO) plants with relative degree one or two. The case of relative degree one, was completely extended to the MIMO case only recently. The corresponding extension of the relative degree two case remained hitherto unpublished. While MIMO MRAC schemes exist which can deal with arbitrary relative degree, the one presented here has the significant advantage of possessing an explicit Lyapunov function which easily leads to a stability and error convergence proof. It can also be regarded as a passivity-based approach. As a result, it becomes easier to guarantee stability when connecting such adaptive system to other adaptive control systems with similar passivity properties, e.g., in adaptive visual servoing of robot manipulators