2013/07/17 by Loria, Antonio
#34H15 #60E60 #70Q05 #93C10 #93C95 #FOS: Mathematics #I.2.8 #I.2.9 #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1307.4659
We obviate the use of observers for the purpose of output feedback tracking control of Lagrangian systems and solve some long-standing yet well-documented open problems. As often implemented in control practice, we replace unavailable derivatives with approximate differentiation. Our contribution consists in establishing uniform global asymptotic stability in closed-loop, for Lagrangian systems without dissipative forces (friction) using only position feedback. Firstly, for fully-actuated relative-degree-two systems, the controller is reminiscent of passivity-based controllers for robot manipulators and consists in a linear dynamic system together with a globally-Lipschitz control law. Establishing a global uniform result, all the more with such a simple controller, is particularly valuable relatively to the literature of output-feedback control of systems with non-globally-Lipschitz nonlinearities in the unmeasured variables. This first contribution solves a long-standing open problem and, as a matter of fact, recasted in a general context this result is at the edge of what is achievable -see [24]. Then, we show that our control approach may be applied to a more general problem, that of tracking control of Lagrangian systems augmented by a chain of integrators (with relative degree greater than two). As a corollary, we solve the global-tracking position-feedback control problem for flexible-joint robots but also for systems coupled with output-feedback linearizable actuator dynamics. Finally, we discuss remaining open problems of fairly general interest in the realm of analysis and design of robust nonlinear systems.