On Optimizing Nonlinear Adaptive Control Allocation With Actuator Dynamics

Abstract

In this work we address the optimizing control allocation problem for a nonlinear over-actuated time-varying system where parameters af ne in the dynamic actuator and effector model may be assumed unknown. In-stead of nding the optimal control allocation at each time instant, a dynamic approach is considered by constructing update-laws that represent asymptotically optimal allocation search and adaptation. Using Lyapunov analysis for cascaded set-stable systems, uniform global/local asymptotic stability is guaranteed for the optimal set described by the system, the optimal allocation update-law and the adaptive update-law. Simulations of a scaled-model ship, manoeuvred at low-speed, demonstrate the performance of the proposed allocation scheme.

Control allocation—A survey

“…An adaptive approach where uncertain parameters θ in the effector model h(u, x,t, θ ) are stably adapted using an adaptation law that is designed by augmenting the control Lyapunov-function in a standard way was proposed in (Tjønnås & Johansen 2005, Tjønnås & Johansen 2008). This framework was further extended to dynamically account for actuator dynamics within the control allocation in (Tjønnås & Johansen 2007b, Tjønnås & Johansen 2007a, and internal dynamics in the context of model reference adaptive control (Liao, Lum, Wang & Benosman 2009b, Liao, Lum, Wang & Benosman 2009a). …”

Optimizing Adaptive Control Allocation With Actuator Dynamics

“…The proof of Proposition 1 involves similar steps as in the proof of the main result in (Tjønnås and Johansen, 2007) and is therefore omitted here.…”

“…The example we present here is based on (Lindegaard and Fossen, 2003), and is also studied in (Johansen, 2004), (Tjønnås and Johansen, 2005) and (Tjønnås and Johansen, 2007). In the considered model there are five force producing devices; the two main propellers aft of the hull, in conjunction with two rudders, and one tunnel thruster going through the hull of the vessel.…”

“…In (Tjønnås and Johansen, 2005) the results were extended by allowing uncertain parameters, associated with an adaptive law, in the effector model, and by applying set-stability analysis in order to also conclude asymptotic stability of the optimal solution. The results in (Tjønnås and Johansen, 2005) are extended in (Tjønnås and Johansen, 2007) by considering actuator dynamic and relaxing some conditions using the theory in (Tjønnås et al, 2006). In the present paper we extend the result in (Tjønnås and Johansen, 2007) by a slightly different parameterization of (2) and (3).…”

“…The results in (Tjønnås and Johansen, 2005) are extended in (Tjønnås and Johansen, 2007) by considering actuator dynamic and relaxing some conditions using the theory in (Tjønnås et al, 2006). In the present paper we extend the result in (Tjønnås and Johansen, 2007) by a slightly different parameterization of (2) and (3).…”