Model predictive path-following for constrained nonlinear systems

IFAC Proceedings Volumes

Hagenmeyer

Findeisen

2011

Abstract:We propose an optimization approach to calculate optimal feedforward controls for exact path-following problems of differentially flat systems. Besides the derivation of a small dimensional optimal control problem, we give easily checkable conditions on the existence of inputs guaranteeing that a given path is exactly followable in the presence of constraints on states and inputs. Our approach is based on the projection of the feedforward controlled, nonlinear MIMO dynamics along a geometric path onto a linear single-input system in Brunovsky normal form. The presented results indicate how the computation of admissible trajectories for set-point changes can be simplified by relying on steady state consistent paths. The set-point change of a Van der Vusse reactor is considered as an example.

Section: Introductionmentioning

confidence: 98%

“…Faulwasser et al (2009). Secondly, it is in general not easy to verify that an arbitrarily shaped geometric path can be exactly followed if constraints on states and inputs are present.…”

Section: Exact Feedforward Path-followingmentioning

confidence: 99%

Optimal Exact Path-Following for Constrained Differentially Flat Systems

IFAC Proceedings Volumes

Hagenmeyer

Findeisen

2011

“…[4], [6], [11]. Results on predictive control for path-following problems are also available [5]. So far only limited results for the application of NMPC to problems governed by time-varying dynamics are available, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…In standard quasi-infinite horizon NMPC approaches ( [4], [6]) one often computes a suitable level set E = {e ∈ R n | V (t, e) ≤ c 2 } such that for all e ∈ E conditions similar to (5) hold. This is restrictive, since the level set is defined by a constant.…”

Section: B Invariant Time-varying Setsmentioning

confidence: 99%

A model predictive control approach to trajectory tracking problems via time-varying level sets of Lyapunov functions

IEEE Conference on Decision and Control and European Control Conference

Findeisen

2011

Abstract-We discuss a model predictive control approach to trajectory tracking problems of constrained nonlinear continuous time systems, where the reference trajectory is a priori known and asymptotically constant. The proposed NMPC scheme is able to explicitly consider input and state constraints while guaranteeing recursive feasibility. To handle the timevarying nature of the tracking problem we advocate the use of time-varying level sets of Lyapunov functions as terminal regions. We prove a necessary and sufficient condition for positive invariance of these sets and show how these sets can be efficiently computed, if a quadratic Lyapunov function is available. As an example we consider a nonlinear CSTR reactor.

“…[8][9][10]15 The conceptual idea of path following is based on a simple observation: If the desired flight path is described as a reference trajectory it implies an explicit requirement when to be where on the reference. In a path-following setup, however, the flight path is considered as a geometric reference.…”

mentioning

confidence: 99%

Optimization-based Feedforward Path Following for Model Reference Adaptive Control of an Unmanned Helicopter

Dauer

AIAA Guidance, Navigation, and Control (GNC) Conference

Lorenz

et al. 2013

This paper presents an optimization-based approach to let an unmanned helicopter follow a geometrically defined path. In particular, this approach extends reference model following concepts. Instead of using a model of the vehicle dynamics, the optimization is based on the reference model of the controller. By this means, we can calculate the timewise progress on the path by means of dynamic optimization without exact knowledge of the real helicopter dynamics. The progression on the path, is defined as a dynamic system subject to an additional virtual control input. The inputs of the reference model and that of the timing law are the decision variables used in the dynamic optimization which is so far performed offline. It will be shown that hereby, an accurate following of the path is possible although the actually identified flight mechanical model is limited to a linear hover model. Furthermore, the approach allows to take constraints on inputs and states into account. Simulation results as well as flight tests conducted with the artis testbed underline that good performance and constraints satisfaction can be achieved.