114 research outputs found
Reducing the Prediction Horizon in NMPC: An Algorithm Based Approach
In order to guarantee stability, known results for MPC without additional
terminal costs or endpoint constraints often require rather large prediction
horizons. Still, stable behavior of closed loop solutions can often be observed
even for shorter horizons. Here, we make use of the recent observation that
stability can be guaranteed for smaller prediction horizons via Lyapunov
arguments if more than only the first control is implemented. Since such a
procedure may be harmful in terms of robustness, we derive conditions which
allow to increase the rate at which state measurements are used for feedback
while maintaining stability and desired performance specifications. Our main
contribution consists in developing two algorithms based on the deduced
conditions and a corresponding stability theorem which ensures asymptotic
stability for the MPC closed loop for significantly shorter prediction
horizons.Comment: 6 pages, 3 figure
Analysis of unconstrained nonlinear MPC schemes with time varying control horizon
For discrete time nonlinear systems satisfying an exponential or finite time
controllability assumption, we present an analytical formula for a
suboptimality estimate for model predictive control schemes without stabilizing
terminal constraints. Based on our formula, we perform a detailed analysis of
the impact of the optimization horizon and the possibly time varying control
horizon on stability and performance of the closed loop
Stability of Constrained Adaptive Model Predictive Control Algorithms
Recently, suboptimality estimates for model predictive controllers (MPC) have
been derived for the case without additional stabilizing endpoint constraints
or a Lyapunov function type endpoint weight. The proposed methods yield a
posteriori and a priori estimates of the degree of suboptimality with respect
to the infinite horizon optimal control and can be evaluated at runtime of the
MPC algorithm. Our aim is to design automatic adaptation strategies of the
optimization horizon in order to guarantee stability and a predefined degree of
suboptimality for the closed loop solution. Here, we present a stability proof
for an arbitrary adaptation scheme and state a simple shortening and
prolongation strategy which can be used for adapting the optimization horizon.Comment: 6 pages, 2 figure
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