Improved stability conditions for unconstrained nonlinear model predictive control by using additional weighting terms

In this work, we present two unconstrained MPC schemes using additional weighting terms which allow to obtain improved stability conditions. First, we consider unconstrained MPC with general terminal cost functions. If the terminal cost is not a control Lyapunov function, but satisfies a relaxed condition, then our results yield improved estimates for a stabilizing prediction horizon. Furthermore, our analysis also allows to recover two well-known results as special cases: if the terminal cost function is chosen as zero, we recover previous conditions on the length of the prediction horizon such that stability is guaranteed; and if the terminal cost is a control Lyapunov function conform to the stage cost, stability follows independently of the length of the prediction horizon. Second, we propose to use an exponential weighting on the stage cost in order to improve the stability properties of the closed-loop. This also allows to consider local controllability assumptions in combination with a suitable terminal constraints and thereby gives a connection to the classical MPC approaches using terminal constraints.</p

A unifying framework for stability in MPC using a generalized integral terminal cost

This work presents a novel model predictive control (MPC) scheme using a generalized integral terminal cost term. This generalized scheme exhibits close connections to recent results on unconstrained MPC as well as classical MPC using control Lyapunov functions as terminal weights. In particular, we show that both previous results can be regarded as limit cases of our setup. An example illustrates possible advantages provided by the increased flexibility of the proposed scheme compared to the previous results

Stochastic stability and performance estimates of packetized unconstrained model predictive control for networked control systems

In this work, we consider the control of discrete-time nonlinear systems over unreliable packet-based communication networks subject to random packet-dropouts. In order to mitigate the influence of the packet dropouts, the controller transmits packets containing control inputs for more than one future time instant. A suitable buffering is then applied at the plant actuator side. Since we do not assume the number of consecutive packet dropouts to be bounded, we are interested in stochastic stability of the closed-loop. For the calculation of the control inputs, we propose an unconstrained model predictive control (MPC) scheme without additional terminal weighting term. This unconstrained MPC scheme shows two significant advantages. First, we do not require the knowledge of a global control Lyapunov function, but instead only a less restrictive controllability assumption, in order to guarantee stochastic stability. Second, guaranteed performance bounds on the expected infinite horizon cost of the closed-loop can be obtained