Abstract
We present results on numerical regulator design for sampled-data nonlinear plants via their approximate discrete-time plant models. The regulator design is based on an approximate discrete-time plant model and is carried out either via an infinite horizon optimization problem or via a finite horizon with terminal cost optimization problem. In both cases, we discuss situations when the sampling period T and the integration period h used in obtaining the approximate discrete-time plant model are the same or they are independent of each other. We show that, using this approach, practical and/or semiglobal stability of the exact discrete-time model is achieved under appropriate conditions.
Highlights
Stabilization of controlled systems is one of the central topics in control theory that has lead to a wealth of different stabilization techniques
An important set of stabilization methods is based on optimization techniques, such as receding horizon control (RHC) or model predictive control (MPC)
Because of the fact that we are considering parameterized systems and costs, the examples illustrate that given arbitrarily small sampling period there exists a cost function for which the controller that is optimal for the approximate model would destabilize the exact model
Summary
Stabilization of controlled systems is one of the central topics in control theory that has lead to a wealth of different stabilization techniques. It is typically assumed in the optimization based stabilization literature that the exact discrete-time plant model is available for controller design (see for instance [6, 14, 13, 12, 11, 1]). Results in [15, 17] present a framework for controller design via approximate discrete-time models but they do not explain how the actual controller design can be carried out within this framework It is the purpose of this paper to investigate several situations when the optimization based stabilization is done within the framework of [15, 17].
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