Abstract-We propose a model predictive control approach to path-following problems of constrained nonlinear systems. We directly consider input and state constraints. Furthermore, we introduce an extended corridor path-following problem, which allows to add spatial degrees of freedom to the path formulation. We give sufficient stability conditions for predictive solutions to 1d and corridor path-following problems. To illustrate the performance of our approach we discuss the example of an autonomous vehicle subject to input constraints.Index Terms-Nonlinear model predictive control, corridor path-following, input and state constraints, stability.
This paper discusses set invariance notions for decentralized discrete time systems which are physically interconnected. We employ independent set-dynamics induced by the underlying subsystems subject to the available information in the decentralized setting. The main novelty of the approach lies within the fact that the concept of set invariance for independent set-dynamics is formalized by employing appropriate families of sets. The complexity of the exact notion is alleviated by introducing a practical set invariance notion which is then complemented with the corresponding relaxed stability analysis. Under mild assumptions, the introduced notion allows for safe, stable and independent operation of the subsystems forming the overall decentralized system.
This note introduces practical set invariance notions for physically interconnected, discrete-time systems, subject to additive but bounded disturbances. The developed approach provides a decentralized, non-conservative and computationally tractable way to study desirable robust positive invariance and stability notions for the overall system as well as to guarantee safe and independent operation of the constituting subsystems. These desirable properties are inherited, under mild assumptions, from the classical stability and invariance properties of the associated vector-valued dynamics which capture in a simple but appropriate and nonconservative way the dynamical behavior induced by the underlying set-dynamics of interest.
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