Guaranteed Constraint Satisfaction in Continuous-Time Control Problems

In the context of continuous-time control systems, we address the problem of guaranteeing that the constraints imposed along the trajectory are in fact satisfied for all times. The problem is relevant and non-trivial in situations in which a continuous-time internal representation of the system is u...

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Bibliographic Details
Published in:IEEE control systems letters 2019-01, Vol.3 (1), p.13-18
Main Authors: Fontes, Fernando A. C. C., Paiva, Luis Tiago
Format: Article
Language:English
Subjects:
Adaptation models
Adaptive mesh-refinement
Constrained control
Nonlinear systems
numerical methods
Numerical models
Optimal control
Predictive control
sampled-data control
Trajectory
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Summary:In the context of continuous-time control systems, we address the problem of guaranteeing that the constraints imposed along the trajectory are in fact satisfied for all times. The problem is relevant and non-trivial in situations in which a continuous-time internal representation of the system is used with a digital device, such as in sampled-data model-based control, in an optimal control solver, or in sampled-data model predictive control. In this letter, we establish a condition that when verified on a finite set of time instants (using limited computational power) can guarantee that the trajectory constraints are satisfied on an uncountable set of times. The case of constrained optimal control problems is further explored here. We develop an algorithm for the numerical solution of constrained nonlinear optimal control problems that combines a guaranteed constraint satisfaction strategy with an adaptive mesh refinement strategy.
ISSN:2475-1456
2475-1456
DOI:10.1109/LCSYS.2018.2849853