Optimization-Free Control of Safety-Critical Systems Subject to the Intersection of Multiple Time-Varying Concave Constraints

The explicit reference governor (ERG) is an
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unit that provides the constraint handling capability to a pre-stabilized system by providing the system with an applied reference which is the best approximation of the desired reference at any time and converges to the desired reference. One of the main strengths of ERG is that it does not make use of any online optimization, which makes it an appropriate solution for real-time applications; in particular, it has been shown that ERG has potential to control safety-critical systems that are subject to time-varying constraints. This paper proposes a systematic approach for designing an ERG for the control of systems that are subject to the intersections of multiple time-varying concave constraints. Under certain conditions on the change-rate of the constraints and system dynamics, constraints satisfaction and convergence properties are proven rigorously. The effectiveness of the proposed scheme is demonstrated through simulation studies on two relevant problems in the field of robotics: i) automated packaging line; and ii) non-cooperative household robots.