Feasibility of Simultaneous Input-Output Constraints for Tracking in a Class of LTI Systems: Part I
Junhyeok Yoon, Heather Hussain, Anuradha M. Annaswamy
Abstract
This paper addresses the problem of simultaneous satisfaction of input and output constraints for LTI systems with multiple inputs with state feedback and integral action using a Control Barrier Function based governor. Necessary and sufficient conditions for the CBF-based governor to have a feasible solution and for the closed-loop solutions to be bounded and forward-invariant are derived. A systematic design procedure for choosing the free parameters of the CBF-governor is also provided. These free parameters are associated with high-order CBFs, bounds on feasible command signals, and control input magnitude. A companion paper provides several numerical examples to illustrate the results of this paper, especially the feasibility (or infeasibility) of the CBF governor when the conditions are satisfied (or not satisfied).
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