A Terminal Set Feasibility Governor for Linear Model Predictive Control

A Terminal State Feasibility Governor for Real-Time Nonlinear Model Predictive Control Over Arbitrary Horizons

“…Polyhedral feasible sets are relatively easy to compute offline by orthogonal projections [15] for which several toolboxes are available [16], [17]. The downside is that projection methods suffer from the curse of dimensionality, and inner-approximations [18], [19] are usually required even for moderately sized systems (e.g., see [20,Fig. 3]).…”

“…Recently, a terminal set FG [20] was proposed that does not require an explicit estimate of the feasible set nor OCP modifications. As opposed to [12], the formulation avoids the issue of offline computational intractability that arises when performing high-dimensional set-valued polyhedral projections to compute the feasible set.…”

“…In conclusion, computational intractability of the feasible and terminal sets makes the application domain of existing FGs [12], [20] limited to linear dynamics, polyhedral constraints, and where all constraints are known before run-time, as online re-computation of these sets would exceed the realtime requirements. Hence, these methods cannot be applied to agile quadrotor flight through a priori unknown environments populated with obstacles that can only be detected on-the-fly.…”

A Computationally Efficient Robust Model Predictive Control Framework for Uncertain Nonlinear Systems

“…Chisci and Zappa (2003); Chisci et al (2005) propose a feasibility recovery mode, which similarly adjusts the reference before passing it to an MPC to ensure feasibility. External loops to adjust the reference in MPC schemes are also used by Mayne and Falugi (2016) and Skibik et al (2021Skibik et al ( , 2022. The following exposition utilizes the framework of artificial references, which includes this reference computation in the MPC formulation.…”

“…The reduction in conservatism is due to the difference between the achieved convergence of the closed-loop tracking MPC and the a priori worst-case bound based on the local contraction rate ρ < 1 of the terminal control law k f . Skibik et al (2022) propose a similar strategy for the special case of linear systems, steady states (T = 1), and synchronous updates (M = 1).…”