An Execution-time-certified QP Algorithm for ℓ_1 penalty-based Soft-constrained MPC
arxiv(2024)
摘要
Providing an execution time certificate and handling possible infeasibility
in closed-loop are two pressing requirements of Model Predictive Control (MPC).
To simultaneously meet these two requirements, this paper uses ℓ_1
penalty-based soft-constrained MPC formulation and innovatively transforms the
resulting non-smooth QP into a box-constrained QP, which is solved by our
previously proposed direct and execution-time certified algorithm with only
dimension-dependent (data-independent) and exact number of iterations [1]. This
approach not only overcomes the limitation of our previously proposed algorithm
[1], only applicable to input-constrained MPC, but also enjoys exact recovery
feature (exactly recover the same solution when the original problem is
feasible) of ℓ_1 penalty-based soft-constrained MPC formulation without
suffering numerical difficulty of the resulting non-smoothness. Other various
real-time QP applications, not limited to MPC, will also benefit from our QP
algorithm with execution-time certificate and global feasibility.
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