Predictive Cost Adaptive Control: A Numerical Investigation of Persistency, Consistency, and Exigency

Abstract

Among the multitude of modern control methods, model predictive control (MPC) is one of the most successful <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> – <xref ref-type="bibr" rid="ref2" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> <xref ref-type="bibr" rid="ref3" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> <xref ref-type="bibr" rid="ref4" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[4]</xref> . As noted in “Summary,” this success is largely due to the ability of MPC to respect constraints on controls and enforce constraints on outputs, both of which are difficult to handle with linear control methods, such as linear quadratic regulator (LQR) and linear quadratic Gaussian (LQG), and nonlinear control methods, such as feedback linearization and sliding mode control. Although MPC is computationally intensive, it is more broadly applicable than Hamilton–Jacobi–Bellman-based control and more suitable for feedback control than the minimum principle. In many cases, the constrained optimization problem for receding-horizon optimization is convex, which facilitates computational efficiency <xref ref-type="bibr" rid="ref5" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[5]</xref> .