کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
756514 896182 2011 9 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Conditions under which suboptimal nonlinear MPC is inherently robust
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی کنترل و سیستم های مهندسی
پیش نمایش صفحه اول مقاله
Conditions under which suboptimal nonlinear MPC is inherently robust
چکیده انگلیسی

We address the inherent robustness properties of nonlinear systems controlled by suboptimal model predictive control (MPC), i.e., when a suboptimal solution of the (generally nonconvex) optimization problem, rather than an element of the optimal solution set, is used for the control. The suboptimal control law is then a set-valued map, and consequently, the closed-loop system is described by a difference inclusion. Under mild assumptions on the system and cost functions, we establish nominal exponential stability of the equilibrium, and with a continuity assumption on the feasible input set, we prove robust exponential stability with respect to small, but otherwise arbitrary, additive process disturbances and state measurement/estimation errors. These results are obtained by showing that the suboptimal cost is a continuous exponential Lyapunov function for an appropriately augmented closed-loop system, written as a difference inclusion, and that recursive feasibility is implied by such (nominal) exponential cost decay. These novel robustness properties for suboptimal MPC are inherited also by optimal nonlinear MPC. We conclude the paper by showing that, in the absence of state constraints, we can replace the terminal constraint with an appropriate terminal cost, and the robustness properties are established on a set that approaches the nominal feasibility set for small disturbances. The somewhat surprising and satisfying conclusion of this study is that suboptimal MPC has the same inherent robustness properties as optimal MPC.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Systems & Control Letters - Volume 60, Issue 9, September 2011, Pages 747–755
نویسندگان
, , ,