An Input-to-State-Stability Approach to Economic Optimization in Model Predictive Control

摘要

This paper presents a model predictive control (MPC) scheme where a combination of a stabilizing stage cost and an economic stage cost is employed to allow the minimization of an economic performance index while still guaranteeing convergence toward a desired steady state. Input-to-state-stability with respect to the economic stage cost is provided. More precisely, for the case of an economic stage cost converging to zero, the economic optimization only affects the transient behavior of the closed-loop trajectories preserving the convergence to the desired steady state. Alternatively, if the economic stage cost is merely bounded, or convergent to a bound, the closed-loop state trajectory is ultimately bounded around the desired steady state with the size of the bound being monotonically increasing with the magnitude of the economic stage cost. The loosening of the closed-loop guarantees, i.e., moving from convergence to ultimate boundedness, gives space to the increase of economic performance. Numerical results illustrate the effectiveness of the proposed method on an energy efficient trajectory-tracking control problem of a marine robotic vehicle navigating in the presence of water currents.