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In this paper, we consider the problem of periodic optimal control ofnonlinear systems subject to online changing and periodically time-varyingeconomic performance measures using model predictive control (MPC). Theproposed economic MPC scheme uses an online optimized artificial periodic orbitto ensure recursive feasibility and constraint satisfaction despiteunpredictable changes in the economic performance index. We demonstrate thatthe direct extension of existing methods to periodic orbits does notnecessarily yield the desirable closed-loop economic performance. Instead, wecarefully revise the constraints on the artificial trajectory, which ensuresthat the closed-loop average performance is no worse than a locally optimalperiodic orbit. In the special case that the prediction horizon is set to zero,the proposed scheme is a modified version of recent publications usingperiodicity constraints, with the important difference that the resultingclosed loop has more degrees of freedom which are vital to ensure convergenceto an optimal periodic orbit. In addition, we detail a tailored offlinecomputation of suitable terminal ingredients, which are both theoretically andpractically beneficial for closed-loop performance improvement. Finally, wedemonstrate the practicality and performance improvements of the proposedapproach on benchmark examples.

Periodic optimal control of nonlinear constrained systems using economic model predictive control