Agricultural production of annual crops is often hampered by annual weeds, which compete with planted crops and persist through the collection of dormant seeds in the soil called the weed seed bank. Conventional weed management relies heavily on chemical herbicides, which are not sustainable. A complementary method that reduces the need for herbicides is ‘cultural control’, in which the crop rotation is designed in part to manage the weed population. We propose a methodology that optimizes the crop rotation, here defined as periodic crop planting densities, subject to periodic weed dynamics. We adopt a well-established model of discrete-time annual weed seed bank dynamics with crop planting density inputs, and show that any periodic weed seed bank trajectory corresponding to a periodic crop rotation is globally exponentially stable. This guarantees convergence to the optimal periodic trajectory obtained by solving a nonlinear optimal control problem with periodic constraints, which we formulate as a nonlinear program.

We propose a frequency-domain state representation to improve the performance and reduce the computation and data requirements of reinforcement learning. This approach is tailored to tracking tasks of periodic trajectories. We apply the proposed methodology to an active knee prosthesis application. Using the high-fidelity simulator MuJoCo, we demonstrate significant performance improvements (in terms of Bellman error) for the proposed frequency-domain state representation relative to the current state-of-the-art time-domain state representation used in these applications.

We establish a collection of closed-loop guarantees and propose a scalable optimization algorithm for distributionally robust model predictive control (DRMPC) applied to linear systems, convex constraints, and quadratic costs. Via standard assumptions for the terminal cost and constraint, we establish distributionally robust long-term and stagewise performance guarantees for the closed-loop system. We further demonstrate that a common choice of the terminal cost, i.e., via the discrete-algebraic Riccati equation, renders the origin input-to-state stable for the closed-loop system. This choice also ensures that the exact long-term performance of the closed-loop system is independent of the choice of ambiguity set for the DRMPC formulation. Thus, we establish conditions under which DRMPC does not provide a long-term performance benefit relative to stochastic MPC. To solve the DRMPC optimization problem, we propose a Newton-type algorithm that empirically achieves superlinear convergence and guarantees the feasibility of each iterate. We demonstrate the implications of the closed-loop guarantees and the scalability of the proposed algorithm via two examples. To facilitate the reproducibility of the results, we also provide open-source code to implement the proposed algorithm and generate the figures.

We establish sufficient conditions for the terminal cost and constraint such that economic model predictive control (MPC) is robustly recursively feasible and economically robust to small disturbances without any assumptions of dissipativity. Moreover, we demonstrate that these sufficient conditions can be satisfied with standard design methods. A small example is presented to illustrate the inherent robustness of economic MPC to small disturbances.