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A nonlinear model predictive control approach is studied, for problems where a fixed terminal instant and corresponding terminal set to be reached are imposed. The new technique features a shrinking horizon, rather than the most common receding one, and an input parametrization strategy to reduce computational burden. The property of transferability of the parametrization strategy is introduced. Under this property, theoretical convergence guarantees in nominal conditions are obtained by construction. Two relaxed techniques are then proposed to retain recursive feasibility in presence of bounded additive input disturbance. A bound on the constraint violation achieved by these relaxed techniques as a function of the uncertainty bound is derived, too. The developed strategy is applied to the problem of energy-efficient operation of trains, in either a fully autonomous mode (with continuous input values) or a driver assistance mode (with discrete input values, resulting in a nonlinear integer program if no parametrization is used). Realistic simulation results in this context illustrate the effectiveness of the approach.

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Precise neuromodulation systems are needed to identify the role of neural oscillatory dynamics in brain function, and to advance the development of electrical stimulation therapies tailored to each patient's signature of brain dysfunction. Low-frequency, local field potentials (LFPs) are of increasing interest for the development of these systems because they reflect the synaptic inputs to a recorded neuronal population and can be chronically recorded in humans. Here, we identified stimulation pulse sequences to optimally minimize or maximize the 2-norm of frequency-specific LFP oscillations using a generalized mathematical model of spontaneous and stimulation-evoked LFP activity, and a subject-specific model of neural dynamics in the pallidum of a Parkinson's disease patient. We leveraged convex and mixed-integer optimization tools to identify the pulse patterns, and employed constraints on the pulse frequency and amplitude that are required to keep electrical stimulation within its safety envelope. Our analysis revealed that a combination of phase, amplitude, and frequency pulse modulation is needed to attain optimal suppression or amplification of the targeted oscillations. Phase modulation is sufficient to modulate oscillations with a constant amplitude envelope. To attain optimal modulation for oscillations with a time-varying envelope, a trade-off between frequency and amplitude pulse modulation is needed. The optimized pulse sequences identified here were invariant to changes in the dynamics of stimulation-evoked neural activity, including the damping and natural frequency or complexity (i.e., generalized vs. patient-specific model). Our results reveal the structure of pulse sequences that can be used in closed-loop brain stimulation devices to control neural activity in real-time.