Constrained Spectrum Control

A novel Nonlinear Model Predictive Control (NMPC) scheme is proposed in order to shape the harmonic response of constrained nonlinear systems. The salient ingredient is the short-time Fourier transform (STFT) of the system's output signal, which is constrained in an NMPC problem, leading to the novel formulation of so-called spectrum constraints. Recursive feasibility and asymptotic stability of the proposed NMPC scheme with such spectrum constraints are guaranteed by means of an appropriate ellipsoidal terminal invariant set. The efficacy of the proposed approach is demonstrated on a nonlinear vibration damping problem

Constrained spectrum control using MPC

Well-known model predictive control (MPC) theory for constrained linear time-invariant (LTI) systems is extended to accommodate hard constraints and cost penalizations on the spectra of the system’s output trajectories. Thus the proposed method facilitates enforcing constraints, and placing weights, on the harmonic content of input-, state- and output-trajectories, in addition to the usual constrained control objectives. The proposed methods are demonstrated by the example problem of reducing torsional vibrations in a drive-shaft

Spectrogram MPC: Enforcing hard constraints on system's output spectra

A novel model predictive control (MPC) scheme that allows one to enforce hard constraints on the spectrum of a constrained system’s output signal is presented. The approach is based on a time-local analysis of the spectrum of output signals by means of the short-time Fourier transform (STFT), and its squared magnitude, called the spectrogram. It is shown that an MPC problem with spectrogram constraints can be formulated as a quadratically constrained quadratic program (QCQP). We prove recursive feasibility and stability of the proposed spectrogram MPC scheme via an ellipsoidal invariant set, including spectrogram constraints. Moreover, it is pointed out how the proposed spectrogram MPC approach can be extended to MPC for tracking while ensuring recursive feasibility. Finally, we present simulation results of spectrogram MPC applied to a resonant system. Our simulations show that, by employing the proposed spectrogram MPC approach, oscillations can be attenuated in the system output, tracking a reference signal, by explicitly enforcing hard constraints on its spectrum

Stochastic Model Predictive Control: Controlling the Average Number of Constraint Violations

This paper considers linear discrete-time systems with additive bounded disturbances subject to hard control input bounds and constraints on the expected number of state-constraint violations averaged over time, or, equivalently, constraints on the probability of a state-constraint violation averaged over time. This specification facilitates the exploitation of the information on the number of past constraint violations, and consequently enables a significant reduction in conservatism. For the type of constraint considered we develop a recursively feasible receding horizon scheme, and, as a simple modification of our approach, we show how a bound on the average number of violations can be enforced robustly. The computational complexity (online as well as offline) is comparable to existing model predictive control schemes. The effectiveness of the proposed methodology is demonstrated by means of a numerical example