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DOI: 10.23952/cot.2025.13
Received January 22, 2024; Accepted April 2, 2024; Published online December 9, 2024
Abstract. Sinusoidal signals with time varying frequency are widely encountered in real life applications. In this paper, we address the problem of tracking such signals using noisy measurements based on deterministic control, where the estimated trajectory of the signal is determined via an optimal control policy. The objective function is the cumulative squared error between the measurements and the signal trajectory plus a control regularization. In particular, we consider the penalty as a control’s deviation from a constant reference and its total variation. For a continuous time problem, the optimal control law for the control’s deviation is achieved using the Pontryagin minimum principle, and for the total variation penalty we use an Euler-Lagrange based method. To further obtain a closed-form solution, we discretize the time, state and control space and use a Markov decision problem setup, where the optimal control policy is obtained based on Bellman’s optimality principle. The optimal policy in discrete time uses the Viterbi algorithm.
How to Cite this Article:
R.J. Evans, C. Liu, G.N. Nair, S. Suvorova, B. Moran, Tracking sinusoidal signals with time varying frequency using optimal control, Commun. Optim. Theory 2025 (2025) 13.