Finite-Horizon Discrete-Time LQR with Sparse Inputs
Rupam Kalyan Chakraborty (TU Delft - Signal Processing Systems)
Vaibhav Katewa (Indian Institute of Science)
Chandra R. Murthy (Indian Institute of Science)
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Abstract
The Linear Quadratic Regulator (LQR) is a classical problem in optimal control theory which deals with operating a linear dynamical system with optimized cost. In this work, we study the discrete-time LQR problem with sparsity constraints on the inputs. This problem has a combinatorial complexity. We develop a convex optimization-based approach to relax the problem into a semidefinite program which can be solved with polynomial complexity. We explore two cases for input sparsity: fixed temporal support and time-varying support. Moreover, we also solve the minimum-energy control problem with sparse inputs. Finally, using numerical simulations, we show that our algorithms give near-optimum performance with very good accuracy and time complexity.
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File under embargo until 23-02-2026