A primal-dual approach to double-risk-constrained LQR for practical control under non-Gaussian noise

This paper presents a double-risk-constrained linear quadratic regulator (DRC-LQR) for practical control of partially observable systems under non-Gaussian and biased disturbances. Unlike conventional risk-neutral or single-risk formulations, the proposed approach jointly constrains state and output variability through a computationally tractable primal-dual optimization framework, enabling explicit compensation for noise skewness and heavy tails. As the first infinite-horizon formulation ensuring joint stability and constraint satisfaction under general non-Gaussian conditions, the DRC-LQR achieves both theoretical rigor and real-world feasibility. Comprehensive simulations on aircraft flight control and voltage regulation tasks demonstrate over 60% improvement in regulation accuracy, 93.7% faster convergence, and 99.8% constraint satisfaction compared with standard LQR, confirming its superior robustness and practicality. These results establish DRC-LQR as a systematic and implementable extension of LQR, advancing risk-sensitive control design for safety-critical systems subject to extreme disturbances.