Continuous-time constrained linear quadratic regulator for switched linear systems - Gori, Pietro; Pierallini, Michele; Angelini, Franco; Garabini, Manolo (Nonlinear analysis. Hybrid systems, 2025)
Switched systems, characterized by a family of subsystems governed by a switching rule, widely apply to complex real-world scenarios. However, their inherent switching dynamics pose significant challenges in phase analysis and control design. To address these challenges, we propose a framework for solving the Continuous-Time Constrained Linear Quadratic Regulator (CT-CLQR) problem for switched linear systems. Our approach partitions the time horizon into a finite number of intervals, each associated with a specific system mode. The duration of these intervals is parameterized by the switching instants, enabling a reformulation of the problem. We indirectly optimize the switching sequence by fixing the switching sequence and optimizing the interval durations. We derive analytical expressions for the cost function and its gradient, which are critical for efficient optimization. Unlike state-of-the-art methods that impose equality constraints on state evolution, our approach inherently considers the state evolution in the cost function. This not only simplifies the problem formulation but also reduces computational overhead by precomputing shared terms offline, enhancing efficiency during online operations. The proposed method significantly advances existing techniques, offering improved computational efficiency and flexibility. We demonstrate the effectiveness of our approach through comprehensive numerical examples, showcasing its potential for practical applications. •The considered LQR optimizes control inputs and switching instants.•Time partitioning is crucial for the problem reformulation.•Parameterizing the switching sequence reduces the complexity against standard methods.•Offline pre-calculation of shared terms reduces numerical computational load.