Title: Advanced Control Synthesis for Switched Affine Systems under Unmeasured Disturbances: A Non-Smooth Optimization and Hybrid Systems Approach.

Description: This PhD thesis focuses on the synthesis of a novel control architecture for Switched Affine Systems (SAS) subject to exogenous disturbances. Building upon the established expertise of the supervisors in hybrid/switched systems and state-space representations of power converters [9, 19, 8], this thesis addresses the fundamental challenge of stabilizing SAS when the equilibrium point is uncertain due to the inevitable effect of unmeasured perturbations.

The project hinges upon a novel nonlinear control structure based on four ingredients: a switched observer for simultaneous state and disturbance reconstruction, a nonlinear observer for the estimation of the unknown equilibrium to be stabilized, integrated with an optimization mechanism allowing for efficient online gradient-based selection of an optimal operating point and a switched stabilizer. The core theoretical innovation is threefold: (i) managing the inherent non-smoothness of cost functions (e.g., L1-norm penalties) through sub-gradients and differential inclusions (ii) exploring the use of modern nonquadratic Lyapunov certificates of asymptotic stability of the error dynamics leveraging recent advances in nonlinear integral action [1] (iii) using modern hybrid dynamical systems tools and reduction theory [16] to establish desirable stability and optimality properties of the interconnected scheme. This work aims to transcend standard quadratic constraints by to ensure global asymptotic stability in complex switching environments.

The full subject is given here: sujet-thèse-luya