Fernando Castaños

Fernando Castaños, Hannah Michalska, Dmitry Gromov et al.

Implicit representations of finite-dimensional port-Hamiltonian systems are studied from the perspective of their use in numerical simulation and control design. Implicit representations arise when a system is modeled in Cartesian coordinates and when the system constraints are applied in the form of additional algebraic equations (the system model is in a DAE form). Such representations lend themselves better to sample-data approximations. An implicit representation of a port-Hamiltonian system is given and it is shown how to construct a sampled-data model that preserves the port-Hamiltonian structure under sample and hold.

Fernando Castaños, Edgar Estrada, Sabine Mondié et al.

The PI control of first-order linear passive systems through a delayed communication channel is revisited in light of the relative stability concept called sigma-stability. Treating the delayed communication channel as a transport PDE, the passivity of the overall control-loop is guaranteed, resulting in a closed-loop system of neutral nature. Spectral methods are then applied to the system to obtain a complete stability map. In particular, we perform the D-subdivision method to declare the exact sigma-stability regions in the space of PI parameters. This framework is then utilized to analytically determine the maximum achievable exponential decay rate of the system while achieving the PI tuning as an explicit function of the decay rate and the system parameters.

Félix A. Miranda, Fernando Castaños, Alexander Poznyak

The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set (i.e., there exist only finitely many possible models for the plant). Uncertainty is dealt with using a min-max approach (i.e., we seek the best control for the worst possible plant). The optimal control is derived using a multi-model version of Lagrange's multipliers method, which specifies the control in terms of a discrete-time Riccati equation and an optimization problem over a simplex. A numerical algorithm for computing the optimal control is proposed and tested by simulation.

Félix A. Miranda, Fernando Castaños

The use of multivalued controls derived from a special maximal monotone operator are studied in this note. Starting with a strictly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control law is derived, ensuring regulation of the output to a desired value. The methodology used falls in a passivity-based control context, where we study how the multivalued control affects the dissipation equation of the closed-loop system, from which we derive its robustness properties. Finally, some numerical examples together with implementation issues are presented to support the main result.