Robust explicit MPC based on approximate multiparametric convex programming

Many robust model predictive control (MPC) schemes require the online solution of a computationally demanding convex program. For deterministic MPC schemes, multiparametric programming was successfully applied to move offline most of the computation. In this paper, we adopt a general approximate multiparametric algorithm recently suggested for convex problems and propose to apply it to a classical robust MPC scheme. This approach enables one to implement a robust MPC controller in real time for systems with polytopic uncertainty, ensuring robust constraint satisfaction and robust convergence to a given bounded set.     

Stabilizing Model Predictive Control of Hybrid Systems

In this note, we investigate the stability of hybrid systems in closed-loop with model predictive controllers (MPC). A priori sufficient conditions for Lyapunov asymptotic stability and exponential stability are derived in the terminal cost and constraint set fashion, while allowing for discontinuous system dynamics and discontinuous MPC value functions. For constrained piecewise affine (PWA) systems as prediction models, we present novel techniques for computing a terminal cost and a terminal constraint set that satisfy the developed stabilization conditions. For quadratic MPC costs, these conditions translate into a linear matrix inequality while, for MPC costs based on 1, infin-norms, they are obtained as norm inequalities. New ways for calculating low complexity piecewise polyhedral positively invariant sets for PWA systems are also presented. An example illustrates the developed theory     

On the influence of residual stress on nano-mechanical characterization of thin coatings

In the present paper, the effect of residual stress on the mechanical behavior of thin hard coatings has been investigated by a new methodology based on the combined use of focused ion beam (FIB) micro-machining techniques and nanoindentation testing. Surface elastic residual stress were determined by nanoindentation testing on Focused Ion Beam (FIB) milled micro-pillars. The average residual stress present in a 3.8 microm CAE-PVD TiN coating on WC-Co substrate was calculated by the comparison of two different sets of load-depth curves, the first one obtained at centre of stress relieved pillars, the second one on the undisturbed (residually stressed) surface. Results for stress measurement were in good agreement with the estimate obtained by XRD (sin2 psi method) analysis on the same sample, adopting the same elastic constants. In addition, nanoindentation on stress relieved pillars also allowed to perform a more accurate evaluation of elastic modulus and hardness of the coating. The effect of residual stress on crack propagation modes was quantitatively analyzed by high-load nanoindentation and application of energy methods for fracture toughness evaluation. It is found that compressive residual stress plays a relevant role in determining the fracture behavior and failure modes of the coating. Finally, Microstructural observations of the deformation mechanisms of the TiN coating were performed by TEM analysis on the cross section of the indentation, obtained by FIB lamella thinning. Results showed that plastic deformation at the nanoscale essentially occurs by formation of shear bands inside the columnar grains, independently of residual stress. A transition between intra-granular shear deformation and columnar grain sliding is also observed as a function of the applied load.