A parsimonious algorithm for the solution of continuous-time constrained LQR problems with guaranteed convergence

Polyhedral control Lyapunov functions (PCLFs) are exploited in this paper to propose a linear model predictive control (MPC) formulation that guarantees a “large” domain of attraction (DoA) even for short horizon. In particular, the terminal region of the proposed finite-horizon MPC formulation is chosen as a level set of an appropriate PCLF. For small dimensional systems, this terminal region can be explicitly computed as an arbitrarily close approximation to the entire (infinite-horizon) stabilizable set. Global stability of the origin is guaranteed by using an “inflated” PCLF as terminal cost. The proposed MPC scheme can be formulated as a (small dimensional) quadratic programming problem by introducing one additional scalar variable. Numerical examples show the main benefits and achievements of the proposed formulation in terms of trade-off between volume of the DoA, computational time and closed-loop performance

Predictive control of systems with fast dynamics using computational reduction based on feedback control information

Predictive control is a method, which is suitable for control of linear discrete dynamical systems. However, control of systems with fast dynamics could be problematic using predictive control. The calculation of a predictivecontrol algorithm can exceed the sampling period. This situation occurs in case with higher prediction horizons and many constraints on variables in the predictive control. In this contribution, an improving of the classical approach is presented. The reduction of the computational time is performed using an analysis of steady states in the control. The presented approach is based on utilization of information from the feedback control. Then this information is applied in the control algorithm. Finally, the classical method is compared to the presented modification using the time analyses. © Springer International Publishing Switzerland 2015

Performance of Sensitivity based NMPC Updates in Automotive Applications

In this work we consider a half car model which is subject to unknown but measurable disturbances. To control this system, we impose a combination of model predictive control without stabilizing terminal constraints or cost to generate a nominal solution and sensitivity updates to handle the disturbances. For this approach, stability of the resulting closed loop can be guaranteed using a relaxed Lyapunov argument on the nominal system and Lipschitz conditions on the open loop change of the optimal value function and the stage costs. For the considered example, the proposed approach is realtime applicable and corresponding results show significant performance improvements of the updated solution with respect to comfort and handling properties.Comment: 6 pages, 2 figure

Grain Surface Models and Data for Astrochemistry

AbstractThe cross-disciplinary field of astrochemistry exists to understand the formation, destruction, and survival of molecules in astrophysical environments. Molecules in space are synthesized via a large variety of gas-phase reactions, and reactions on dust-grain surfaces, where the surface acts as a catalyst. A broad consensus has been reached in the astrochemistry community on how to suitably treat gas-phase processes in models, and also on how to present the necessary reaction data in databases; however, no such consensus has yet been reached for grain-surface processes. A team of ∼25 experts covering observational, laboratory and theoretical (astro)chemistry met in summer of 2014 at the Lorentz Center in Leiden with the aim to provide solutions for this problem and to review the current state-of-the-art of grain surface models, both in terms of technical implementation into models as well as the most up-to-date information available from experiments and chemical computations. This review builds on the results of this workshop and gives an outlook for future directions

On the use of suboptimal solvers for efficient cooperative distributed linear MPC

We address the problem of efficient implementations of distributed Model Predictive Control (MPC) systems for large-scale plants. We explore two possibili- ties of using suboptimal solvers for the quadratic program associated with the local MPC problems. The first is based on an active set method with early termination. The second is based on Partial Enumeration (PE), an approach that allows one to compute the (sub)optimal solution by using a solution table which stores the infor- mation of only a few most recently optimal active sets. The use of quick suboptimal solvers, especially PE, is shown to be beneficial because more cooperative iterations can be performed in the allowed given decision time. By using the available compu- tation time for cooperative iterations rather than local iterations, we can improve the overall optimality of the strategy. We also discuss how input constraints that involve different units (for example, on the summation of common utility consumption) can be handled appropriately. Our main ideas are illustrated with a simulated example comprising three units and a coupled input constraint