Model predictive control techniques for hybrid systems

This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

Synthesis of Minimal Error Control Software

Software implementations of controllers for physical systems are at the core of many embedded systems. The design of controllers uses the theory of dynamical systems to construct a mathematical control law that ensures that the controlled system has certain properties, such as asymptotic convergence to an equilibrium point, while optimizing some performance criteria. However, owing to quantization errors arising from the use of fixed-point arithmetic, the implementation of this control law can only guarantee practical stability: under the actions of the implementation, the trajectories of the controlled system converge to a bounded set around the equilibrium point, and the size of the bounded set is proportional to the error in the implementation. The problem of verifying whether a controller implementation achieves practical stability for a given bounded set has been studied before. In this paper, we change the emphasis from verification to automatic synthesis. Using synthesis, the need for formal verification can be considerably reduced thereby reducing the design time as well as design cost of embedded control software. We give a methodology and a tool to synthesize embedded control software that is Pareto optimal w.r.t. both performance criteria and practical stability regions. Our technique is a combination of static analysis to estimate quantization errors for specific controller implementations and stochastic local search over the space of possible controllers using particle swarm optimization. The effectiveness of our technique is illustrated using examples of various standard control systems: in most examples, we achieve controllers with close LQR-LQG performance but with implementation errors, hence regions of practical stability, several times as small.Comment: 18 pages, 2 figure

Simulation-based solution of stochastic mathematical programs with complementarity constraints: Sample-path analysis

We consider a class of stochastic mathematical programs with complementarity constraints, in which both the objective and the constraints involve limit functions or expectations that need to be estimated or approximated. Such programs can be used for modeling \\average" or steady-state behavior of complex stochastic systems. Recently, simulation-based methods have been successfully used for solving challenging stochastic optimization problems and equilibrium models. Here we broaden the applicability of so-called the sample-path method to include the solution of certain stochastic mathematical programs with equilibrium constraints. The convergence analysis of sample-path methods rely heavily on stability conditions. We first review necessary sensitivity results, then describe the method, and provide sufficient conditions for its almost-sure convergence. Alongside we provide a complementary sensitivity result for the corresponding deterministic problems. In addition, we also provide a unifying discussion on alternative set of sufficient conditions, derive a complementary result regarding the analysis of stochastic variational inequalities, and prove the equivalence of two different regularity conditions.simulation;mathematical programs with equilibrium constraints;stability;regularity conditions;sample-path methods;stochastic mathematical programs with complementarity constraints