Showing papers by "Wpmh Maurice Heemels published in 2004"

A Bayesian approach to identification of hybrid systems

Abstract: In this paper, we present a novel procedure for the identification of hybrid systems in the class of piecewise ARX systems. The presented method facilitates the use of available a priori knowledge on the system to be identified, but can also be used as a black-box method. We treat the unknown parameters as random variables, described by their probability density functions. The identification problem is posed as the problem of computing the a posteriori probability density function of the model parameters, and subsequently relaxed until a practically implementable method is obtained. A particle filtering method is used for a numerical implementation of the proposed procedure. A modified version of the multicategory robust linear programming classification procedure, which uses the information derived in the previous steps of the identification algorithm, is used for estimating the partition of the piecewise ARX map. The proposed procedure is applied for the identification of a component placement process in pick-and-place machines.

On the Controllability of Bimodal Piecewise Linear Systems

Abstract: This paper studies controllability of bimodal systems that consist of two linear dynamics on each side of a given hyperplane. We show that the controllability properties of these systems can be inferred from those of linear systems for which the inputs are constrained in a certain way. Inspired by the earlier work on constrained controllability of linear systems, we derive necessary and sufficient conditions for a bimodal piecewise linear system to be controllable.

Stabilization conditions for model predictive control of constrained PWA systems

Abstract: Model predictive control (MPC) has recently been applied to several relevant classes of hybrid systems with promising results. These developments generated an increasing interest towards issues such as stability and computational problems that arise in hybrid MPC. Stability aspects have been addressed only marginally. In this paper we present an extension of the terminal cost and constraint set method for guaranteeing stability in MPC to the class of constrained piecewise affine systems. Semidefinite programming is used to calculate the employed terminal weight matrix that ensures stability for quadratic cost based MPC. A procedure for computing a robust positively invariant set for piecewise linear systems is also developed. The implementation of the proposed method is illustrated by an example.

Energy management strategies for vehicle power nets

Abstract: In the near future a significant increase in electric power consumption in vehicles is to be expected. To limit the associated increase in fuel consumption and exhaust emissions, smart strategies for the generation, storage/retrieval, distribution, and consumption of the electric power can be used. This paper presents a case study on controlling the vehicle power net using knowledge of the driving pattern to minimize fuel use, by generating and storing extra energy only at the most suitable moments. For this purpose, both off-line and online optimization methods are developed and tested in a simulation environment. Results show a reduction in fuel use, even without an accurate prediction of the drive cycle.

Stability of hybrid model predictive control

Abstract: In this paper we investigate the stability of hybrid systems in closed-loop with Model Predictive Controllers (MPC) and we derive a priori sufficient conditions for Lyapunov asymptotic stability and exponential stability. A general theory is presented which proves that Lyapunov stability is achieved for both terminal cost and constraint set and terminal equality constraint hybrid MPC, even though the considered Lyapunov function and the system dynamics may be discontinuous. For particular choices of MPC criteria and constrained Piecewise Affine (PWA) systems as the prediction models we develop novel algorithms for computing the terminal cost and the terminal constraint set. For a quadratic MPC cost, the stabilization conditions translate into a linear matrix inequality while, for an 1-norm based MPC cost, they are obtained as 1-norm inequalities. It is shown that by using 1-norms, the terminal constraint set is automatically obtained as a polyhedron or a finite union of polyhedra by taking a sublevel set of the calculated terminal cost function. New algorithms are developed for calculating polyhedral or piecewise polyhedral positively invariant sets for PWA systems. In this manner, the on-line optimization problem leads to a mixed integer quadratic programming problem or to a mixed integer linear programming problem, which can be solved by standard optimization tools. Several examples illustrate the effectiveness of the developed methodology.

Comparison of three procedures for the identification of hybrid systems

Abstract: In This work, three recently proposed procedures for the identification of piece-wise autoregressive exogenous (PWARX) models are compared. Quantitative measures for the quality of the obtained models are proposed. Using one dimensional examples, specific behaviors of the methods are pointed out. An experimental example is considered as well.

Well-posedness of hybrid systems

Abstract: Well-posedness problems arise in hybrid systems theory as a consequence of the use of implicit descriptions and of solution concepts that are based on relaxations. Examples show that the well-posedness issue is considerably more complex in hybrid systems than in continuous systems, as a result of a number of factors including the possible presence of sliding modes, the interaction of guards and invariants, and the occurrence of left or right accumulations of event times. Description formats that are based on implicit or relaxed specifications are typically connected to particular subclasses of hybrid systems, and so there is no general theory of well-posedness of hybrid systems; however, the questions that need to be answered are similar in each case. This chapter surveys several description formats and solution concepts that are used for hybrid systems. We concentrate on well-posedness in the sense of existence and uniqueness of solution, without requiring continuous dependence on initial conditions. A selection of results available in the literature is presented for the subclasses of multi-modal linear systems, complementarity systems, and differential equations with discontinuous righthand sides.

Stabilizing receding horizon control of piecewise linear systems: An LMI approach

Abstract: Receding horizon control has recently been used for regulating discrete-time Piecewise Affine (PWA) systems. One of the obstructions for implementation consists in guaranteeing closed-loop stability a priori. This is an issue that has only been addressed marginally in the literature. In this paper we present an extension of the terminal cost method for guaranteeing stability in receding horizon control to the class of unconstrained Piecewise Linear (PWL) systems. A linear matrix inequalities set-up is developed to calculate the terminal weight matrix and the auxiliary feedback gains that ensure stability for quadratic cost based receding horizon control. It is shown that the PWL statefeedback control law employed in the stability proof globally asymptotically stabilizes the origin of the PWL system. The additional conditions needed to extend these results to constrained PWA systems are also pointed out. The implementation of the proposed method is illustrated by an example.

Identification of an industrial hybrid system

Abstract: In this paper we present an experimental study in the identification of an industrial hybrid system. Piecewise ARX models, that consist of a number of ARX models, together with the partition of the regressor space into regions where each of the models is valid, were identified Effects of dry friction, and mechanical constraints in the experimental setup are demonstrated, and their infl uence on the identification procedure is discussed. Com- parison of the simulated responses of the identified models with the responses of the real system shows that the obtained models are able to describe relevant aspects of the dynamics of the experimental setup. Ways to improve the identification procedure are proposed.