François Chaplais

Handling constraints in optimal control with saturation functions and system extension

A method is presented to systematically transform a general inequality-constrained optimal control problem (OCP) into a new equality-constrained OCP by means of saturation functions. The transformed OCP can be treated more conveniently within the standard calculus of variations compared to the original constrained OCP. In detail, state constraints are substituted by saturation functions and successively constructed dynamical subsystems, which constitute a (dynamical) system extension. The dimension of the subsystems corresponds to the relative degree (or order) of the respective state constraints. These dynamical subsystems are linked to the original dynamics via algebraic coupling equations. The approach results in a new equality-constrained OCP with extended state and input vectors. An additional regularization term is used in the cost to regularize the new OCP with respect to the new inputs. The regularization term has to be successively reduced to approach the original constrained solution. The new OCP can be solved in a convenient manner, since the stationarity conditions are easily determined and exploited. An important aspect of the saturation function formulation is that the constraints cannot be violated during the numerical solution. The approach is illustrated for an extended version of the well-known Goddard problem with thrust and dynamic pressure constraints and using a collocation method for its numerical solution.

Thermal building model identification using time-scaled identification methods

The aim of this paper is to propose a robust and accurate method for the parametric identification of the thermal behaviour of low consumption buildings. These buildings are known to have a two-time scale structure, which, if not handled properly, results in poor conditioning of the parametric identification.

TWO TIME SCALED PARAMETER IDENTIFICATION BY COORDINATION OF LOCAL IDENTIFIERS

Abstract Contradictory requirements on the precision in L ∞ and L 2 norms prevent the classical least square procedure from identifying two time scaled systems accurately. A new identification procedure, explicitly using the time scale structure of the system, is proposed here, and is proved to solve the problem of accurate parameter estimation.

Investigating the ability of various buildings in handling load shiftings

In modern constructions of residential buildings, several energy saving technologies exist. Therefore, when such buildings are renovated, various investments can be considered. The contribution of this article is a method for evaluating the ability of several renovating configurations to keep the inhabitants in a comfortable situation during load shifting periods. This question is of importance in the relationship, and then in the price setting, between the users (inhabitants) and the energy provider who uses these load shifting periods to optimize his production on a regional or national scale.

Design of penalty functions for optimal control of linear dynamical systems under state and input constraints

This paper addresses the problem of solving a constrained optimal control for a general single-input single output linear time varying system by means of an unconstrained method. The exposed methodology uses a penalty function approach, commonly considered in finite dimensional optimization problem, and extended here it to the considered infinite dimensional (functional optimization) case. The main novelty is that both the bounds on the control variable and on a freely chosen output variable are considered and studied theoretically. It is shown that a relatively simple and constructive choice of penalty functions allows to completely alleviate the usual difficulties of handling such constraints in optimal control. An illustrative example is provided to show the potential of the method.

Numerical optimal control as a method to evaluate the benefit of thermal management in hybrid electric vehicles

Abstract In this paper, a numerical solution of the optimal thermal management problem for a parallel hybrid electric vehicle is presented by taking into account the engine temperature. This temperature influences the fuel consumption and has a dynamical behavior which is controlled by the engine torque. Simulation results are presented to evaluate the benefit of adding this new state variable to the optimization problem, by comparison to the simplified problem where only the State Of Charge (SOC) is taken into account.

Inversion in indirect optimal control: constrained and unconstrained cases

This paper focuses on using non linear inversion in optimal control problems. This technique allows us to rewrite the stationarity conditions derived from the calculus of variations under a higher order form with a reduced number of variables. After a brief tutorial overview of the multi- input multi-output cases for which the cost functions have a positive definite Hessian with respect to control variables, we address the case of linear systems with a control affine cost to be minimized under input constraints. This is the main contribution of this paper. We study the switching function between singular and regular arcs and explain how higher order stationarity conditions can be obtained. An example from the literature (energy optimal trajectory for a car) is addressed.

Redundant wavelet filter banks on the half-axis with applications to signal denoising with small delays

A wavelet transform on the negative half real axis is developed using an average-interpolation scheme. This transform is redundant and can be used to perform causal wavelet processing, such as signal denoising, without delay. Nonetheless, in practice some boundary effects occur and thus a small amount of delay is required to reduce them. The theory is implemented on a challenging signal with large noise and sharp transients. Results from the experimental implementation of the proposed algorithm for the denoising of a feedback signal for controlling a three-phase permanent-magnet synchronous brushless DC motor are also presented.

Comparison of several strategies for HEV energy management system including engine and catalyst temperatures

In this paper, we investigate the benefits of considering advanced modeling of engine and after-treatment system (3-way catalyst) in the design of Energy Management System (EMS) for a parallel Hybrid-Electric light-duty Vehicle (HEV) (passenger car with gasoline engine). The evaluation is based on a comparative study of optimal control problems formulated using three distinct levels of model complexity. Starting with a single state dynamics (battery state-of-charge), successively, we consider the engine temperature and the 3-way catalyst temperature, yielding increased complexity. As is shown, the increased complexity brings only little improvement in fuel economy and emissions reduction. We provide quantitative results to assess this observation.

On the impact of model simplification in input constrained optimal control: Application to HEV energy-thermal management

In this paper, we propose a result allowing to simplify the statement of input constrained optimal control problems. In details, it is shown that perturbation terms of magnitude ε appearing in the dynamics and the cost function can be neglected, because they only yield an improvement of magnitude ε2 in the optimal cost. This result, which is is handy for practical applications, is here proven by means of an interior penalty method to deal with input constraints. For illustration, an example of energy management system for a Hybrid Electric Vehicle (HEV) is treated. As is expected, the complexity of the problem can be reduced at very little expense of sub-optimality. Based on simulations, quantitative results in term of fuel consumption are provided.