Sensitivity and out-of-sample error in continuous time data assimilation

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically though, these two requirements cannot both be met at the same time–tracking the observations is not possible without the trajectory deviating from the proposed model equations, while adherence to the model requires deviations from the observations. Thus, data assimilation faces a trade-off. In this contribution, the sensitivity of the data assimilation with respect to perturbations in the observations is identified as the parameter which controls the trade-off. A relation between the sensitivity and the out-of-sample error is established, which allows the latter to be calculated under operational conditions. A minimum out-of-sample error is proposed as a criterion to set an appropriate sensitivity and to settle the discussed trade-off. Two approaches to data assimilation are considered, namely variational data assimilation and Newtonian nudging, also known as synchronization. Numerical examples demonstrate the feasibility of the approach.

On equilibrium prices in continuous time

We combine general equilibrium theory and théorie générale of stochastic processes to derive structural results about equilibrium state prices.

Continuous-time and discrete-time sliding mode control accomplished using a computer

A computer-based sliding mode control (SMC) is analysed. The control law is accomplished using a computer and A/D and D/A converters. Two SMC designs are presented. The first one is a continuous-time conventional SMC design, with a variable structure law, which does not take into consideration the sampling period. The second one is a discrete-time SMC design, with a smooth sliding law, which does not have a structure variable and takes into consideration the sampling period. Both techniques are applied to control an inverted pendulum system. The performance of both the continuous-time and discrete-time controllers are compared. Simulations and experimental results are shown and the effectiveness of the proposed techniques is analysed.

Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Nonsmooth continuous-time optimization problems: Necessary conditions

We consider Lipschitz continuous-time nonlinear optimization problems and provide first-order necessary optimality conditions of both Fritz John and Karush-Kuhn-Tucker types. (C) 2001 Elsevier B.V. Ltd. All rights reserved.

Nonsmooth continuous-time optimization problems: Sufficient conditions

We discuss sufficient conditions of optimality for nonsmooth continuous-time nonlinear optimization problems under generalized convexity assumptions. These include both first-order and second-order criteria. (C) 1998 Academic Press.

Comments, with reply on 'Continuous time relay-controlled model reference adaptive-system' by A. Abdulkareem and R. Nagarajam

An adaptive scheme is shown by the authors of the above paper (ibid. vol. 71, no. 2, pp. 275-276, Feb. 1983) for continuous time model reference adaptive systems (MRAS), where relays replace the usual multipliers in the existing MRAS. The commenter shows an error in the analysis of the hyperstability of the scheme, such that the validity of this configuration becomes an open question.

A note on KKT-invexity in nonsmooth continuous-time optimization

We introduce the notion of KKT-inverity for nonsmooth continuous-time nonlinear optimization problems and prove that this notion is a necessary and sufficient condition for every KKT solution to be a global optimal solution.

A continuous-time MILP model for short-term scheduling of make-and-pack production processes

In process industries, make-and-pack production is used to produce food and beverages, chemicals, and metal products, among others. This type of production process allows the fabrication of a wide range of products in relatively small amounts using the same equipment. In this article, we consider a real-world production process (cf. Honkomp et al. 2000. The curse of reality – why process scheduling optimization problems are diffcult in practice. Computers & Chemical Engineering, 24, 323–328.) comprising sequence-dependent changeover times, multipurpose storage units with limited capacities, quarantine times, batch splitting, partial equipment connectivity, and transfer times. The planning problem consists of computing a production schedule such that a given demand of packed products is fulfilled, all technological constraints are satisfied, and the production makespan is minimised. None of the models in the literature covers all of the technological constraints that occur in such make-and-pack production processes. To close this gap, we develop an efficient mixed-integer linear programming model that is based on a continuous time domain and general-precedence variables. We propose novel types of symmetry-breaking constraints and a preprocessing procedure to improve the model performance. In an experimental analysis, we show that small- and moderate-sized instances can be solved to optimality within short CPU times.