A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the di erent approaches, the choices that have to be made and what considerations are relevant for a successful system identi cation application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping from observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function expansion. The basis functions are typically formed from one simple scalar function which is modi ed in terms of scale and location. The expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach. Basic techniques for estimating the parameters in the structures are criterion minimization, as well as two step procedures, where rst the relevant basis functions are determined, using data, and then a linear least squares step to determine the coordinates of the function approximation. A particular problem is to deal with the large number of potentially necessary parameters. This is handled by making the number of \used" parameters considerably less than the number of \o ered" parameters, by regularization, shrinking, pruning or regressor selection. A more mathematically comprehensive treatment i s g i v en in a companion paper (Juditsky et al., 1995).

This paper presents a novel convex modeling approach which allows for a simultaneous optimization of battery size and energy management of a plug-in hybrid powertrain by solving a semidefinite convex problem. The studied powertrain belongs to a city bus which is driven along a perfectly known bus line with fixed charging infrastructure. The purpose of the paper is to present the convexifying methodology and validate the necessary approximations by comparing with results obtained by Dynamic programming when using the original nonlinear, non-convex, mixed-integer models. The comparison clearly shows the importance of the gear and engine on/off decisions, and it also shows that the convex optimization and Dynamic Programming point toward similar battery size and operating cost when the same gear and engine on/off heuristics are used. The main conclusion in the paper is that due to the low computation time, the convex modeling approach enables optimization of problems with two or more state variables, e.g. allowing for thermal models of the components; or to include more sizing variables, e.g. sizing of the engine and the electric machine simultaneously.

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This paper presents a model-based algorithm that estimates how the driver of a vehicle can either steer, brake, or accelerate to avoid colliding with an arbitrary object. In this algorithm, the motion of the vehicle is described by a linear bicycle model, and the perimeter of the vehicle is represented by a rectangle. The estimated perimeter of the object is described by a polygon that is allowed to change size, shape, position, and orientation at sampled time instances. Potential evasive maneuvers are modeled, parameterized, and approximated such that an analytical expression can be derived to estimate the set of maneuvers that the driver can use to avoid a collision. This set of maneuvers is then assessed to determine if the driver needs immediate assistance to avoid or mitigate an accident. The proposed threat-assessment algorithm is evaluated using authentic data from both real traffic conditions and collision situations on a test track and by using simulations with a detailed vehicle model. The evaluations show that the algorithm outperforms conventional threat-assessment algorithms at rear-end collisions in terms of the timing of autonomous brake activation. This is crucial for increasing the performance of collisionavoidance systems and for decreasing the risk of unnecessary braking. Moreover, the algorithm is computationally efficient and can be used to assist the driver in avoiding or mitigating collisions with all types of road users in all kinds of traffic scenarios.

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