A revealed preference analysis of the rational addiction model.

We provide a revealed preference analysis of the rational addiction model. The revealed preference approach avoids the need to impose an, a priori unverifiable, functional form on the underlying utility function. Our results extend the previously established revealed preference characterizations for the life cycle model and the one-lag habits model. We show that our characterization is easily testable by means of linear programming methods and we demonstrate its practical usefulness by means of an application to Spanish household consumption data.

A revealed preference analysis of the rational addiction model

We provide a revealed preference analysis of the rational addiction model. The revealed preference approach avoids the need to impose an, a priori unverifiable, functional form on the underlying utility function. Our results extend the previously established revealed preference characterizations for the life cycle model and the one-lag habits model. We show that our characterization is easily testable by means of linear programming methods and we demonstrate its practical usefulness by means of an application to Spanish household consumption data.

Commitment in intertemporal household consumption: a revealed preference analysis

We present a revealed preference methodology for analyzing intertemporal household consumption behavior. In doing so, we follow a collective approach, which explicitly recognizes that multi-member households consist of multiple decision makers with their own rational preferences. Following original work of Mazzocco (2007), we develop tests that can empirically verify whether observed consumption behavior is consistent with (varying degrees of) intrahousehold commitment. In our set-up, commitment means that households choose consumption allocations on the ex ante Pareto frontier. The distinguishing feature of our tests is that they are entirely nonparametric, i.e. their implementation does not require an a priori (typically non-verifiable) specification of the intrahousehold decision process (e.g. individual utilities). We demonstrate the practical usefulness of our methodology by means of an empirical application. For the data at hand, our results suggest using a so-called limited commitment model that allows for household-specific commitment patterns. Importantly, our application also shows that bringing intertemporal dynamics in the empirical analysis can substantially increases the discriminatory power of the revealed preference methodology.

Square wave periodic solutions of a differential delay equation

We prove the existence of periodic solutions of the differential delay equation εx˙(t)+x(t)=f(x(t−1)),ε>0 under the assumptions that the continuous nonlinearity f(x) satisfies the negative feedback condition, x⋅f(x)<0,x≠0, has sufficiently large derivative at zero |f′(0)|, and possesses an invariant interval I∋0,f(I)⊆I, as a dimensional map. As ε→0+ we show the convergence of the periodic solutions to a discontinuous square wave function generated by the globally attracting 2-cycle of the map f

Empirical Differential Balancing for Nonlinear Systems

In this paper, we consider empirical balancing of nonlinear systems by using its prolonged system, which consists of the original nonlinear system and its variational system. For the prolonged system, we define differential reachability and observability Gramians, which are matrix valued functions of the state trajectory (i.e. the initial state and input trajectory) of the original system. The main result of this paper is showing that for a fixed state trajectory, it is possible to compute the values of these Gramians by using impulse and initial state responses of the variational system. By using the obtained values of the Gramians, balanced truncation is doable along the fixed state trajectory without solving nonlinear partial dierential equations. An example demonstrates our proposed method to compute a reduced order model along a limit cycle of a coupled van der Pol oscillator

Observability of systems with delay convoluted observation

This paper analyzes finite dimensional linear time-invariant systems with observation of a delay, where that delay satisfies a particular implicit relation with the state variables, rendering the entire problem nonlinear. The objective is to retrieve the state variables from the measured delay. The first contribution involves the direct inversion of the delay, the second is the design of a finite dimensional state observer, and the third involves the derivation of certain properties of the delay - state relation. Realistic examples treat vehicles with ultrasonic position sensor

Optimal path planning of multi-agent cooperative systems with rigid formation

In this article, we consider the path-planning problem of a cooperative homogeneous robotic system with rigid formation. An optimal controller is designed for each agent in such rigid systems based on Pontryagin's minimum principle theory. We found that the optimal control for each agent is equivalent to the optimal control for the Center of Mass (CoM). This equivalence is then proved by using some analytical mechanics. Three examples are finally simulated to illustrate our theoretical results. One application could be utilizing this equivalence to simplify the original multi-agent optimal control problem