Results 1  10
of
1,120
A Unified Framework for Hybrid Control: Model and Optimal Control Theory
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 1998
"... Complex natural and engineered systems typically possess a hierarchical structure, characterized by continuousvariable dynamics at the lowest level and logical decisionmaking at the highest. Virtually all control systems todayfrom flight control to the factory floorperform computercoded chec ..."
Abstract

Cited by 184 (8 self)
 Add to MetaCart
Complex natural and engineered systems typically possess a hierarchical structure, characterized by continuousvariable dynamics at the lowest level and logical decisionmaking at the highest. Virtually all control systems todayfrom flight control to the factory floorperform computercoded checks and issue logical as well as continuousvariable control commands. The interaction of these different types of dynamics and information leads to a challenging set of "hybrid" control problems. We propose a very general framework that systematizes the notion of a hybrid system, combining differential equations and automata, governed by a hybrid controller that issues continuousvariable commands and makes logical decisions. We first identify the phenomena that arise in realworld hybrid systems. Then, we introduce a mathematical model of hybrid systems as interacting collections of dynamical systems, evolving on continuousvariable state spaces and subject to continuous controls and discrete transitions. The model captures the identified phenomena, subsumes previous models, yet retains enough structure on which to pose and solve meaningful control problems. We develop a theory for synthesizing hybrid controllers for hybrid plants in an optimal control framework. In particular, we demonstrate the existence of optimal (relaxed) and nearoptimal (precise) controls and derive "generalized quasivariational inequalities" that the associated value function satisfies. We summarize algorithms for solving these inequalities based on a generalized Bellman equation, impulse control, and linear programming.
Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization
, 2000
"... ..."
Flatness and defect of nonlinear systems: Introductory theory and examples
 International Journal of Control
, 1995
"... We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman’s controllability. The distance to flatness is ..."
Abstract

Cited by 175 (15 self)
 Add to MetaCart
We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman’s controllability. The distance to flatness is measured by a nonnegative integer, the defect. We utilize differential algebra which suits well to the fact that, in accordance with Willems ’ standpoint, flatness and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of planar curves. The three nonflat examples, the simple, double and variable length pendulums, are borrowed from nonlinear physics. A high frequency control strategy is proposed such that the averaged systems become flat. ∗This work was partially supported by the G.R. “Automatique ” of the CNRS and by the D.R.E.D. of the “Ministère de l’Éducation Nationale”. 1 1
Heterogeneous Beliefs and Routes to Chaos in a Simple Asset Pricing Model
, 1998
"... This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their `beliefs' in each period in a boundedly rational way, according to a `fitness mea ..."
Abstract

Cited by 167 (13 self)
 Add to MetaCart
This paper investigates the dynamics in a simple present discounted value asset pricing model with heterogeneous beliefs. Agents choose from a finite set of predictors of future prices of a risky asset and revise their `beliefs' in each period in a boundedly rational way, according to a `fitness measure' such as past realized profits. Price fluctuations are thus driven by an evolutionary dynamics between different expectation schemes (`rational animal spirits'). Using a mixture of local bifurcation theory and numerical methods, we investigate possible bifurcation routes to complicated asset price dynamics. In particular, we present numerical evidence of strange, chaotic attractors when the intensity of choice to switch prediction strategies is high.
Persistent route oscillations in interdomain routing
 Computer Networks
, 1996
"... Hopbyhop interdomain routing protocols, such as BGP and IDRP, use independent route selection to realize domains ’ local policies. A domain chooses its routes based on path attributes present in a route. It is widely believed that these interdomain routing protocols always converge. We show that ..."
Abstract

Cited by 131 (3 self)
 Add to MetaCart
Hopbyhop interdomain routing protocols, such as BGP and IDRP, use independent route selection to realize domains ’ local policies. A domain chooses its routes based on path attributes present in a route. It is widely believed that these interdomain routing protocols always converge. We show that there exist domain policies that cause BGP/IDRP to exhibit persistent oscillations. In these oscillations, each domain repeatedly chooses a sequence of routes to a destination. Complex oscillation patterns can occur even in very simple topologies. We analyze the conditions for persistent route oscillations in a simple class of interdomain topologies and policies. Using this analysis, we evaluate ways to prevent or avoid persistent oscillations in general topologies. We conclude that if a hopbyhop interdomain routing protocol allows unconstrained route selection at a domain, the protocol may be susceptible to route oscillations. Constraining route selection to a provably “safe ” procedure (such as shortest path) can reduce the number of realizable policies. Alternatively, a routing policy registry can help detect unsafe policies.
Revisiting the edge of chaos: Evolving cellular automata to perform computations
 Complex Systems
, 1993
"... We present results from an experiment similar to one performed by Packard [24], in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton’s λ parameter [17], and interp ..."
Abstract

Cited by 100 (10 self)
 Add to MetaCart
We present results from an experiment similar to one performed by Packard [24], in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA rules as a function of Langton’s λ parameter [17], and interpreted the results of his experiment as giving evidence for the following two hypotheses: (1) CA rules able to perform complex computations are most likely to be found near “critical ” λ values, which have been claimed to correlate with a phase transition between ordered and chaotic behavioral regimes for CA; (2) When CA rules are evolved to perform a complex computation, evolution will tend to select rules with λ values close to the critical values. Our experiment produced very different results, and we suggest that the interpretation of the original results is not correct. We also review and discuss issues related to λ, dynamicalbehavior classes, and computation in CA. The main constructive results of our study are identifying the emergence and competition of computational strategies and analyzing the central role of symmetries in an evolutionary system. In particular, we demonstrate how symmetry breaking can impede the evolution toward higher computational capability.
Advanced Spectral Methods for Climatic Time Series
, 2001
"... The analysis of uni or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical eld of ..."
Abstract

Cited by 96 (29 self)
 Add to MetaCart
The analysis of uni or multivariate time series provides crucial information to describe, understand, and predict climatic variability. The discovery and implementation of a number of novel methods for extracting useful information from time series has recently revitalized this classical eld of study. Considerable progress has also been made in interpreting the information so obtained in terms of dynamical systems theory.
Computation at the onset of chaos
 The Santa Fe Institute, Westview
, 1988
"... Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For perioddoubl ..."
Abstract

Cited by 84 (14 self)
 Add to MetaCart
Computation at levels beyond storage and transmission of information appears in physical systems at phase transitions. We investigate this phenomenon using minimal computational models of dynamical systems that undergo a transition to chaos as a function of a nonlinearity parameter. For perioddoubling and bandmerging cascades, we derive expressions for the entropy, the interdependence ofmachine complexity and entropy, and the latent complexity of the transition to chaos. At the transition deterministic finite automaton models diverge in size. Although there is no regular or contextfree Chomsky grammar in this case, we give finite descriptions at the higher computational level of contextfree Lindenmayer systems. We construct a restricted indexed contextfree grammar and its associated oneway nondeterministic nested stack automaton for the cascade limit language. This analysis of a family of dynamical systems suggests a complexity theoretic description of phase transitions based on the informational diversity and computational complexity of observed data that is independent of particular system control parameters. The approach gives a much more refined picture of the architecture of critical states than is available via
Monetary Policy and Multiple Equilibria
, 1998
"... In this paper, we study interest rate feedback rules whereby the nominal interest rate is set as an increasing function of the in ation rate and characterize conditions under which such rules generate multiple equilibria. We show that these conditions depend not only on the monetary scal regime (as ..."
Abstract

Cited by 79 (10 self)
 Add to MetaCart
In this paper, we study interest rate feedback rules whereby the nominal interest rate is set as an increasing function of the in ation rate and characterize conditions under which such rules generate multiple equilibria. We show that these conditions depend not only on the monetary scal regime (as emphasized in the scal theory of the price level) but also on the way in which money is assumed to enter preferences and technology. We analyze this issue in exible and sticky price environments. We provide a number of examples in which, contrary to what is commonly believed, active monetary policy in combination with a scal policy that preserves government solvency gives rise to multiple equilibria and passive monetary policy renders the equilibrium unique.
Backward Error Analysis for Numerical Integrators
 SIAM J. Numer. Anal
, 1996
"... We consider backward error analysis of numerical approximations to ordinary differential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modified differential equation. A simple recursive definition of the modified equation is stated. This recursion is used ..."
Abstract

Cited by 69 (7 self)
 Add to MetaCart
We consider backward error analysis of numerical approximations to ordinary differential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modified differential equation. A simple recursive definition of the modified equation is stated. This recursion is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to an appropriate truncation of the modified equation. We also discuss qualitative properties of the modified equation and apply these results to the symplectic variable stepsize integration of Hamiltonian systems, the conservation of adiabatic invariants, and numerical chaos associated to homoclinic orbits. 3 S. Reich, Backward error analysis 4