On Topological Equivalence of Linear Lows with Applications to Bilinear Control Systems

This paper classifies continuous linear flows using concepts and techniques from topological dynamics. Specifically, the concepts of equivalence and conjugacy are adapted to flows on vector bundles, and the Lyapunov decomposition is characterized using the induced flows on the Grassmann and the flag bundles. These results are then applied to bilinear control systems, for which their behavior in , on the projective space , and on the Grassmannians is characterized. This research was partially supported by Proyecto FONDECYT No. 1060981 and Proyecto FONDECYT de Incentivo a la Cooperación Internacional No. 7020439.     

The instance theory of automaticity: Why the Weibull?

It is shown that in order to derive the Weibull shape for the response time distribution in the instance theory of automaticity (G. D. Logan, 1988) by an asymptotic argument from the theory of extreme value statistics, it is necessary to determine the domain of attraction of the underlying parent distribution. An alternative, nonasymptotic characterization property equivalent to the power law of practice is presented here that gives a more feasible justification for the choice of the Weibull. This result leads to a different emphasis on the empirical conditions testing the theory. Some problems arising from the use of the asymptotic theory of extreme value statistics for the stochastic modeling of behavioral data are discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Temporal logic for process specification and recognition

Acting intelligently in dynamic environments involves anticipating surrounding processes, for example to foresee a dangerous situation by recognizing a process and inferring respective safety zones. Process recognition is thus key to mastering dynamic environments including surveillance tasks. In this paper, we are concerned with a logic-based approach to process specification, recognition, and interpretation. We demonstrate that linear temporal logic (LTL) provides the formal grounds on which processes can be specified. Recognition can then be approached as a model checking problem. The key feature of this logic-based approach is its seamless integration with logic inference which can sensibly supplement the incomplete observations of the robot. Furthermore, logic allows us to query for process occurrences in a flexible manner and it does not rely on training data. We present a case study with a robotic observer in a warehouse logistics scenario. Our experimental evaluation demonstrates that LTL provides an adequate basis for process recognition.     

A note on the stop-signal paradigm, or how to observe the unobservable.

A new theoretical analysis of the stop-signal paradigm is proposed. With the concepts of crude and net hazard functions, the nonobservable control-latency distribution can be estimated from observable reaction times. This result allows a test of Logan & Cowan's (1984) model without any simplifying assumptions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Topological Fiber Entropy for Linear Flows on Vector Bundles

For linear flows on vector bundles, it is shown that the topological entropy of lower dimensional subspaces in the fibers is determined by the Morse spectrum over chain recurrent components of the induced flows on Grassmann bundles.     

Growth rates for persistently excited linear systems

We consider a family of linear control systems \(\dot{x}=Ax+\alpha Bu\) on \(\mathbb {R}^d\) , where \(\alpha \) belongs to a given class of persistently exciting signals. We seek maximal \(\alpha \) -uniform stabilization and destabilization by means of linear feedbacks \(u=Kx\) . We extend previous results obtained for bidimensional single-input linear control systems to the general case as follows: if there exists at least one \(K\) such that the Lie algebra generated by \(A\) and \(BK\) is equal to the set of all \(d\times d\) matrices, then the maximal rate of convergence of \((A,B)\) is equal to the maximal rate of divergence of \((-A,-B)\) . We also provide more precise results in the general single-input case, where the above result is obtained under the simpler assumption of controllability of the pair \((A,B)\) .     

Invariance entropy for outputs

For continuous time control systems, this paper analyzes output invariance entropy as a measure for the information necessary to achieve invariance of compact subsets of the output space. For linear control systems with compact control range, relations to controllability and observability properties are studied. Furthermore, the notion of asymptotic output invariance entropy is introduced and characterized for these systems.     

Hyperbolic Control Sets and Chain Control Sets

A shadowing lemma for hyperbolic control flows is proved. A consequence is that hyperbolic chain control sets are closures of control sets.     

Limits of input-to-state stability

The relations between attractors, input-to-state-stability, and controllability properties are discussed. In particular it is shown that loss of the attractor property under perturbations is connected with a qualitative change in the controllability properties due to a ‘merger’ with a control set.