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The stability of a model of the dynamics of a class of split-gate radar range trackers is considered, under both deterministic and stochastic target models. The emphasis is on stability as a means toward studying the dynamics of the tracker in the presence of both an actual target and a decoy target. The model employed reflects Automatic Gain Control action for noise attenuation as well as nonlinear detector laws for target resolution. The deterministic and stochastic stability of track points are studied using deterministic and stochastic Liapunov functions, and stochastic bifurcation issues are discussed.

This work is concerned with asymptotic properties of singularly perturbed Markov chains in discrete time with finite state spaces. We study asymptotic expansions of the probability distribution vectors and derive a mean square estimate on a sequence of occupation measures. Assuming that the state space of the underlying Markov chain can be decomposed into several groups of recurrent states and a group of transient states, by treating the states within each recurrent class as a single state, we define an aggregated process, and show that its continuous-time interpolation converges to a continuous-time Markov chain. In addition, we prove that a sequence of suitably scaled occupation measures converges to a switching diffusion process weakly. Next, control problems of large-scale nonlinear dynamic systems driven by singularly perturbed Markov chains are studied. It is demonstrated that a reduced limit system can be derived, and that by applying nearly optimal controls of the limit system to the original one, nearly optimal controls of the original system can be obtained.

This paper reports a tight bound on the data capacity a feedback channel must provide in order to stabilize a right half-plane pole of a linear, time-invariant control system. The proof is constructive, and involves considering a general class of quantized control realizations of classical feedback designs. Even for the coarsest quantizations—with two-element control input sets, which we refer to as a —the bound is achievable in the scalar case. The open question of whether bounded trajectories in higher order systems could be produced by a binary realization is answered in the affirmative—again via an explicit construction for a system with two-dimensional state space. It is also shown how binary realizations of classical feedback designs organize the way in which the controller pays to different open-loop modes in the plant.

Let be an open bounded smooth domain of ℝ, and let = be its boundary. We denote by the normal vector at the boundary , oriented towards the outside of . Let us consider the canonical process

We consider a Black-Scholes market in which the underlying economy, as modelled by the parameters and volatility of the processes, switches between a finite number of states. The switching is modelled by a hidden Markov chain. European options are priced and a Black-Scholes equation obtained.

Under some reasonable conditions imposed on the moving average part () of the multi-dimensional system () = () it is shown that for stability of (), which means that all zeros of det () are outside the closed unit disk, the necessary and sufficient condition is the stability of the system in the mean square sense, by which it is meant that the long run average of the squared output is bounded:

The aim of this contribution is to describe main features in the development of system identification, in the sense of modelling from time series data. Given the restrictions in space, such an effort is necessarely fragmentary. Clearly, subjective judgements cannot be avoided. System identification has been developed in a number of different scientific communities, the most important of which are econometrics, statistics and system- and control theory.

Max-plus stochastic processes are counterparts of Markov diffusion processes governed by Ito sense stochastic differential equations. In this framework, expectations are linear operations with respect to max-plus arithmetic. Max-plus stochastic control problems are considered, in which a minimizing control enters the state dynamics and running cost. The minimum max-plus expected cost is equal to the upper Elliott-Kalton value of an associated differential game.

An extension of the classical Merton model with consumption is considered when the diffusion coefficient of the asset prices depends on some economic factor. The objective is to maximize total expected discounted HARA utility of consumption. Optimal controls are provided as well as a characterization of the value function in terms of the associated Hamilton-Jacobi-Bellman equation.

The time-varying dynamics and non-stationarity of epileptic seizures makes their detection difficult. Osorio et. al. in ([]) proposed an adaptable seizure detection algorithm (‘SDA’), however, that has had great success. In this presentation, we begin with an overview of the original detection algorithm’s architecture, describing its degrees of freedom that provide flexibility and outline a procedure to adapt the method to improve performance.

The adaptation consists of generating multiple candidate digital filters using various techniques from signal processing, defining a practical optimization criteria, and using this criteria to select the best filter candidate. Coupled within the procedure is the selection of a corresponding optimal percentile value for use in the nonlinear (order statistic) filtering step that follows in the algorithm.

Finally, we discuss how the algorithm has been utilized for closed-loop therapy, in which seizure detections are used to trigger electrical stimulations in the brain designed to prevent the development of a seizure before its disabling effects occur.