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The regression-based reconstruction of spatial fields by static sensors requires the number of measurements be at least equal to the number of unknown parameters in order to provide a unique solution. Improvements include the use of mobile sensor networks to arrive at higher accuracy estimates. An alternate approach utilizes adaptive techniques to update the parameter estimates online. Such adaptive techniques need persistence of excitation to ensure convergence of the parameter and function estimates. It is shown that the motion of just a single sensor is a necessary condition for persistence of excitation and, subsequently, of function convergence. Having a prescribed sensor guidance is also a sufficient condition for function convergence. First, a Lyapunov-based adaptation and guidance is presented and it is shown that persistence of excitation necessitates the time dependence of the outer product of the regressor vector with itself and which in turn requires the motion of the sensor within the spatial domain. Subsequently, a gradient-based adaptive scheme relaxes the Lyapunov-based sensor guidance to any user-defined guidance as long as the outer product of the associated rank-one regressor vector with itself has a uniformly positive definite integral. The latter adaptation is conducive to the inclusion of platform dynamics resulting in a vehicle control design needed to attain parameter convergence. Extension of the centralized solution to distributed estimation using a network of mobile sensors is also examined. These results are demonstrated with simulations in one and two dimensions.

This paper is concerned with the use of \BBH2-control performance metrics in finding optimal actuator locations for a class of infinite-dimensional systems. Conditions that guarantee convergence of the optimal actuator location for the finite-dimensional representation of the infinite-dimensional system to the optimal actuator location of the original infinite-dimensional system are provided. Minimizing an \BBH2-performance index, parameterized by the possible actuator locations and disturbance functions, leads to optimal locations that in addition to enhanced performance, also provide robustness with respect to the spatial distribution of disturbances. Numerical studies for a cantilever beam and a diffusion problem are used to demonstrate the effects of the spatial distribution of disturbances on the optimal actuator location. The effect of the diffusivity parameter on the best actuator locations is also considered. [ABSTRACT FROM AUTHOR]

The aim of this note is to investigate the agreement between state and parameter estimates for a class of infinite dimensional systems that utilize distributed adaptive filters. It is assumed that the unknown parameters take the form of a structured perturbation with an unknown constant parameter, and the nominal system satisfies an infinite dimensional analog of positive real lemma. The proposed adaptive observers generated by m agents follow the structure of adaptive identifiers for infinite dimensional systems with the added feature of a penalty term in both the state and parameter estimates. Unlike earlier efforts, the proposed adaptive laws include a penalty term of the mismatch between the parameter estimates generated by the other agents. Conditions that provide uniform boundedness of the estimator dynamics and the parameter estimates are examined. Additionally, the effects of these modifications on the agreement amongst the state and parameter estimates are studied. The convergence of the deviation from the mean estimate is established as a metric for the performance of the consensus filters for both state and parameter estimates. The effects of the proposed consensus enforcement are illustrated with a diffusion partial differential equation example, which yield convincing numerical findings. [ABSTRACT FROM AUTHOR]

The main focus of this work is on the inclusion of vehicle dynamics for the control of spatially distributed processes utilizing mobile actuators and sensors. It is assumed that spatially collocated actuator/sensor pairs, affixed on vehicles, are capable of moving within the spatial domain and a combined control law-plus-guidance law is proposed in order to better address the effects of spatiotemporally varying disturbances. The proposed control architecture is simplified by using static output feedback combined with adaptation of the feedback gains. A Lyapunov redesign approach is employed to derive the guidance laws via the appropriate use of the vehicle control torques. Such guidance laws are gradient-based and tend to move the vehicle to spatial locations with large spatial gradients. The novelty here is that vehicle dynamics are directly coupled to the process dynamics and their motion is solely and explicitly dictated by the control performance of the spatially distributed process. Extensive numerical studies of a 2-D diffusion PDE with a mobile robot are included and which demonstrate the effectiveness of the proposed combined control law-plus-guidance law. [ABSTRACT FROM AUTHOR]

Investigates a feedback control computational methodology for reducing acoustic sound pressure levels in a two-dimensional cavity with a flexible boundary. Information on the mathematical model used; Finite-dimensional approximation.