Papers by Constantino Lagoa
IEEE Transactions on Intelligent Transportation Systems, 2015
ABSTRACT This paper describes a dynamical model-based method for the localization of road vehicle... more ABSTRACT This paper describes a dynamical model-based method for the localization of road vehicles using terrain data from the vehicle's onboard sensors. Road data are encoded using linear dynamical models and then, during travel, the location is identified through continuous comparison of a bank of linear models. The approach presented has several advantages over previous methods described in the literature. First, it creates computationally efficient linear model map representations of the road data. Second, the use of linear models eliminates the need for metrics during the localization process. Third, the localization algorithm is a computationally efficient approach that can have a bounded localization distance in the absence of noise, given certain uniqueness assumptions on the data. Fourth, encoding road data using linear models has the potential to compress the data, while retaining the sensory information. Finally, performing only linear operations on observed noisy data simplifies the creation of noise mitigation algorithms.
52nd IEEE Conference on Decision and Control, 2013
In this paper, we address the problem of designing probabilistic robust controllers for discrete-... more In this paper, we address the problem of designing probabilistic robust controllers for discrete-time systems whose objective is to reach and remain in a given target set with high probability. More precisely, given probability distributions for the initial state, uncertain parameters and disturbances, we develop algorithms for designing a control law that i) maximizes the probability of reaching the target set in N steps and ii) makes the target set robustly positively invariant. As defined the problem is nonconvex. To solve this problem, a sequence of convex relaxations is provided, whose optimal value is shown to converge to solution of the original problem. In other words, we provide a sequence of semidefinite programs of increasing dimension and complexity which can arbitrarily approximate the solution of the probabilistic robust control design problem addressed in this paper. Two numerical examples are presented to illustrate preliminary results on the numerical performance of the proposed approach.
ASME 2011 Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control, Volume 2, 2011
ABSTRACT
2012 IEEE Signal Processing in Medicine and Biology Symposium (SPMB), 2012
ABSTRACT Linear measures such as cross-correlation, coherence, and directed transfer functions ha... more ABSTRACT Linear measures such as cross-correlation, coherence, and directed transfer functions have previously been applied to investigate the functional connectivity between brain regions. However, such methods do not account for nonlinear interactions between the signals. Separately, dopaminergic cell transplants have been shown to provide symptomatic amelioration and partial electrophysiological normalization of aberrant basal ganglia firing patterns in Parkinson's Disease. However, the precise extent and mechanisms of basal ganglia electrophysiological normalization have remained unclear. In this experiment we computed the transfer entropy between electroencephalograms (EEGs) and basal ganglia local field potentials (LFPs) from urethane-anesthetized rats, in order to investigate both linear and nonlinear interactions. We used the 6-hydroxy-dopamine lesioned medial forebrain bundle hemiparkinsonian (HP) rat model, and recorded from the substantia nigra and subthalamic nucleus of normal rats, HP rats, and HP rats with murine fetal ventral mesencephalic cell transplants, looking separately at slow wave EEG epochs versus global activation epochs. We found that both the crosscorrelation and the transfer entropy between the motor cortical EEG and basal ganglia LFPs was increased in the HP group (p
52nd IEEE Conference on Decision and Control, 2013
ABSTRACT Using terrain data and dynamical models is a promising approach to map-based passenger v... more ABSTRACT Using terrain data and dynamical models is a promising approach to map-based passenger vehicle localization. In this approach, dynamical models are extracted from terrain data collected by a vehicle with a known location. The dynamical models are stored as a “map” of the data onto other vehicles. These vehicles can then discern their own location by comparing the newly acquired terrain data against the pre-extracted models. This approach has been shown to be an effective method of localization. However, system noise remains a significant challenge, affecting both model extraction and localization. This paper introduces a novel approach to model extraction that maximizes the robustness of the extracted model map to inertial measurement unit noise. Three mechanisms are employed. First, the model map is represented as a tiered tree, with models describing successively finer data decimations in lower tree levels. Second, during the extraction process, the models and the transitions between models are chosen to accentuate the outlier end point that denotes the transition event. Finally, the extracted models are forced to have specific properties that address the noise added by the inertial measurement unit. An additional benefit of the presented algorithm is that it generates model maps independently given a fixed model order. This provides a convenient method of efficiently adding new information to the vehicle's map. The approach is tested using vehicle pitch data collected in State College, Pennsylvania USA.
2014 American Control Conference, 2014
ABSTRACT This paper presents a chance constrained approach to extracting linear models from refer... more ABSTRACT This paper presents a chance constrained approach to extracting linear models from reference data to be used in subsequence identification or pattern matching. Due to the ordered nature of time series data, the extracted models are sequential, with feasible domains separated by transition points. In a sequence of models, a transition point is defined as the point where one model is invalid and the next model is valid. This study contributes a probabilistic description for transition points. This probabilistic framework identifies the transition points and corresponding models such that in the presence of white Gaussian noise during subsequence detection, the transitions will still be discernible. When compared to previous work in subsequence identification, the approach in this paper has several advantages. First, it provides a rigorous selection criteria for each transition point. Second, the probabilistic method described herein effectively incorporates a priori knowledge about the expected noise characteristics. Lastly, employing this criteria in reference map creation leads to the extraction of compact model reference maps that further speed up computation online. The presented algorithm is tested using vehicle pitch data obtained from a vehicle's Inertial Measurement Unit during road data collection experiments. When compared to previously published model (in)validation work, the testing shows that the extracted reference map here is much more compact and correspondingly computationally efficient for subsequence identification.
In this paper, we present preliminary results on a general approach to chance constrained algebra... more In this paper, we present preliminary results on a general approach to chance constrained algebraic problems. In this type of problems, one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally complex. With the objective of developing systematic numerical procedures to solve such problems, a sequence of convex relaxations is provided, whose optimal value is shown to converge to solution of the original problem. In other words, we provide a sequence of semidefinite programs of increasing dimension and complexity which can arbitrarily approximate the solution of the probability maximization problem. Two numerical examples are presented to illustrate preliminary results on the numerical performance of the proposed approach.
Computational and Mathematical Methods in Medicine, 2012
Electrical signals between connected neural nuclei are difficult to model because of the complexi... more Electrical signals between connected neural nuclei are difficult to model because of the complexity and high number of paths within the brain. Simple parametric models are therefore often used. A multiscale version of the autoregressive with exogenous input (MS-ARX) model has recently been developed which allows selection of the optimal amount of filtering and decimation depending on the signal-to-noise ratio and degree of predictability. In this paper, we apply the MS-ARX model to cortical electroencephalograms and subthalamic local field potentials simultaneously recorded from anesthetized rodent brains. We demonstrate that the MS-ARX model produces better predictions than traditional ARX modeling. We also adapt the MS-ARX results to show differences in internuclei predictability between normal rats and rats with 6OHDA-induced parkinsonism, indicating that this method may have broad applicability to other neuroelectrophysiological studies.
This dissertation concentrates on a new line of research called probabilistic robustness. To this... more This dissertation concentrates on a new line of research called probabilistic robustness. To this end, a new paradigm is described and some recent results are first summarized. This sets the stage for the dissertation results to follow. Central to the new theory is the notion of a risk-adjusted robustness margin. One main objective of this work is to provide results which enlarge the class of problems and the classes of probability distributions for the uncertain parameters for which a risk-adjusted robustness margin can be computed. Some of the main results involve a new concept called unirectangularity. Whereas existing results in the literature require satisfaction of a certain convexity condition, the results presented here enable solution of many nonconvex problems which only satisfy a unirectangularity condition. In addition, some new results related to the so-called Truncation and Uniformity Principles are presented. That is, under certain conditions, we prove the existence of a risk-maximizing truncation and extend the domain of applicability of the Uniformity Principle to a class of non-symmetric convex sets representing the performance specifications for the uncertain parameters. Another contribution of this dissertation involves the description of new classes of probability distributions to address robustness problems not considered to date. Finally, we present some preliminary results aimed at controller design within the probabilistic robustness framework. ii Acknowledgements I would like to express my sincere appreciation to my dissertation advisor, Professor B. Ross Barmish, for his advice, encouragement and patience during these years we worked together. Not only did he guide me through the work which culminated with this dissertation but he also gave me invaluable advice concerning my academic career. for serving on my dissertation advisory committee and for their helpful suggestions. I would also like to thank Professor Peter Ney for serving on my preliminary committee. Last, but by no means least, I would like to thank Marta, my parents, my sister and my brother for all the continuous encouragement, incentive and support and to my friend Saeed Asgari whose encouragement was a constant. Preface The research presented in this dissertation is part of a new line of research called probabilistic robustness. My initial work introducing the basic paradigm, was carried out in collaboration with Professor Barmish and published in [3]. The work in [3] also includes our two initial results: the Truncation Principle and the Uniformity Principle. This dissertation also describes the results in [4] and [5] which were carried out
Proceedings of the IEEE Conference on Decision and Control
ABSTRACT
This paper provides a new mathematical framework for analysis of control systems which are operat... more This paper provides a new mathematical framework for analysis of control systems which are operated with admissible values of uncertain parameters which exceed the bounds speci ed by classical robustness theory. In such a case, it is important to quantify the tradeo s between risk of performance degradation and increased tolerance of uncertainty. If a large increase in the uncertainty bound can be established, an acceptably small risk may often be justi ed. Since robustness problem formulations do not include statistical descriptions of the uncertainty, the question arises whether it is possible to provide such assurances in a \distribution-free" manner. In other words,
Proceedings of the IEEE Conference on Decision and Control
ABSTRACT
Understanding the TCP congestion control mech- anism from a global optimization point of view is ... more Understanding the TCP congestion control mech- anism from a global optimization point of view is not only im- portant on its own right but also crucial to the design of other transport layer traffic control protocols with provable proper- ties. In this paper, we derive a global utility function and the corresponding optimal control law, known as TCP control law, which maximizes the global utility. The TCP control law cap- tures the essential behaviors of TCP, including slow start, con- gestion avoidance, multiplicative decrease phases, and the bi- nary nature of congestion feedbacks of TCP. We find that the utility function of TCP is linear in the slow start phase and pro- portional to the additive increase rate in the congestion avoid- ance phase. Our study shows that the TCP slow start phase with a dynamically changing slow start threshold plays a moderate role. However, we find that understanding the slow start phase with a fixed slow start threshold is critical to the design of ...
Understanding the TCP congestion control mech-anism from a global optimization point of view is n... more Understanding the TCP congestion control mech-anism from a global optimization point of view is not only im-portant in its own right, but also crucial to the design of other transport layer traffic control protocols with provable proper-ties. In this paper, we derive a global utility function and the corresponding optimal control law, known as TCP control law, which maximizes the global utility. The TCP control law cap-tures the essential behaviors of TCP, including slow start, con-gestion avoidance, and the binary nature of congestion feedback in TCP. We find that the utility function of TCP is linear in the slow start phase and approaches the well-known logarithm function as the data rate becomes large in the congestion avoid-ance phase. We also find that understanding the slow start phase with a fixed threshold is critical to the design of new transport layer control protocols to enable quality of service features. Fi-nally, we design an optimal, minimum-rate-guaranteed (MRG) tra...
We propose efficient techniques for generating independent identically distributed uniform random... more We propose efficient techniques for generating independent identically distributed uniform random samples inside semialgebraic sets. The proposed algorithm leverages recent results on the approximation of indicator functions by polynomials %\cite{DabHen:13} to develop acceptance/rejection based sample generation algorithms with guaranteed performance in terms of rejection rate (the number of samples that should be generated in order to obtain an accepted sample). Moreover, the {acceptance} rate is shown to be is asymptotically optimal, in the sense that it tends to one (all samples accepted) as the degree of the polynomial approximation increases. The performance of the proposed method is illustrated by a numerical example.
Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 2009
ABSTRACT
Proceedings of the 2011 American Control Conference, 2011
ABSTRACT
Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1999
... Constantino M. Lagoa EE Department, The Pennsylvania State University lagoa@engr ... in [6], ... more ... Constantino M. Lagoa EE Department, The Pennsylvania State University lagoa@engr ... in [6], the existence of a transfer matrix M E RH”,X1 and a complex-valued function a(.) satisfying the condition above for all w E R U {co} is equivalent to the existence of a trans-fer function a ...
Uploads
Papers by Constantino Lagoa