Approximate Gaussian Conjugacy: Parametric Recursive Filtering Under Nonlinearity, Multimodal, Uncertainty, and Constraint, and Beyond

This is a post-peer-review, pre-copyedit version of an article published in Frontiers of Information Technology & Electronic Engineering. The final authenticated version is available online at: https://doi.org/10.1631/FITEE.1700379Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Design and verification of Guidance, Navigation and Control systems for space applications

In the last decades, systems have strongly increased their complexity in terms of number of functions that can be performed and quantity of relationships between functions and hardware as well as interactions of elements and disciplines concurring to the definition of the system. The growing complexity remarks the importance of defining methods and tools that improve the design, verification and validation of the system process: effectiveness and costs reduction without loss of confidence in the final product are the objectives that have to be pursued. Within the System Engineering context, the modern Model and Simulation based approach seems to be a promising strategy to meet the goals, because it reduces the wasted resources with respect to the traditional methods, saving money and tedious works. Model Based System Engineering (MBSE) starts from the idea that it is possible at any moment to verify, through simulation sessions and according to the phase of the life cycle, the feasibility, the capabilities and the performances of the system. Simulation is used during the engineering process and can be classified from fully numerical (i.e. all the equipment and conditions are reproduced as virtual model) to fully integrated hardware simulation (where the system is represented by real hardware and software modules in their operational environment). Within this range of simulations, a few important stages can be defined: algorithm in the loop (AIL), software in the loop (SIL), controller in the loop (CIL), hardware in the loop (HIL), and hybrid configurations among those. The research activity, in which this thesis is inserted, aims at defining and validating an iterative methodology (based on Model and Simulation approach) in support of engineering teams and devoted to improve the effectiveness of the design and verification of a space system with particular interest in Guidance Navigation and Control (GNC) subsystem. The choice of focusing on GNC derives from the common interest and background of the groups involved in this research program (ASSET at Politecnico di Torino and AvioSpace, an EADS company). Moreover, GNC system is sufficiently complex (demanding both specialist knowledge and system engineer skills) and vital for whatever spacecraft and, last but not least the verification of its behavior is difficult on ground because strong limitations on dynamics and environment reproduction arise. Considering that the verification should be performed along the entire product life cycle, a tool and a facility, a simulator, independent from the complexity level of the test and the stage of the project, is needed. This thesis deals with the design of the simulator, called StarSim, which is the real heart of the proposed methodology. It has been entirely designed and developed from the requirements definition to the software implementation and hardware construction, up to the assembly, integration and verification of the first simulator release. In addition, the development of this technology met the modern standards on software development and project management. StarSim is a unique and self-contained platform: this feature allows to mitigate the risk of incompatibility, misunderstandings and loss of information that may arise using different software, simulation tools and facilities along the various phases. Modularity, flexibility, speed, connectivity, real time operation, fidelity with real world, ease of data management, effectiveness and congruence of the outputs with respect to the inputs are the sought-after features in the StarSim design. For every iteration of the methodology, StarSim guarantees the possibility to verify the behavior of the system under test thanks to the permanent availability of virtual models, that substitute all those elements not yet available and all the non-reproducible dynamics and environmental conditions. StarSim provides a furnished and user friendly database of models and interfaces that cover different levels of detail and fidelity, and supports the updating of the database allowing the user to create custom models (following few, simple rules). Progressively, pieces of the on board software and hardware can be introduced without stopping the process of design and verification, avoiding delays and loss of resources. StarSim has been used for the first time with the CubeSats belonging to the e-st@r program. It is an educational project carried out by students and researchers of the “CubeSat Team Polito” in which StarSim has been mainly used for the payload development, an Active Attitude Determination and Control System, but StarSim’s capabilities have also been updated to evaluate functionalities, operations and performances of the entire satellite. AIL, SIL, CIL, HIL simulations have been performed along all the phases of the project, successfully verifying a great number of functional and operational requirements. In particular, attitude determination algorithms, control laws, modes of operation have been selected and verified; software has been developed step by step and the bugs-free executable files have been loaded on the micro-controller. All the interfaces and protocols as well as data and commands handling have been verified. Actuators, logic and electrical circuits have been designed, built and tested and sensors calibration has been performed. Problems such as real time and synchronization have been solved and a complete hardware in the loop simulation test campaign both for A-ADCS standalone and for the entire satellite has been performed, verifying the satisfaction of a great number of CubeSat functional and operational requirements. The case study represents the first validation of the methodology with the first release of StarSim. It has been proven that the methodology is effective in demonstrating that improving the design and verification activities is a key point to increase the confidence level in the success of a space mission

On-line estimation approaches to fault-tolerant control of uncertain systems

This thesis is concerned with fault estimation in Fault-Tolerant Control (FTC) and as such involves the joint problem of on-line estimation within an adaptive control system. The faults that are considered are significant uncertainties affecting the control variables of the process and their estimates are used in an adaptive control compensation mechanism. The approach taken involves the active FTC, as the faults can be considered as uncertainties affecting the control system. The engineering (application domain) challenges that are addressed are: (1) On-line model-based fault estimation and compensation as an FTC problem, for systems with large but bounded fault magnitudes and for which the faults can be considered as a special form of dynamic uncertainty. (2) Fault-tolerance in the distributed control of uncertain inter-connected systems The thesis also describes how challenge (1) can be used in the distributed control problem of challenge (2). The basic principle adopted throughout the work is that the controller has two components, one involving the nominal control action and the second acting as an adaptive compensation for significant uncertainties and fault effects. The fault effects are a form of uncertainty which is considered too large for the application of passive FTC methods. The thesis considers several approaches to robust control and estimation: augmented state observer (ASO); sliding mode control (SMC); sliding mode fault estimation via Sliding Mode Observer (SMO); linear parameter-varying (LPV) control; two-level distributed control with learning coordination

Design of Energy Management Strategies for a Battery-Ultracapacitor Electric Vehicle

The battery pack is the most expensive component in electric vehicles. Electric vehicles are prone to accelerated battery degradation due to the high charging/discharging cycles and high peak power demand. One solution to this issue would be increasing the battery capacity to meet the high energy requests. However, increasing the battery size is not reasonable due to the high cost and volume. An alternative solution is integrating other energy storage systems into the vehicle powertrain. The additional energy storage system highlights an energy management strategy to distribute the power among onboard energy storage systems effectively. Energy management systems incorporate different strategies classified based on their computational time, implementability in real-time, and measurable performance to be optimized. This thesis considers the case study of Chevy Spark model year 2015 with a hybrid energy storage system including battery and ultracapacitor. First, an overview of diffrent energy storage systems is presented, followed by a review of different hybrid energy storage' configurations. Second, energy management strategies are categorized into three main classifications: rule-based, optimization-based, and data-based algorithms. Third, the selected vehicle model with an embedded rule-based energy management strategy is developed in MATLAB Simulink, and battery performance is validated against available real-world data. Optimal power distribution among battery and ultracapacitor is achieved through an offline global optimal algorithm in chapter 5 in a way to improve battery life. Finally, optimal results are used as a training dataset for an online data-based energy management strategy. Results prove the strategy's effectiveness by improving battery life by an average of 16% compared to the rule-based and 12% difference from the globally optimal strategy on various driving conditions. The proposed energy management strategy provides near-optimal performance while it is real-time implementable and does not need to have beforehand knowledge of driving cycles

A Foot Placement Strategy for Robust Bipedal Gait Control

This thesis introduces a new measure of balance for bipedal robotics called the foot placement estimator (FPE). To develop this measure, stability first is defined for a simple biped. A proof of the stability of a simple biped in a controls sense is shown to exist using classical methods for nonlinear systems. With the addition of a contact model, an analytical solution is provided to define the bounds of the region of stability. This provides the basis for the FPE which estimates where the biped must step in order to be stable. By using the FPE in combination with a state machine, complete gait cycles are created without any precalculated trajectories. This includes gait initiation and termination. The bipedal model is then advanced to include more realistic mechanical and environmental models and the FPE approach is verified in a dynamic simulation. From these results, a 5-link, point-foot robot is designed and constructed to provide the final validation that the FPE can be used to provide closed-loop gait control. In addition, this approach is shown to demonstrate significant robustness to external disturbances. Finally, the FPE is shown in experimental results to be an unprecedented estimate of where humans place their feet for walking and jumping, and for stepping in response to an external disturbance

Summary of Research 1994

The views expressed in this report are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government.This report contains 359 summaries of research projects which were carried out under funding of the Naval Postgraduate School Research Program. A list of recent publications is also included which consists of conference presentations and publications, books, contributions to books, published journal papers, and technical reports. The research was conducted in the areas of Aeronautics and Astronautics, Computer Science, Electrical and Computer Engineering, Mathematics, Mechanical Engineering, Meteorology, National Security Affairs, Oceanography, Operations Research, Physics, and Systems Management. This also includes research by the Command, Control and Communications (C3) Academic Group, Electronic Warfare Academic Group, Space Systems Academic Group, and the Undersea Warfare Academic Group

Participation d'un système de stockage à la stabilité des réseaux insulaires

Frequency of isolated microgrids is highly sensitive to active power variation of loads and productions because of the inertia equivalent of this grid is small (limited number of thermal generators). Furthermore, the increasing of renewable energy in this grid causes frequency more risky to be instable because of its intermittency of power. In this thesis, energy storage is the selected solution to maintain the frequency stability of isolated microgrids with high penetration rate of renewable energy. It will participate to the primary frequency control which is the first control that takes action to limit the frequency deviation after disturbance. Therefore, the objective of this thesis is to design the appropriate size and strategy of energy storage in isolated microgrids with high penetration rate of photovoltaic. Proposed strategies will link to power variation of PV. Therefore, the different situations of photovoltaic power variations and their impacts on the system frequency had been firstly characterized and studied in order to specify the critical situation of frequency variation. Then, different strategies for energy storage and their sizes were defined from these two studies. The strategy limit dPpv diagram and filter strategy were proposed to define the participated power of energy storage in primary frequency control from the measured power variation of PV. Furthermore, controller H infinity which is robust control was also proposed. Finally, energy storage control system was validated by RTLAB (real time simulation) which enable us to simulate the hardware. The results show that energy storage by proposed strategies is able to stabilize frequency of the power system by limiting the frequency deviation to be within an acceptable range after occurrence of any disturbance. The proposed strategies can increase larger participated power of the energy storage with less frequently than the classic droop control.Un réseau insulaire est un système fragile et sensible aux variations de charge ou de production notamment d'origine renouvelable et intermittent. Ce problème devient crucial avec l'augmentation dans ces réseaux de production éolien ou PV en remplacement des sources actuelles (diesel, etc.). Cela impacte directement la stabilité du réseau, notamment la fréquence. Les moyens de stockage pourraient dès lors participer au réglage primaire de la fréquence, en limitant des variations après une perturbation. L'objectif de cette thèse consiste ainsi à étudier la participation du stockage pour maintenir la stabilité en fréquence dans un réseau insulaire en augmentant le taux de pénétration d'énergie renouvelable. Un algorithme de dimensionnement et différentes stratégies de contrôle du système de stockage ont ainsi été développés en fonction de variations réellement observées sur un parc PV. Notre étude est séparée en 2 parties. La première partie concerne la modélisation de l'intermittence de la production PV. La puissance PV a ainsi été caractérisée en fonction de son impact sur la variation de la fréquence, afin de définir toute situation critique. Ensuite, la technologie et les critères de dimensionnement du dispositif de stockage et la stratégie de pilotage et de contrôle-commande pour surveiller et contrôler le système de stockage ont été proposés et validées à partir de simulations. Ces stratégies ont été élaborées soit à partir de critères qualitatifs définie dans le domaine temporel, soit à partir d'une stratégie de filtrage fréquentiel des différentes sources. Par ailleurs, pour garantir des critères de robustesse vis-à-vis des incertitudes paramétriques notamment sur la mesure des variations PV, une commande robuste (utilisant un contrôleur H infinie) a été conçu et validé. Les différentes stratégies proposées peuvent plus ou moins réduire la variation de la fréquence suite à perturbation et permettre de réduire significativement la participation de la source principale d'énergie au réglage de la fréquence. Par ailleurs, les résultats ont permis de faire un lien entre le taux de pénétration des énergies renouvelables photovoltaïques dans un micro réseau et la tenue en fréquence dans ce réseau