Nonlinear Control and Estimation with General Performance Criteria

This dissertation is concerned with nonlinear systems control and estimation with general performance criteria. The purpose of this work is to propose general design methods to provide systematic and effective design frameworks for nonlinear system control and estimation problems. First, novel State Dependent Linear Matrix Inequality control approach is proposed, which is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. By solving a state dependent linear matrix inequality at each time step, the sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this dissertation unify existing results on nonlinear quadratic regulator, Hinfinity and positive real control. Secondly, an H2-Hinfinity State Dependent Riccati Equation controller is proposed in this dissertation. By solving the generalized State Dependent Riccati Equation, the optimal control solution not only achieves the optimal quadratic regulation performance, but also has the capability of external disturbance reduction. Numerically efficient algorithms are developed to facilitate effective computation. Thirdly, a robust multi-criteria optimal fuzzy control of nonlinear systems is proposed. To improve the optimality and robustness, optimal fuzzy control is proposed for nonlinear systems with general performance criteria. The Takagi-Sugeno fuzzy model is used as an effective tool to control nonlinear systems through fuzzy rule models. General performance criteria have been used to design the controller and the relative weighting matrices of these criteria can be achieved by choosing different coefficient matrices. The optimal control can be achieved by solving the LMI at each time step. Lastly, since any type of controller and observer is subject to actuator failures and sensors failures respectively, novel robust and resilient controllers and estimators are also proposed for nonlinear stochastic systems to address these failure problems. The effectiveness of the proposed control and estimation techniques are demonstrated by simulations of nonlinear systems: the inverted pendulum on a cart and the Lorenz chaotic system, respectively

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 Of Robust Feedback Controllers For A Laser Beam Stabilizer

This work addresses this challenge by employing two different control strategies, namely, Proportional Integral Derivative (PID) and State Feedback with an observer for control

A Comprehensive Review of Digital Twin -- Part 1: Modeling and Twinning Enabling Technologies

As an emerging technology in the era of Industry 4.0, digital twin is gaining unprecedented attention because of its promise to further optimize process design, quality control, health monitoring, decision and policy making, and more, by comprehensively modeling the physical world as a group of interconnected digital models. In a two-part series of papers, we examine the fundamental role of different modeling techniques, twinning enabling technologies, and uncertainty quantification and optimization methods commonly used in digital twins. This first paper presents a thorough literature review of digital twin trends across many disciplines currently pursuing this area of research. Then, digital twin modeling and twinning enabling technologies are further analyzed by classifying them into two main categories: physical-to-virtual, and virtual-to-physical, based on the direction in which data flows. Finally, this paper provides perspectives on the trajectory of digital twin technology over the next decade, and introduces a few emerging areas of research which will likely be of great use in future digital twin research. In part two of this review, the role of uncertainty quantification and optimization are discussed, a battery digital twin is demonstrated, and more perspectives on the future of digital twin are shared

Robust state estimation for the control of flexible robotic manipulators

In this thesis, a novel robust estimation strategy for observing the system state variables of robotic manipulators with distributed flexibility is established. Motivation for the derived approach stems from the observation that lightweight, high speed, and large workspace robotic manipulators often suffer performance degradation because of inherent structural compliance. This flexibility often results in persistent residual vibration, which must be damped before useful work can resume. Inherent flexibility in robotic manipulators, then, increases cycle times and shortens the operational lives of the robots. Traditional compensation techniques, those which are commonly used for the control of rigid manipulators, can only approach a fraction of the open-loop system bandwidth without inducing significant excitation of the resonant dynamics. To improve the performance of these systems, the structural flexibility cannot simply be ignored, as it is when the links are significantly stiff and approximate rigid bodies. One thus needs a model to design a suitable compensator for the vibration, but any model developed to correct this problem will contain parametric error. And in the case of very lightly damped systems, like flexible robotic manipulators, this error can lead to instability of the control system for even small errors in system parameters. This work presents a systematic solution for the problem of robust state estimation for flexible manipulators in the presence of parametric modeling error. The solution includes: 1) a modeling strategy, 2) sensor selection and placement, and 3) a novel, multiple model estimator. Modeling of the FLASHMan flexible gantry manipulator is accomplished using a developed hybrid transfer matrix / assumed modes method (TMM/AMM) approach to determine an accurate low-order state space representation of the system dynamics. This model is utilized in a genetic algorithm optimization in determining the placement of MEMs accelerometers for robust estimation and observability of the system’s flexible state variables. The initial estimation method applied to the task of determining robust state estimates under conditions of parametric modeling error was of a sliding mode observer type. Evaluation of the method through analysis, simulations and experiments showed that the state estimates produced were inadequate. This led to the development of a novel, multiple model adaptive estimator. This estimator utilizes a bank of similarly designed sub-estimators and a selection algorithm to choose the true value from a given set of possible system parameter values as well as the correct state vector estimate. Simulation and experimental results are presented which demonstrate the applicability and effectiveness of the derived method for the task of state variable estimation for flexible robotic manipulators.Ph.D

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

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

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