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

On the Benefits of Surrogate Lagrangians in Optimal Control and Planning Algorithms

This paper explores the relationship between numerical integrators and optimal control algorithms. Specifically, the performance of the differential dynamical programming (DDP) algorithm is examined when a variational integrator and a newly proposed surrogate variational integrator are used to propagate and linearize system dynamics. Surrogate variational integrators, derived from backward error analysis, achieve higher levels of accuracy while maintaining the same integration complexity as nominal variational integrators. The increase in the integration accuracy is shown to have a large effect on the performance of the DDP algorithm. In particular, significantly more optimized inputs are computed when the surrogate variational integrator is utilized

Filter And Observer Design For Polynomial Discrete-Time Systems: A Sum Of Squares Based Approach

The polynomial discrete-time systems are the type of systems where the dynamics of the systems are described in polynomial forms.This system is classified as an important class of nonlinear systems due to the fact that many nonlinear systems can be modelled as,transformed into,or approximated by polynomial systems.The focus of this thesis is to address the problem of filter and observer design for polynomial discrete-time systems.The main reason for focusing on this area is because the filter and observer design for such polynomial discrete-time systems is categorised as a difficult problem.This is due to the fact that the relation between the Lyapunov matrix and the filter and observer gain is not jointly convex when the parameter-dependent or state-dependent Lyapunov function is under consideration.Therefore the problem cannot possibly be solved via semidefinite programming (SDP).In light of the aforementioned problem, we establish novel methodologies of designing filters for estimating the state of the systems both with and without H∞ performance and also designing an observer for state estimation and also as a controller.We show that through our proposed methodologies,a less conservative design procedure can be rendered for the filter and observer design.In particular,a so-called integrator method is proposed in this research work where an integrator is incorporated into the filter and observer structures.In doing so, the original systems can be transformed into augmented systems.Furthermore,the state-dependent function is selected in a way that its matrix is dependent only upon the original system state.Through this selection,a convex solution to the filter and observer design can be obtained efficiently.The existence of such filter and observer are given in terms of the solvability of polynomial matrix inequalities (PMIs).The problem is then formulated as sum of squares (SOS) constraints,therefore it can be solved by any SOS solvers.In this research work,SOSTOOLS is used as a SOS solver.Finally,to demonstrate the effectiveness and advantages of the proposed design methodologies in this thesis,numerical examples are given in filter design system.The simulation results show that the proposed design methodologies can estimate and stabilise the systems and achieve the prescribed performance requirements

Cooperation of unmanned systems for agricultural applications: A theoretical framework

Agriculture 4.0 comprises a set of technologies that combines sensors, information systems, enhanced machinery, and informed management with the objective of optimising production by accounting for variabilities and uncertainties within agricultural systems. Autonomous ground and aerial vehicles can lead to favourable improvements in management by performing in-field tasks in a time-effective way. In particular, greater benefits can be achieved by allowing cooperation and collaborative action among unmanned vehicles, both aerial and ground, to perform in-field operations in precise and time-effective ways. In this work, the preliminary and crucial step of analysing and understanding the technical and methodological challenges concerning the main problems involved is performed. An overview of the agricultural scenarios that can benefit from using collaborative machines and the corresponding cooperative schemes typically adopted in this framework are presented. A collection of kinematic and dynamic models for different categories of autonomous aerial and ground vehicles is provided, which represents a crucial step in understanding the vehicles behaviour when full autonomy is desired. Last, a collection of the state-of-the-art technologies for the autonomous guidance of drones is provided, summarising their peculiar characteristics, and highlighting their advantages and shortcomings with a specific focus on the Agriculture 4.0 framework. A companion paper reports the application of some of these techniques in a complete case study in sloped vineyards, applying the proposed multi-phase collaborative scheme introduced here

Semi-blind robust indentification and robust control approach to personalized anemia management.

The homeostatic blood hemoglobin (Hb) content of a healthy individual varies between the range of 14-18 g/dL for a male and 12-16 g/dL for a female. This quantity provides an estimate of red blood cell (RBC) count in circulation at any given moment. RBC is a protein carrying substance that transports oxygen from the lungs to other tissues in the body and is synthesized by the kidney through a process known as erythropoiesis where erythropoietin is secreted in response to hypoxia. In this regard, the kidneys act not only as a controller but also as a sensor in regulating RBC levels. Patients with chronic kidney diseases (CKD) have dysfunctional kidneys that compromise these fundamental kidney functions. Consequently, anemia is developed. Anemics of CKD have low levels of Hb that must be controlled and properly regulated to the appropriate therapeutic range. Until the discovery of recombinant human erythropoietin (EPO) over three decades ago, treatment procedure of anemia conditions primarily involved repeated blood transfusions–a process known to be associated with several other health related complications. This discovery resulted in a paradigm shift in anemia management from blood transfusions to dosage therapies. The main objective of anemia management with EPO is to increase patients’ hemoglobin level from low to a suitable therapeutic range as defined by the National Kidney Foundation-Kidney Disease Outcomes Quality Initiative (NKF-KDOI) to be in the range of 10 - 12 g/dL while avoiding response values beyond 14 g/dL to prevent other complications associated with EPO medication. It is therefore imperative that clinicians balance dosage efficacy and toxicity in anemia management therapies. At most treatment facilities, protocols are developed to conform to NKF-KDOI recommendations. These protocols are generally based on EPO packet inserts and the expected Hb responses from the average patient. The inevitable variability within the patient group makes this “one-size-fits-all” dosing scheme non-optimal, at best, and potentially dangerous for certain group of patients that do not adhere to the notion of expected “average” response. A dosing strategy that is tailored to the individual patients’ response to EPO medication could provide a better alternative to the current treatment methods. An objective of this work is to develop EPO dosing strategies tailored to the individual patients using robust identification techniques and modern feedback control methods. First, a unique model is developed based on Hb responses and dosage EPO of the individual patients using semi-blind robust identification techniques. This provides a nominal model and a quantitative information on model uncertainty that accounts for other possible patient’s dynamics not considered in the modeling process. This is in the framework of generalized interpolation theory. Then, from the derived nominal model and the associated uncertainty information, robust controller is designed via the =H1-synthesis methods to provide a new dosing strategies for the individual patients. The H1 control theory has a feature of minimizing the influence of some unknown worst case gain disturbance on a system. Finally, a framework is provided to strategize dosing protocols for newly admitted patients

Load Disturbance Torque Estimation for Motor Drive Systems with Application to Electric Power Steering System

Motors are widely used in industries due to its ability to provide high mechanical power in speed and torque applications. Its flexibility to control and quick response are other reasons for its widespread use. Disturbance torque acting on the motor shaft is a major factor which affects the motor performance. Considering the load disturbance torque while designing the control for the motor makes the system more robust to load changes. Most disturbance observers are designed for steady state load conditions. The observer designed here considers a general case making no assumptions about the load torque dynamics. The observer design methods to be used under different disturbance conditions are also discussed and the performances compared. The designed observer is tested in a Hardware-in-Loop (HIL) setup for different load conditions. A motor load torque estimation based Fault Tolerant Control (FTC) is then designed for an Electric Power Steering (EPS) system

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

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