Output Feedback Stochastic MPC with Hard Input Constraints

We present an output feedback stochastic model predictive controller (SMPC) for constrained linear time-invariant systems. The system is perturbed by additive Gaussian disturbances on state and additive Gaussian measurement noise on output. A Kalman filter is used for state estimation and an SMPC is designed to satisfy chance constraints on states and hard constraints on actuator inputs. The proposed SMPC constructs bounded sets for the state evolution and a tube-based constraint tightening strategy where the tightened constraints are time-invariant. We prove that the proposed SMPC can guarantee an infeasibility rate below a user-specified tolerance. We numerically compare our method with a classical output feedback SMPC with simulation results which highlight the efficacy of the proposed algorithm.Comment: IEEE American Control Conference (ACC) 2023, May 31 - June 2, San Diego, CA, US

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

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

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

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

Robust Nonlinear Model Predictive Control using Polynomial Chaos Expansions

The performance of model predictive controllers (MPCs) is largely dependent on the accuracy of the model predictions as compared to the actual plant outputs. Irrespective of the model used, first-principles (FP) or empirical, plant-model mismatch is unavoidable. Consequently, model based controllers must be robust to mismatch between the model predictions and the actual process behavior. Controllers that are not robust may result in poor closed loop response and even instability. Model uncertainty can generally be formulated into two broader forms, parametric uncertainty and unstructured uncertainty. Most of the current robust nonlinear MPC have been based on FP-model where only robustness to bounded disturbances rather than parametric uncertainty has been addressed. Systematically accounting for parametric uncertainty in the robust design has been difficult in FP-models due to varying forms in which uncertain parameters occur in the models. To address parametric uncertainty robustness tests based on Structured Singular Value (SSV) and Linear Matrix Inequalities (LMI) have been proposed previously, however these algorithms tend to be conservative because they consider worst-case scenarios and they are also computationally expensive. For instance the SSV calculation is NP-hard and as a result it is not suitable for fast computations. This provides motivation to work on robust control algorithms addressing both parametric and unstructured uncertainty with fast computation times. To facilitate the design of robust controllers which can be computed fast, empirical models are used in which parametric uncertainty is propagated using Polynomial Chaos Expansion (PCE) of parameters. PCE assists in speeding up the computations by providing an analytical expression for the L^2-norm of model predictions while also eliminating the need to design for the worst-case scenario which results in conservatism. Another way of speeding up computations in MPC algorithms is by grouping subsets of available the inputs and outputs into subsystems and by controlling each of the subsystems by MPC controllers of lower dimensions. This latter approach, referred in the literature as Distributed MPC, has been tackled by different strategies involving different degrees of coordination between subsystems but it has not been studied in terms of robustness to model error. Based on the above considerations the current work investigates different robustness aspects of predictive control algorithms for nonlinear processes with special emphasis on the following three situations, i) a nonlinear predictive control based on a Volterra series model where the uncertain parameters are formulated as PCE’s, ii) The application of a PCE-based approach to control and optimization of bioreactors where the model is based on dynamic flux metabolic models, and iii) A Robust Distributed MPC with a robust estimator that is needed to account for the interactions between sub-systems in distributed control

Optimal Control of Multiple Quadrotors for Transporting a Cable Suspended Payload

In this thesis, the main aim is to improve the flight control performance for a cable suspended payload with single and two quadrotors based on optimised control techniques. The study utilised optimal controllers, such as the Linear Quadratic Regulator LQR, the Iterative based LQR (ILQR), the Model Predictive Control MPC and the dynamic game controller to solve tracking control problems in terms of stabilisation, accuracy, constraints and collision avoidance. The LQR control was applied to the system as the first control method and compared with the classical Proportional-Derivative controller PD. It was used to achieve the load path tracking performance for single and two quadrotors with a cable slung load. The second controller was ILQR, which was developed based on the LQR control method to deal with the model nonlinearity. The MPC technique was also applied to the linearised nonlinear model LMPC of two quadrotors with a payload suspended by cables and compared with a nonlinear MPC (NMPC). Both MPC controllers LMPC and NMPC considered the constraints imposed on the system states and control inputs. The dynamic game control method was developed based on an incentive strategy for a leader-follower framework with the consideration of different optimal cost functions. It was applied to the linearised nonlinear model. Selecting these control techniques led to a number of achievements. Firstly, they improved the system performance in terms of achieving the system stability and reducing the steady-state errors. Secondly, the system parameter uncertainties were taken into consideration by utilising the ILQR controller. Thirdly, the MPC controllers guaranteed the handling of constraints and external disturbances in linear and nonlinear systems. Finally, avoiding collision between the leader and follower robots was achieved by applying the dynamic game controller. The controllers were tested in MATLAB simulation and verified for various desired predefined trajectories. In real experiments, these controllers were used as high-level controllers, which produce the optimised trajectory points. Then a low-level controller (PD controller) was used to follow the optimised trajectory points