Variable Horizon Model Predictive Control (VH-MPC) is a form of predictive control that includes the horizon length as a decision variable in the constrained optimisation problem solved at each iteration. It has been recently applied to completion problems, where the system state is to be steered to a closed set in finite time. The behaviour of the system once completion has occurred is not considered part of the control problem. This thesis is concerned with three aspects of robustness and optimality in VH-MPC completion problems. In particular, the thesis investigates robustness to well defined but unpredictable changes in system and controller parameters, robustness to bounded disturbances in the presence of certain input parameterisations to reduce computational complexity, and optimal robustness to bounded disturbances using tightened constraints. In the context of linear time invariant systems, new theoretical contributions and algorithms are developed. Firstly, changing dynamics, constraints and control objectives are addressed by introducing the notion of feasible contingencies. A novel algorithm is proposed that introduces extra prediction variables to ensure that anticipated new control objectives are always feasible, under changed system parameters. In addition, a modified constraint tightening formulation is introduced to provide robust completion in the presence of bounded disturbances. Different contingency scenarios are presented and numerical simulations demonstrate the formulation’s efficacy. Next, complexity reduction is considered, using a form of input parameterisation known as move blocking. After introducing a new notation for move blocking, algorithms are presented for designing a move-blocked VH-MPC controller. Constraints are tightened in a novel way for robustness, whilst ensuring that guarantees of recursive feasibility and finite-time completion are preserved. Simulations are used to illustrate the effect of an example blocking scheme on computation time, closed-loop cost, control inputs and state trajectories. Attention is now turned towards mitigating the effect of constraint tightening policies on a VH-MPC controller’s region of attraction. An optimisation problem is formulated to maximise the volume of an inner approximation to the region of attraction, parameterised in terms of the tightening policy. Alternative heuristic approaches are also proposed to deal with high state dimensions. Numerical examples show that the new technique produces substantially improved regions of attraction in comparison to other proposed approaches, and greatly reduces the maximum required prediction horizon length for a given application. Finally, a case study is presented to illustrate the application of the new theory developed in this thesis to a non-trivial example system. A simplified nonlinear surface excavation machine and material model is developed for this purpose. The model is stabilised with an inner-loop controller, following which a VH-MPC controller for autonomous trajectory generation is designed using a discretised, linearised model of the stabilised system. Realistic simulated trajectories are obtained from applying the controller to the stabilised system and incorporating the ideas developed in this thesis. These ideas improve the applicability and computational tractability of VH-MPC, for both traditional applications as well as those that go beyond the realm of vehicle manœuvring.

With numerous distinct advantages, quadrotors have found a wide range of applications, such as structural inspection, traffic control, search and rescue, agricultural surveillance, etc. To better serve applications in cluttered environment, quadrotors are further equipped with vision sensors to enhance their state sensing and environment perception capabilities. Moreover, visual information can also be used to guide the motion control of the quadrotor. This is referred to as visual servoing of quadrotor. In this thesis, we identify the challenging problems arising in the area of visual servoing of the quadrotor and propose effective control strategies to address these issues. The control objective considered in this thesis is to regulate the relative pose of the quadrotor to a ground target using a limited number of sensors, e.g., a monocular camera and an inertia measurement unit. The camera is attached underneath the center of the quadrotor and facing down. The ground target is a planar object consisting of multiple points. The image features are selected as image moments defined in a ``virtual image plane". These image features offer an image kinematics that is independent of the tilt motion of the quadrotor. This independence enables the separation of the high level visual servoing controller design from the low level attitude tracking control. A high-gain observer-based model predictive control (MPC) scheme is proposed in this thesis to address the image-based visual servoing of the quadrotor. The high-gain observer is designed to estimate the linear velocity of the quadrotor which is part of the system states. Due to a limited number of sensors on board, the linear velocity information is not directly measurable. The high-gain observer provides the estimates of the linear velocity and delivers them to the model predictive controller. On the other hand, the model predictive controller generates the desired thrust force and yaw rate to regulate the pose of the quadrotor relative to the ground target. By using the MPC controller, the tilt motion of the quadrotor can be effectively bounded so that the scene of the ground target is well maintained in the field of view of the camera. This requirement is referred to as visibility constraint. The satisfaction of visibility constraint is a prerequisite of visual servoing of the quadrotor. Simulation and experimental studies are performed to verify the effectiveness of the proposed control strategies. Moreover, image processing algorithms are developed to extract the image features from the captured images, as required by the experimental implementation. / Graduate / 2020-12-11

Stochastic model predictive control (MPC) is a fascinating field for research and of increasing practical importance since optimal control techniques have been intensively investigated in modern control system design. With the development of computer technologies and communication networks, networked control systems (NCSs) or cyber-physical systems (CPSs) have become an interest of research due to the comprehensive integration of physical systems, such as sensors, actuators and plants, with intricate cyber components, possessing information communication and computation. In CPSs, advantages of low installation cost, high reliability, flexible modularity, improved efficiency, and greater autonomy can be obtained by the tight coordination of physical and cyber components. Several sectors, including robotics, transportation, health care, smart buildings, and smart grid, have witnessed the successful application of CPSs design. The integration of extensive cyber capability and physical plants with ubiquitous uncertainties also introduces concerns over communication efficiency, robustness and stability of the CPSs. Thus, to achieve satisfactory performance metrics of efficiency, robustness and stability, a detailed investigation into control synthesis of CPSs under the stochastic model predictive control framework is of importance. The stochastic model predictive control synthesis plays a vital role in CPSs design since the multivariable stochastic system subject to probabilistic constraints can be controlled in an optimized way. On the other hand, aperiodically sampled, or event-based, model predictive control has also been applied to CPSs extensively to improve communication efficiency. In this thesis, the control synthesis and analysis of aperiodically sampled stochastic model predictive control for CPSs is considered. Chapter 1 provides an introductory literature review of the current development of stochastic MPC, distributed stochastic MPC and event-based MPC. Chapter 2 presents a stochastic self-triggered model predictive control scheme for linear systems with additive uncertainty and with the states and inputs being subject to chance constraints. In the proposed control scheme, the succeeding sampling time instant and current control inputs are computed online by solving a formulated optimization problem. Chapter 3 discusses a stochastic self-triggered model predictive control algorithm with an adaptive prediction horizon. The communication cost is explicitly considered by adding a damping factor in the cost function. Sufficient conditions are provided to guarantee closed-loop chance constraints satisfactions. Furthermore, the recursive feasibility of the algorithm is analyzed, and the closed-loop system is shown to be stable. Chapter 4 proposes a distributed self-triggered stochastic MPC control scheme for CPSs under coupled chance constraints and additive disturbances. Based on the assumptions on stochastic disturbances, both local and coupled probabilistic constraints are transformed into the deterministic form using the tube-based method, and improved terminal constraints are constructed to guarantee the recursive feasibility of the control scheme. Theoretical analysis has shown that the overall closed-loop CPSs are quadratically stable. Numerical examples illustrate the efficacy of the proposed control method in terms of data transmission reductions. Chapter 5 concludes the thesis and suggests some promising directions for future research. / Graduate / 2022-01-15

Cyber-physical systems (CPS), integrating advanced computation, communication, and control technologies with the physical process, are widely applied in industry applications such as smart production and manufacturing systems, robotic and automotive control systems, and smart grids. Due to possible exposure to unreliable networks and complex physical environments, CPSs may simultaneously face multiple cyber and physical issues including cyber threats (e.g., malicious cyber attacks) and resource constraints (e.g., limited networking resources and physical constraints). As one of the essential topics in designing efficient CPSs, the controller design for CPSs, aiming to achieve secure and resource-aware control objectives under such cyber and physical issues, is very significant yet challenging. Emphasizing optimality and system constraint handling, model predictive control (MPC) is one of the most widely used control paradigms, notably famous for its successful applications in chemical process industry. However, the conventional MPC methods are not specifically tailored to tackle cyber threats and resource constraints, thus the corresponding theory and tools to design the secure and resource-aware controller are lacking and need to be developed. This dissertation focuses on developing MPC-based methodologies to address the i) secure control problem and ii) resource-aware control problem for CPSs subject to cyber threats and resource constraints. In the resource-aware control problem of CPSs, the nonlinear system with additive disturbance is considered. By using an integral-type event-triggered mechanism and an improved robustness constraint, we propose an integral-type event-triggered MPC so that smaller sampling frequency and robustness to the additive disturbance can be obtained. The sufficient conditions for guaranteeing the recursive feasibility and the closed-loop stability are established. For the secure control problem of CPSs, two aspects are considered. Firstly, to achieve the secure control objective, we design a secure dual-mode MPC framework, including a modified initial feasible set and a new positively invariant set, for constrained linear systems subject to Denial-of-Service (DoS) attacks. The exponential stability of the closed-loop system is guaranteed under several conditions. Secondly, to deal with cyber threats and take advantage of the cloud-edge computing technology, we propose a model predictive control as a secure service (MPCaaSS) framework, consisting of a double-layer controller architecture and a secure data transmission protocol, for constrained linear systems in the presence of both cyber threats and external disturbances. The rigorous recursive feasibility and robust stability conditions are established. To simultaneously address the secure and resource-aware control problems, an event-triggered robust nonlinear MPC framework is proposed, where a new robustness constraint is introduced to deal with additive disturbances, and a packet transmission strategy is designed to tackle DoS attacks. Then, an event-triggered mechanism, which accommodates DoS attacks occurring in the communication network, is proposed to reduce the communication cost for resource-constrained CPSs. The recursive feasibility and the closed-loop stability in the sense of input-to-state practical stable (ISpS) are guaranteed under the established sufficient conditions. / Graduate

This thesis investigates autonomous landing of a micro air vehicle (MAV) on a nonstationary ground platform. Unmanned aerial vehicles (UAVs) and micro air vehicles (MAVs) are becoming every day more ubiquitous. Nonetheless, many applications still require specialized human pilots or supervisors. Current research is focusing on augmenting the scope of tasks that these vehicles are able to accomplish autonomously. Precise autonomous landing on moving platforms is essential for self-deployment and recovery of MAVs, but it remains a challenging task for both autonomous and piloted vehicles. Model Predictive Control (MPC) is a widely used and effective scheme to control constrained systems. One of its variants, output-feedback tube-based MPC, ensures robust stability for systems with bounded disturbances under system state reconstruction. This thesis proposes a MAV control strategy based on this variant of MPC to perform rapid and precise autonomous landing on moving targets whose nominal (uncommitted) trajectory and velocity are slowly varying. The proposed approach is demonstrated on an experimental setup.

In the study of multi-agent systems (MASs), cooperative control is one of the most fundamental issues. As it covers a broad spectrum of applications in many industrial areas, there is a desire to design cooperative control protocols for different system and network setups. Motivated by this fact, in this thesis we focus on elaborating consensus protocol design, via model predictive control (MPC), under two different scenarios: (1) general constrained linear MASs with bounded additive disturbance; (2) linear MASs with input constraints underlying distributed communication networks. In Chapter 2, a tube-based robust MPC consensus protocol for constrained linear MASs is proposed. For undisturbed linear MASs without constraints, the results on designing a centralized linear consensus protocol are first developed by a suboptimal linear quadratic approach. In order to evaluate the control performance of the suboptimal consensus protocol, we use an infinite horizon linear quadratic objective function to penalize the disagreement among agents and the size of control inputs. Due to the non-convexity of the performance function, an optimal controller gain is difficult or even impossible to find, thus a suboptimal consensus protocol is derived. In the presence of disturbance, the original MASs may not maintain certain properties such as stability and cooperative performance. To this end, a tube-based robust MPC framework is introduced. When disturbance is involved, the original constraints in nominal prediction should be tightened so as to achieve robust constraint satisfaction, as the predicted states and the actual states are not necessarily the same. Moreover, the corresponding robust constraint sets can be determined offline, requiring no extra iterative online computation in implementation. In Chapter 3, a novel distributed MPC-based consensus protocol is proposed for general linear MASs with input constraints. For the linear MAS without constraints, a pre-stabilizing distributed linear consensus protocol is developed by an inverse optimal approach, such that the corresponding closed-loop system is asymptotically stable with respect to a consensus set. Implementing this pre-stabilizing controller in a distributed digital setting is however not possible, as it requires every local decision maker to continuously access the state of their neighbors simultaneously when updating the control input. To relax these requirements, the assumed neighboring state, instead of the actual state of neighbors, is used. In our distributed MPC scheme, each local controller minimizes a group of control variables to generate control input. Moreover, an additional state constraint is proposed to bound deviation between the actual and the assumed state. In this way, consistency is enforced between intended behaviors of an agent and what its neighbors believe it will behave. We later show that the closed-loop system converges to a neighboring set of the consensus set thanks to the bounded state deviation in prediction. In Chapter 4, conclusions are made and some research topics for future exploring are presented. / Graduate / 2021-03-31

The models used by model predictive controllers (MPCs) to predict future outcomes are usually unconstrained forms like impulse or step responses and discrete state space models. Certain MPC algorithms allow constraints to be imposed on the inputs or outputs of a system; but they may be infeasible as they are not checked for consistency via the process model. Consistent constraint handling methods - which account for their interdependence and disambiguate the language used to specify constraints – would therefore be an attractive aid when using any MPC package. A rigorous and systematic approach to constraint management has been developed, building on the work of Vinson (2000), Lima (2007) and Georgakis et al. (2003) in interpreting constraint interactions. The method supports linear steady-state system models, and provides routines to obtain the following information: <ul> <li> effects of constraint changes on the corresponding input and output constraints, </li><li> feasibility checks for constraints, </li><li> specification of constraint-set size and</li><li> optimal fitting of constraints within the desirable input and output space.</li></ul> Mathematical rigour and unambiguous language for identifying constraint types were key design criteria. The outputs of the program provide guidance when handling constraints, as opposed to rules of thumb and experience, and promote understanding of the system and its constraints. The metrics presented are not specific to any commercial MPC and can be implemented in the user interfaces of such MPCs. The method was applied to laboratory-scale test rigs to illustrate the information obtained. / Dissertation (MEng)--University of Pretoria, 2011. / Chemical Engineering / unrestricted

This thesis focuses on the development and extension of nonlinear evolutionary model predictive control (NEMPC), a control algorithm previously developed by Phil Hyatt of the BYU RaD Lab. While this controller and its variants are applicable to any high degree-of-freedom (DoF) robotic system, particular emphasis is given in this thesis to control of a soft robot continuum joint. First, speed improvements are presented for NEMPC. Second, a Python package is presented as a companion to NEMPC, as a method of establishing a common interface for dynamic simulators and approximating each system by a deep neural network (DNN). Third, a method of training a DNN approximation of a hardware system that is generalize-able to more complex hardware systems is presented. This method is shown to reduce median tracking error on a soft robot hardware platform by 88%. Finally, particle swarm model predictive control (PSOMPC), a variant of NEMPC, is presented and modified to model and account for uncertainty in a dynamic system. Control performance of NEMPC and PSOMPC are presented for a set of control trials on simulated systems with uncertainty in parameters, states, and inputs, as well as on a soft robot hardware platform. PSOMPC is shown to have an increased robustness to system uncertainty, reducing expected collisions by 71% for a three-link robot arm with parameter uncertainty, input disturbances, and state measurement error.

Traditional robots, while capable of being efficient and effective for the task they were designed, are dangerous when operating in unmodeled environments or around humans. The field of soft robotics attempts to increase the safety of robots thus enabling them to operate in environments where traditional robots should not operate. Because of this, soft robots were developed with different goals in mind than traditional robots and as such the traditional metrics used to evaluate standard robots are not effective for evaluating soft robots. New metrics need to be developed for soft robots so that effective comparison and evaluations can be made. This dissertation attempts to lay the groundwork for that process through a survey on soft robot metrics. Additionally we propose six soft robot actuator metrics that can be used to evaluate and compare characteristics and performance of soft robot actuators. Data from eight different soft robot rotational actuators (five distinct designs) were used to evaluate these soft robot actuator metrics and show their utility. New models, control methods and estimation methods also need to be developed for soft robots. Many of the traditional methods and assumptions for modeling and controlling robotic systems are not able to provide the fidelity that is needed for soft robots to effectively complete useful tasks. This dissertation presents specific developments in each of these areas of soft robot metrics, modeling, control and estimation. We show several incremental improvements to soft robot dynamic models as well as how they were used in control methods for more precise control. We also demonstrate a method for linearizing high degree of freedom models so it can be simplified for use in faster control methods for better performance. Lastly, we present an improved continuum joint configuration estimation method that uses a linear combination of length measurements. All these developments combine to help build the "fundamental engineering framework" that is needed for soft robotics as well as helping to move robots out of their confined spaces and bring them into new unmodeled/unstructured environments.

Optimal control theory has a long history and broad applications. Motivated by the goal of obtaining insights through unification and taking advantage of the abundant capability to generate data, this thesis introduces some suboptimal schemes via abstract dynamic programming models. As our first contribution, we consider deterministic infinite horizon optimal control problems with nonnegative stage costs. We draw inspiration from the learning model predictive control scheme designed for continuous dynamics and iterative tasks, and propose a rollout algorithm that relies on sampled data generated by some base policy. The proposed algorithm is based on value and policy iteration ideas. It applies to deterministic problems with arbitrary state and control spaces, and arbitrary dynamics. It admits extensions to problems with trajectory constraints, and a multiagent structure. In addition, abstract dynamic programming models are used to analyze $\lambda$-policy iteration with randomization algorithms. In particular, we consider contractive models with infinite policies. We show that well-posedness of the $\lambda$-operator plays a central role in the algorithm. The operator is known to be well-posed for problems with finite states, but our analysis shows that it is also well-defined for the contractive models with infinite states. Similarly, the algorithm we analyze is known to converge for problems with finite policies, but we identify the conditions required to guarantee convergence with probability one when the policy space is infinite regardless of the number of states. Guided by the analysis, we exemplify a data-driven approximated implementation of the algorithm for estimation of optimal costs of constrained linear and nonlinear control problems. Numerical results indicate the potentials of this method in practice. / Teorin om optimal reglering har en lång historia och breda tillämpningsområden.I denna avhandling, som motiveras av att få insikter genom att förena och dra nyttaav den goda möjligheten att generera data, introduceras några suboptimala systemvia abstrakta modeller för dynamisk programmering.I vårt första bidrag betraktar vi ett deterministiskt optimalt regleringsproblemmed oändlig horisont och icke-negativa stegkostnader. Vi hämtar inspiration frånmodellprediktiv reglering med inlärning, som är utformad för system med kontinuerligdynamik och iterativa uppgifter, och föreslår en utrullningsalgoritm som bygger påsamplade data som genereras av en viss baspolicy. Den föreslagna algoritmen byggerpå idéer om värde- och policyiteration. Den är tillämpningsbar för deterministiskaproblem med godtyckliga tillstånds- och kontrollrum samt för system med godtyckligdynamik. Slutligen kan den utvidgas till problem med trajektoriebegränsningar ochen struktur med flera agenter.Dessutom används abstrakta modeller för dynamisk programmering för attanalysera lambdapolicyiteration med randomiseringsalgoritmer. Vi betraktar merspecifikt kontraktiva modeller med oändliga strategier. Vi visar att lambdaoperatorns välbestämdhet spelar en central roll i algoritmen. Det är känt att operatorn ärväldefinierad för problem med ändliga tillstånd, men vår analys visar att den ocksåär väldefinierad för de studerade kontraktiva modellerna med oändliga tillstånd.På samma sätt är det känt att den algoritm vi analyserar konvergerar för problemmed ändliga strategier, men vi identifierar de villkor som krävs för att garanterakonvergens med sannolikhet ett när policyrummet är oändligt, oberoende av antalettillstånd. Med hjälp av analysen exemplifierar vi en datadriven approximativ implementering av algoritmen för uppskattning av optimala kostnader för begränsadelinjära och icke-linjära regleringsproblem. Numeriska resultat visar på potentialen iatt använda denna metod i praktiken. / <p>QC 20211129</p>