Algorithms for LQR via Static Output Feedback for Discrete-Time LTI Systems

Randomized and deterministic algorithms for the problem of LQR optimal control via static-output-feedback (SOF) for discrete-time systems are suggested in this chapter. The randomized algorithm is based on a recently introduced randomized optimization method named the Ray-Shooting Method that efficiently solves the global minimization problem of continuous functions over compact non-convex unconnected regions. The randomized algorithm presented here has a proof of convergence in probability to the global optimum. The suggested deterministic algorithm is based on the gradient method and thus can be proved to converge to local optimum only. A comparison between the algorithms is provided as well as the performance of the hybrid algorithm

A computationally efficient approach for robust gain-scheduled output-feedback LQR design for large-scale systems

This paper proposes a novel and simple control design procedure for sub-optimal robust gain-scheduled (GS) output-feedback linear quadratic regulator (LQR) design for large-scale uncertain linear parameter-varying (LPV) systems. First, we introduce a simple and practical technique to convexify the controller design problem in the scheduled parameters. Then, we propose a computationally efficient iterative Newton-based approach for gain-scheduled output-feedback LQR design. Next, we propose a simple modification to the proposed algorithm to design robust GS controllers. Finally, the proposed algorithm is applied for air management and fueling strategy of diesel engines, where the designed robust GS proportional-integral-derivative (PID) controller is validated on a benchmark model using real-world road profile data

Novel Results on Output-Feedback LQR Design

This paper provides novel developments in output-feedback stabilization for linear time-invariant systems within the linear quadratic regulator (LQR) framework. First, we derive the necessary and sufficient conditions for output-feedback stabilizability in connection with the LQR framework. Then, we propose a novel iterative Newton\u27s method for output-feedback LQR design and a computationally efficient modified approach that requires solving only a Lyapunov equation\ua0at each iteration step. We show that the proposed modified approach guarantees convergence from a stabilizing state-feedback to a stabilizing output-feedback solution and succeeds in solving high dimensional problems where other, state-of-the-art methods, fail. Finally, numerical examples illustrate the effectiveness of the proposed methods

Control Theory in Engineering

The subject matter of this book ranges from new control design methods to control theory applications in electrical and mechanical engineering and computers. The book covers certain aspects of control theory, including new methodologies, techniques, and applications. It promotes control theory in practical applications of these engineering domains and shows the way to disseminate researchers’ contributions in the field. This project presents applications that improve the properties and performance of control systems in analysis and design using a higher technical level of scientific attainment. The authors have included worked examples and case studies resulting from their research in the field. Readers will benefit from new solutions and answers to questions related to the emerging realm of control theory in engineering applications and its implementation

On Parametrizations of State Feedbacks and Static Output Feedbacks and Their Applications

In this chapter, we provide an explicit free parametrization of all the stabilizing static state feedbacks for continuous-time Linear-Time-Invariant (LTI) systems, which are given in their state-space representation. The parametrization of the set of all the stabilizing static output feedbacks is next derived by imposing a linear constraint on the stabilizing static state feedbacks of a related system. The parametrizations are utilized for optimal control problems and for pole-placement and exact pole-assignment problems

Control Systems in Engineering and Optimization Techniques

The portfolio diversification strategy study is useful to help investors to plan for the best investment strategy in maximizing return with the given level of risk or minimizing risk. Further, a new set of generalized sufficient conditions for the existence and uniqueness of the solution and finite-time stability has been achieved by using Generalized Gronwall-Bellman inequality. Moreover, a novel development is proposed to solve classical control theory’s difference diagrams and transfer functions. Advanced TCP strategies and free parametrization for continuous-time LTI systems and quality of operation of control systems are presented

Gradient Methods for Large-Scale and Distributed Linear Quadratic Control

This thesis considers methods for synthesis of linear quadratic controllers for large-scale, interconnected systems. Conventional methods that solve the linear quadratic control problem are only applicable to systems with moderate size, due to the rapid increase in both computational time and memory requirements as the system size increases. The methods presented in this thesis show a much slower increase in these requirements when faced with system matrices with a sparse structure. Hence, they are useful for control design for systems of large order, since they usually have sparse systems matrices. An equally important feature of the methods is that the controllers are restricted to have a distributed nature, meaning that they respect a potential interconnection structure of the system. The controllers considered in the thesis have the same structure as the centralized LQG solution, that is, they are consisting of a state predictor and feedback from the estimated states. Strategies for determining the feedback matrix and predictor matrix separately, are suggested. The strategies use gradient directions of the cost function to iteratively approach a locally optimal solution in either problem. A scheme to determine bounds on the degree of suboptimality of the partial solution in every iteration, is presented. It is also shown that these bounds can be combined to give a bound on the degree of suboptimality of the full output feedback controller. Another method that treats the synthesis of the feedback matrix and predictor matrix simultaneously is also presented. The functionality of the developed methods is illustrated by an application, where the methods are used to compute controllers for a large deformable mirror, found in a telescope to compensate for atmospheric disturbances. The model of the mirror is obtained by discretizing a partial differential equation. This gives a linear, sparse representation of the mirror with a very large state space, which is suitable for the methods presented in the thesis. The performance of the controllers is evaluated using performance measures from the adaptive optics community

Investigation of Trajectory and Control Designs for a Solar Sail to the Moon

NASA’s Artemis program and other government and commercial projects are working toward establishing a sustainable human presence on the moon. This thesis investigates the technical feasibility of a solar sail-based spacecraft (sailcraft) as a low-cost method of delivering cargo or science instruments to the moon and demonstrates how this sailcraft could be controlled to change its orbit. The concept is a low-cost, commercial launch vehicle-deployable, CubeSat-based sailcraft with a square sail, assumed attitude control, and a small payload traversing from low-Earth orbit toward the moon with zero propellant use. In this thesis, methods for sailcraft to increase altitude, the trajectory design process, and zero-propellant attitude control actuator options are explored. Three increasingly complex mathematical models were built in MATLAB around thrust vector control designs to get the concept sailcraft from Earth orbit toward the moon and transit simulations conducted. The third and most promising model developed a linear quadratic regulator controller to follow a logarithmic spiral reference trajectory and ensure the stability of the solution. As a result, a robust thrust vector control solution to minimize error from the reference trajectory was found and a solution method to assign the control gain matrix was developed

Design, testing and validation of model predictive control for an unmanned ground vehicle

The rapid increase in designing, manufacturing, and using autonomous robots has attracted numerous researchers and industries in recent decades. The logical motivation behind this interest is the wide range of applications. For instance, perimeter surveillance, search and rescue missions, agriculture, and construction. In this thesis, motion planning and control based on model predictive control (MPC) for unmanned ground vehicles (UGVs) is tackled. In addition, different variants of MPC are designed, analysed, and implemented for such non-holonomic systems. It is imperative to focus on the ability of MPC to handle constraints as one of the motivations. Furthermore, the proliferation of computer processing enables these systems to work in a real-time scenario. The controller's responsibility is to guarantee an accurate trajectory tracking process to deal with other specifications usually not considered or solved by the planner. However, the separation between planner and controller is not necessarily defined uniquely, even though it can be a hybrid process, as seen in part of this thesis. Firstly, a robust MPC is designed and implemented for a small-scale autonomous bulldozer in the presence of uncertainties, which uses an optimal control action and a feed-forward controller to suppress these uncertainties. More precisely, a linearised variant of MPC is deployed to solve the trajectory tracking problem of the vehicle. Afterwards, a nonlinear MPC is designed and implemented to solve the path-following problem of the UGV for masonry in a construction context, where longitudinal velocity and yaw rate are employed as control inputs to the platform. For both the control techniques, several experiments are performed to validate the robustness and accuracy of the proposed scheme. Those experiments are performed under realistic localisation accuracy, provided by a typical localiser. Most conspicuously, a novel proximal planning and control strategy is implemented in the presence of skid-slip and dynamic and static collision avoidance for the posture control and tracking control problems. The ability to operate in moving objects is critical for UGVs to function well. The approach offers specific planning capabilities, able to deal at high frequency with context characteristics, which the higher-level planner may not well solve. Those context characteristics are related to dynamic objects and other terrain details detected by the platform's onboard perception capabilities. In the control context, proximal and interior-point optimisation methods are used for MPC. Relevant attention is given to the processing time required by the MPC process to obtain the control actions at each actual control time. This concern is due to the need to optimise each control action, which must be calculated and applied in real-time. Because the length of a prediction horizon is critical in practical applications, it is worth looking into in further detail. In another study, the accuracies of robust and nonlinear model predictive controllers are compared. Finally, a hybrid controller is proposed and implemented. This approach exploits the availability of a simplified cost-to-go function (which is provided by a higher-level planner); thus, the hybrid approach fuses, in real-time, the nominal CTG function (nominal terrain map) with the rest of the critical constraints, which the planner usually ignores. The conducted research fills necessary gaps in the application areas of MPC and UGVs. Both theoretical and practical contributions have been made in this thesis. Moreover, extensive simulations and experiments are performed to test and verify the working of MPC with a reasonable processing capability of the onboard process