Introduction To Optimization Methods Part 1: Mathematical Review

The following is a review of some basic definitions, notations and relations from linear algebra, geometry, and calculus that will be used frequently throughout this book

The Control of Discrete-Time Uncertain Dynamical Systems

In this project we use the second method of Lyapunov to develop several controllers to stabilize discrete-time dynamical systems with or without parameter uncertainties and/or external disturbances. We also use the notion of a sliding mode on a preferred hyperplane, previously developed for continuous-time variable structure control systems, to stabilize discrete- time dynamical systems. In particular, feedback controllers are proposed that: (i) stabilize discrete systems with no uncertainties by forcing their state trajectories onto prespecified hyperplanes; (ii) provide a needed level of stability robustness to discrete systems with uncertainties which are modeled by cone bounded functions; (iii) robustly stabilize discrete uncertain systems

Control of Dynamic Systems via Neural Networks

This report is devoted to the problem of controlling a class of linear time-invariant dynamic systems via controllers based on additive neural network models. In particular, the tracking and stabilization problems are considered. First, we show how to transform the problem of tracking a reference signal by a control system into the stabilization problem. Then, some concepts from the variable structure control theory are utilized to construct stabilizing controllers. In order to facilitate the stability analysis of the closed-loop systems we employ a special state space transformation. This transformation allows us also to reveal connections between the proposed controllers and the additive neural network models

Federated Learning for Connected and Automated Vehicles: A Survey of Existing Approaches and Challenges

Machine learning (ML) is widely used for key tasks in Connected and Automated Vehicles (CAV), including perception, planning, and control. However, its reliance on vehicular data for model training presents significant challenges related to in-vehicle user privacy and communication overhead generated by massive data volumes. Federated learning (FL) is a decentralized ML approach that enables multiple vehicles to collaboratively develop models, broadening learning from various driving environments, enhancing overall performance, and simultaneously securing local vehicle data privacy and security. This survey paper presents a review of the advancements made in the application of FL for CAV (FL4CAV). First, centralized and decentralized frameworks of FL are analyzed, highlighting their key characteristics and methodologies. Second, diverse data sources, models, and data security techniques relevant to FL in CAVs are reviewed, emphasizing their significance in ensuring privacy and confidentiality. Third, specific and important applications of FL are explored, providing insight into the base models and datasets employed for each application. Finally, existing challenges for FL4CAV are listed and potential directions for future work are discussed to further enhance the effectiveness and efficiency of FL in the context of CAV

OUTPUT FEEDBACK VARIABLE STRUCTURE CONTROLLERS AND STATE ESTIMATORS FOR UNCERTAIN DYNAMIC SYSTEMS

In this paper we propose a new class of output feedback variable structure controllers and state estimators (observers) for uncertain dynamic systems with hounded uncertainties. No statistical information about the uncertain elements is assumed. A variable structure systems (VSS) approach together with the geometric approach to the analysis and synthesis of system zeros are employed in the synthesis of the proposed output feedback controllers and state estimators. The role of system zeros in the output feedback stabilization and state estimation, using the VSS approach, is discussed. Numerical examples included illustrate the feasibility of the proposed stabilization and state estimation schemes

Minimizing Quotient Space Norms Using Penalty Functions

A penalty function method approach is proposed to solve the general problem of quotient space norms minimization. A new class of penalty functions is introduced which allows one to transform constrained optimization problems of quotient space norms minimization by unconstrained optimization problems. The sharp bound on the weight parameter is given for which constrained and unconstrained problems are equivalent. Also a computationally efficient bound on the weight parameter is given. Numerical examples and computer simulations illustrate the results obtained

ON SOLVING CONSTRAINED OPTIMIZATION PROBLEMS WITH NEURAL NETWORKS : A PENALTY FUNCTION METHOD APPROACH

This paper is concerned with utilizing analog circuits to solve various linear and nonlinear programming problems. The dynamics of these circuits are analyzed. Then, the previously proposed circuit implementations for solving optimization problems are examined. A new nonlinear programming network and its circuit implementation is then introduced which utilizes the nonlinearities to eliminate the problems encountered in previous circuit implementations

An introduction to optimization

Praise for the Third Edition "". . . guides and leads the reader through the learning path . . . [e]xamples are stated very clearly and the results are presented with attention to detail.""  -MAA Reviews  Fully updated to reflect new developments in the field, the Fourth Edition of Introduction to Optimization fills the need for accessible treatment of optimization theory and methods with an emphasis on engineering design. Basic definitions and notations are provided in addition to the related fundamental background for linear algebra, geometry, and calculus.  This ne