Design of optimal correlation filters for hybrid vision systems

Research is underway at the NASA Johnson Space Center on the development of vision systems that recognize objects and estimate their position by processing their images. This is a crucial task in many space applications such as autonomous landing on Mars sites, satellite inspection and repair, and docking of space shuttle and space station. Currently available algorithms and hardware are too slow to be suitable for these tasks. Electronic digital hardware exhibits superior performance in computing and control; however, they take too much time to carry out important signal processing operations such as Fourier transformation of image data and calculation of correlation between two images. Fortunately, because of the inherent parallelism, optical devices can carry out these operations very fast, although they are not quite suitable for computation and control type operations. Hence, investigations are currently being conducted on the development of hybrid vision systems that utilize both optical techniques and digital processing jointly to carry out the object recognition tasks in real time. Algorithms for the design of optimal filters for use in hybrid vision systems were developed. Specifically, an algorithm was developed for the design of real-valued frequency plane correlation filters. Furthermore, research was also conducted on designing correlation filters optimal in the sense of providing maximum signal-to-nose ratio when noise is present in the detectors in the correlation plane. Algorithms were developed for the design of different types of optimal filters: complex filters, real-value filters, phase-only filters, ternary-valued filters, coupled filters. This report presents some of these algorithms in detail along with their derivations

Low-Rank Modifications of Riccati Factorizations for Model Predictive Control

In Model Predictive Control (MPC) the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem at each sample in the control loop. The main computational effort is often spent on computing the search directions, which in MPC corresponds to solving unconstrained finite-time optimal control (UFTOC) problems. This is commonly performed using Riccati recursions or generic sparsity exploiting algorithms. In this work the focus is efficient search direction computations for active-set (AS) type methods. The system of equations to be solved at each AS iteration is changed only by a low-rank modification of the previous one, and exploiting this structured change is important for the performance of AS type solvers. In this paper, theory for how to exploit these low-rank changes by modifying the Riccati factorization between AS iterations in a structured way is presented. A numerical evaluation of the proposed algorithm shows that the computation time can be significantly reduced by modifying, instead of re-computing, the Riccati factorization. This speed-up can be important for AS type solvers used for linear, nonlinear and hybrid MPC

Hybrid fuzzy/crisp-logic control of manufacturing systems

In recent years, techniques such as dynamic programming, the maximum principle, linear programming, and genetic algorithms have been used to synthesise optimal control policies for manufacturing systems. However, such techniques are frequently rather opaque and often yield control policies that are implemented by open-loop rather than closed-loop control systems. In this paper, it is therefore shown that closed-loop systems incorporating hybrid fuzzy/crisp-logic controllers can be readily designed for manufacturing systems. This hybrid approach is illustrated by reference to the closed-loop control of a simple manufacturing system producing a single part type.published_or_final_versio

Computational Methods for Optimal Control of Hybrid Systems

This thesis aims to find algorithms for optimal control of hybrid systems and explore them in sufficient detail to be able to implement the ideas in computational tools. By hybrid systems is meant systems with interacting continuous and discrete dynamics. Code for computations has been developed in parallel to the theory. The optimal control methods studied in this thesis are global, i.e. the entire state space is considered simultaneously rather than searching for locally optimal trajectories. The optimal value function that maps each state of the state space onto the minimal cost for trajectories starting in that state is central for global methods. It is often difficult to compute the value function of an optimal control problem, even for a purely continuous system. This thesis shows that a lower bound of the value function of a hybrid optimal control problem can be found via convex optimization in a linear program. Moreover, a dual of this optimization problem, parameterized in the control law, has been formulated via general ideas from duality in transportation problems. It is shown that the lower bound of the value function is tight for continuous systems and that there is no gap between the dual optimization problems. Two computational tools are presented. One is built on theory for piecewise affine systems. Various analysis and synthesis problems for this kind of systems are via piecewise quadratic Lyapunov-like functions cast into linear matrix inequalities. The second tool can be used for value function computation, control law extraction, and simulation of hybrid systems. This tool parameterizes the value function in its values in a uniform grid of points in the state space, and the optimization problem is formulated as a linear program. The usage of this tool is illustrated in a case study

High hybrid power converter performance using modern‐optimization‐methods‐based PWM strategy

Recently, interest in DC networks and converters has increased due to the high number of applications in renewable energy systems. Consequently, the importance of improving the efficiency of the hybrid converters has been highlighted. An optimal control strategy is a significant solution to handle the challenges of controlling the hybrid interleaved boost–Cuk converter. In this article, a modern‐optimization‐methods‐based PWM strategy for a hybrid power converter is developed. In order to improve the performance of the hybrid converter, four modern optimization algorithms—namely, Manta ray foraging optimization (MRFO), Marine Predators Algorithm (MPA), Jellyfish Search Optimizer (JS), and Equilibrium Optimizer (EO)—are employed to minimize the input current ripple under different operation scenarios. The results of the proposed modern optimization algorithms have shown more efficient converter performance and balanced power‐sharing compared with conventional strategies and the literature on optimization algorithms such as Differential Evolution (DE) and Particle Swarm Optimization (PSO). In addition, the results of all operation cases presenting the proposed optimal strategy successfully reduced the input current ripple and improve the performance of power‐sharing at the converter compared with the conventional methods

Predictive Control for Linear and Hybrid Systems

Model Predictive Control (MPC), the dominant advanced control approach in industry over the past twenty-five years, is presented comprehensively in this unique book. With a simple, unified approach, and with attention to real-time implementation, it covers predictive control theory including the stability, feasibility, and robustness of MPC controllers. The theory of explicit MPC, where the nonlinear optimal feedback controller can be calculated efficiently, is presented in the context of linear systems with linear constraints, switched linear systems, and, more generally, linear hybrid systems. Drawing upon years of practical experience and using numerous examples and illustrative applications, the authors discuss the techniques required to design predictive control laws, including algorithms for polyhedral manipulations, mathematical and multiparametric programming and how to validate the theoretical properties and to implement predictive control policies. The most important algorithms feature in an accompanying free online MATLAB toolbox, which allows easy access to sample solutions. Predictive Control for Linear and Hybrid Systems is an ideal reference for graduate, postgraduate and advanced control practitioners interested in theory and/or implementation aspects of predictive control