As control systems are becoming more and more complex, system complexity is rapidly becoming a limiting factor in the efficacy of established techniques for control systems design. To cope with the growing complexity, control architectures often have a hierarchical structure. At the base of the system pyramid lie feedback loops with simple closed-loop control laws. These are followed, at a higher level, by discrete control logics. Such hierarchical systems typically have a hybrid nature. A common approach to addressing these types of complexity consists of decomposing, in the time domain, the control task into a number of modes, i.e. control laws dedicated to carrying out a limited task. This type of control generally involves switching laws among the various modes, and its design poses a major challenge in many application domains. The primary goal of this thesis is to develop a unified framework for addressing this challenge. To this end, the contribution of this thesis is threefold: 1. An algorithmic framework for how to optimize the performance of switched autonomous systems is derived. The optimization concerns both the sequence in which different modes appear in and the duration of each mode. The optimization algorithms are presented together with detailed convergence analyses. 2. Control strategies for how to optimize switched autonomous systems operating in real time, and when the initial state of the system is unknown, are presented. 3. A control strategy for how to optimally navigate an autonomous mobile robot in real-time is presented and evaluated on a mobile robotics platform. The control strategy uses optimal switching surfaces for when to switch between different modes of operations (behaviors).

This thesis presents a feedback design for an active noise cancellation (ANC) headphone. The designed ANC headphone consists of an analog controller, an audio power amplifier, a headphone speaker, a mini microphone, and a microphone amplifier, which constitute a feedback loop. The controller design follows the method of feedback sensitivity shaping with degree constraint introduced by R. Nagamune and A. Blomqvist in 2005. The advantage of this method is that it eliminates the needs for choosing an analytic weighting function and performing model reduction to yield a lower-order controller, as commonly required in conventional H2/H¡Û optimizations. A fifth-order analog controller for the ANC headphone is designed. The experimental result shows a maximum acoustic noise reduction of 19.7 dB near 200 Hz and an overall noise reduction of more than 10 dB in the control frequency band from 107 Hz to 523 Hz. Moreover, the out-of-band noise amplification is limited to a barely noticeable level of 4.26 dB.

The solution of initial value problems (IVPs) provides the evolution of dynamic system state history for given initial conditions. Solving boundary value problems (BVPs) requires finding the system behavior where elements of the states are defined at different times. This dissertation presents a unified framework that applies modified Chebyshev-Picard iteration (MCPI) methods for solving both IVPs and BVPs. Existing methods for solving IVPs and BVPs have not been very successful in exploiting parallel computation architectures. One important reason is that most of the integration methods implemented on parallel machines are only modified versions of forward integration approaches, which are typically poorly suited for parallel computation. The proposed MCPI methods are inherently parallel algorithms. Using Chebyshev polynomials, it is straightforward to distribute the computation of force functions and polynomial coefficients to different processors. Combining Chebyshev polynomials with Picard iteration, MCPI methods iteratively refine estimates of the solutions until the iteration converges. The developed vector-matrix form makes MCPI methods computationally efficient. The power of MCPI methods for solving IVPs is illustrated through a small perturbation from the sinusoid motion problem and satellite motion propagation problems. Compared with a Runge-Kutta 4-5 forward integration method implemented in MATLAB, MCPI methods generate solutions with better accuracy as well as orders of magnitude speedups, prior to parallel implementation. Modifying the algorithm to do double integration for second order systems, and using orthogonal polynomials to approximate position states lead to additional speedups. Finally, introducing perturbation motions relative to a reference motion results in further speedups. The advantages of using MCPI methods to solve BVPs are demonstrated by addressing the classical Lambert’s problem and an optimal trajectory design problem. MCPI methods generate solutions that satisfy both dynamic equation constraints and boundary conditions with high accuracy. Although the convergence of MCPI methods in solving BVPs is not guaranteed, using the proposed nonlinear transformations, linearization approach, or correction control methods enlarge the convergence domain. Parallel realization of MCPI methods is implemented using a graphics card that provides a parallel computation architecture. The benefit from the parallel implementation is demonstrated using several example problems. Larger speedups are achieved when either force functions become more complicated or higher order polynomials are used to approximate the solutions.

In this thesis an integrated, dynamic model for cardiovascular and respiratory systems has been developed. Models of cardiopulmonary system, airway mechanics and gas exchange that preexisted in literature have been reviewed, modified and combined. Combined model composes the systemic and pulmonary circulations, left/right ventricles, tissue/lung compartments, airway/lung mechanics and gas transportation. Airway resistance is partitioned into three parts (upper, middle, small airways). A collapsible airways segment and a viscoelastic element describing lung tissue dynamics and a static chest wall compliance are included. Frank-Starling Law, Bowditch effect and variable cerebral flow are also employed in the model. The combined model predictions have been validated by laboratory data collected from two healthy, young, male subjects, by performing dynamic bicycle exercise tests, using Vmax 229 Sensormedics, Cardiopulmonary Exercise Testing Instrument. The transition from rest to exercise under a constant ergometric workload is simulated. The initial anaerobic energy supply, autoregulation and the dilatation of pulmonary vessels are considered. Mean arterial blood pressure and the blood gas concentrations are assumed to be regulated by the controllers of the central nervous system namely, the heart rate and alveolar ventilation. Cardiovascular and respiratory regulation is modeled by a linear feedback control which minimizes a quadratic cost functional.

Land transportation is the main form of transportation around the world. Since the invention of the car land transportation changed drastically. As the cars took a solid part in human lives with the developments in electronics and robotics unmanned land vehicles are the future of both commercial and military land transportation. Today armies want unmanned land vehicles to provide logistical support to the units near threat zones and commercial firms want them to deliver goods more reliably and with less expense. In this thesis, mainly, a 6DoF dynamical model for a four wheeled land vehicle is developed and an autopilot design is presented using PID techniques. For dynamical modeling of the vehicle internal combustion engines, transmissions, tires, suspensions, aero dynamical drag forces and brakes are studied and the model is tested over some scenarios for evaluating its performance.

Optimal control of PDEs has a crucial place in many parts of sciences and industry. Over the last decade, there have been a great deal in, especially, control problems of elliptic problems. Optimal control problems of Burgers equation that is as a simplifed model for turbulence and in shock waves were recently investigated both theoretically and numerically. In this thesis, we analyze the space-time simultaneous discretization of control problem for Burgers equation. In literature, there have been two approaches for discretization of optimization problems: optimize-then-discretize and discretize-then-optimize. In the first part, we follow optimize-then-discretize appoproach. It is shown that both distributed and boundary time dependent control problem can be transformed into an elliptic pde. Numerical results obtained with adaptive and non-adaptive elliptic solvers of COMSOL Multiphysics are presented for both the unconstrained and the control constrained cases. As for second part, we consider discretize-then-optimize approach. Discrete adjoint concept is covered. Optimality conditions, KKT-system, lead to a saadle point problem. We investigate the numerical treatment for the obtained saddle point system. Both direct solvers and iterative methods are considered. For iterative mehods, preconditioners are needed. The structures of preconditioners for both distributed and boundary control problems are covered. Additionally, an a priori error analysis for the distributed control problem is given. We present the numerical results at the end of each chapter.

In this dissertation the solutions of the dynamics and real-time optimal control of magnetic attitude control and formation flying systems are presented. In magnetic attitude control, magnetic actuators for the time-optimal rest-to-rest maneuver with a pseudospectral algorithm are examined. The time-optimal magnetic control is bang-bang and the optimal slew time is about 232.7 seconds. The start time occurs when the maneuver is symmetric about the maximum field strength. For real-time computations, all the tested samples converge to optimal solutions or feasible solutions. We find the average computation time is about 0.45 seconds with the warm start and 19 seconds with the cold start, which is a great potential for real-time computations. Three-axis magnetic attitude stabilization is achieved by using a pseudospectral control law via the receding horizon control for satellites in eccentric low Earth orbits. The solutions from the pseudospectral control law are in excellent agreement with those obtained from the Riccati equation, but the computation speed improves by one order of magnitude. Numerical solutions show state responses quickly tend to the region where the attitude motion is in the steady state. Approximate models are often used for the study of relative motion of formation flying satellites. A modeling error index is introduced for evaluating and comparing the accuracy of various theories of the relative motion of satellites in order to determine the effect of modeling errors on the various theories. The numerical results show the sequence of the index from high to low should be Hill's equation, non- J2, small eccentricity, Gim-Alfriend state transition matrix index, with the unit sphere approach and the Yan-Alfriend nonlinear method having the lowest index and equivalent performance. A higher order state transition matrix is developed using unit sphere approach in the mean elements space. Based on the state transition matrix analytical control laws for formation flying maintenance and reconfiguration are proposed using low-thrust and impulsive scheme. The control laws are easily derived with high accuracy. Numerical solutions show the control law works well in real-time computations.

In recent years Boolean Networks (BN) and Probabilistic Boolean Networks (PBN) have become popular paradigms for modeling gene regulation. A PBN is a collection of BNs in which the gene state vector transitions according to the rules of one of the constituent BNs, and the network choice is governed by a selection distribution. Intervention in the context of PBNs was first proposed with an objective of avoid- ing undesirable states, such as those associated with a disease. The early methods of intervention were ad hoc, using concepts like mean first passage time and alteration of rule based structure. Since then, the problem has been recognized and posed as one of optimal control of a Markov Network, where the objective is to find optimal strategies for manipulating external control variables to guide the network away from the set of undesirable states towards the set of desirable states. This development made it possible to use the elegant theory of Markov decision processes (MDP) to solve an array of problems in the area of control in gene regulatory networks, the main theme of this work. We first introduce the optimal control problem in the context of PBN models and review our solution using the dynamic programming approach. We next discuss a case in which the network state is not observable but for which measurements that are probabilistically related to the underlying state are available. We then address the issue of terminal penalty assignment, considering long term prospective behavior and the special attractor structure of these networks. We finally discuss our recent work on optimal intervention for the case of a family of BNs. Here we consider simultaneously controlling a set of Boolean Models that satisfy the constraints imposed by the underlying biology and the data. This situation arises in a case where the data is assumed to arise by sampling the steady state of the real biological network.

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Many emerging controls applications have seen increased operational complexity due to the deployment of embedded, networked systems that must interact with the physical environment. In order to manage this complexity, we design different control modes for each system and use motion description languages (MDL) to specify a sequence of these controllers to execute at run-time. Unfortunately, current MDL frameworks lose some of the important details (i.e. power, spatial, or communication capabilities) that affect the execution of the control modes. This work presents several computational tools that work towards closing MDL's specification-to-execution gap, which can result in undesirable behavior of complex systems at run-time. First, we develop the notion of an MDL compiler for control specifications with spatial, energy, and temporal constraints. We define a new MDL for networked systems and develop an algorithm that automatically generates a supervisor to prevent incorrect execution of the multi-agent MDL program. Additionally, we derive conditions for checking if an MDL program satisfies actuator constraints and develop an algorithm to insert new control modes that maintain actuator bounds during the execution of the MDL program. Finally, we design and implement a software architecture that facilitates the development of control applications for systems with power, actuator, sensing, and communication constraints.