This thesis deals with a single feedback fixed-rate channel using some coding strategies. We assess and compare the LQ performance of the different coding methods. The idea of predictive coding is applied at the transmitter side to improve the efficiency of the channel usage by transmission of the quantized innovations signal. We observe a plant stability requirement is necessary to construct the joint density of both the plant and the predictor states at the receiver side. The Bayesian filter is used to compute the optimal feedback control. We compare the closed-loop control performance for three cases. In each of these competing cases, a lower complexity receiver architecture is possible but at the expense of closed-loop control performance.

In addition to predictive coding, we examine specific low-bitrate strategies and

evaluate through their impact on LQ control performance. We consider coding the quantized output signal deploying period-two codes of differing delay versus accuracy tradeoff. We treat the quantizer as the functional composition of an infinitely-long linear staircase function and a saturation. This permits the analysis being subdivided into estimator computations and an escape time evaluation, which connects the control back into the choice of quantizer saturation bound. By limiting the subject to specific strategies, we are able to identify principles underlying coding for control.

A common loop from gas processing is studied from a modeling and control perspective with an emphasis on the simplicity and control-orientation of the model components which comprise the model: pipes, branches, compressor, valves, tanksetc. The process is to take recent component model classes and to lift them to be more realistic and representative of a practical compressor operational area, notably taking into account compressor operation curves. The control objective is to improve transient response of the overall system by developing two-input controllers to manage fluctuations in either compressor suction pressure or discharge pressure in response to supply and delivery changes. The control mechanism is the use of a recycle loop capable of transporting gas from the discharge side to the suction side – this is the faster manipulated variable – together with the slower dynamics of the compressor speed, which regulates overall flow. The return of the recycle valve to closed during steady-state operation is included into the design.

The problem of state estimation for a linear, time-varying, gaussian system from measurements which are communicated over an imperfect channel is considered from several perspectives. The communication imperfections include intermittency, channel noise, quantization, etc. The first part of the thesis examines the stochastic behavior of the state estimation error and of the regulated state itself in situations of intermittent and quantized measurements via the formulation of an escape time problem dealing with the cumulative distribution function of the probability of escape of these signals from a given set. This is compared to and contrasted with earlier analyses which considered the behavior of Kalman filters with intermittent data based on moments and conditional moments, and the evaluation of the minimal number of bits required for mean square stabilization. The main result shows the escape time is characterized by a Markov chain which is amenable to explicit analysis through the calculation of the its cumulative distribution function. The second part of the thesis focuses on developing an exact formulation of the conditional probability density function of the system state given quantized innovations signals communicated from a linear Kalman filter at the transmitter. This is based on Bayesian filtering and extends previous works on the subject but without the requirement for simplifying assumptions. This latter result follows from a simple observation concerning the correct choice of state for the transmitter, which includes the transmitters’ Kalman filter estimate. This leads to an exact and recursive approach.

Model Predictive Control has become a prevailing technique in practice by virtue of its natural inclusion of constraint enforcement in sub-optimal feedback design through repeated solution of finite-horizon, open-loop control problems. However, many approaches are lacking in proper accommodation of output feedback using imperfect measurements, as is normally required in practice. The conventional workaround for this disconnect between control theory and practice is the use of certainty equivalent control laws, which subsume best available state estimates in place of the system state in order to salvage methods available for state-feedback Model Predictive Control.

This dissertation explores Stochastic Model Predictive Control in the general, nonlinear output-feedback setting. Starting the receding horizon development from Stochastic Optimal Control, we attain inherent accommodation of imperfect measurement data through propagation of the conditional state density, the information state. This setup further results in the control signals being of dual, probing nature: the control balances the typically antagonistic requirements of regulation and exploration. However, these conflicting tasks inherent to Stochastic Optimal Control also embody the associated computational intractability. While properties such as optimal probing and numerical performance bounds on the infinite time-horizon require solution of Stochastic Optimal Control problems, obtaining these solutions is typically not possible in practice due to the exorbitant computational demands.

We suggest two methods for tractable Stochastic Model Predictive Control. Firstly, we propose approximation of the information state update by a Particle Filter, which may be merged naturally with scenario optimization to generate control laws. While computationally tractable, this method does not maintain duality without additional measures. Alternatively, the nonlinear output-feedback problem can be approximated - or even cast - as a Partially Observable Markov Decision Process, a special class of systems for which Stochastic Optimal Control is numerically tractable for reasonable problem size, enabling dual optimal control with provable infinite-horizon properties.

Throughout this dissertation, we examine two classes of examples from healthcare: individualized appointment scheduling, a problem not requiring duality; medical treatment decision making, where dual control decisions are often required to balance optimally when to order diagnostic tests and when to apply medical intervention.

In many practical engineering applications, a significant portion of the available information is excluded from the design process due to a lack of obvious mechanisms for its incorporation. In this dissertation, several methods are presented for leveraging such underutilized prior knowledge in application-oriented settings. Three cases, motivated by real-world examples, are considered, addressing controller, estimator, and identification design respectively. In each case, a methodology is presented capturing the key features of the prior knowledge in a characterization which can be readily incorporated into standard solution.

Firstly, a flexible modeling framework is presented for characterizing time-advanced forecast data associated with an exogenous disturbance. The model is incorporated into a disturbance-attenuating feedforward controller which can be synthesized with standard H2 or H∞ methods. The closed-loop performance calculation provides a comparative metric to juxtapose multiple designs and address economic questions, such as sensor placement. A practical example is provided for a wind turbine and lidar sensor with tunable focus range.

Secondly, a modeling framework is presented for characterizing logic-valued measurements that provide timely indication of an associated disturbance event. An estimator is constructed using the fast logic-valued measurement, and known disturbance statistics, to rapidly adjust the disturbance estimate, resulting in improved performance. The framework is applied to a gas turbine (GT) system with transient load disturbance associated with a fast electrical breaker switching measurement. The method is generalized to incorporate multiple disturbance load and breaker pairs.

Finally, a high-fidelity GT (HFGT) model is used to construct a linear GT engine model for control design. The HFGT model generates closed-loop transient simulation data for system identification and the structure of its internal subsystems is leveraged to reduce the complexity of the identification process by excluding unnecessary subsystems. The partition of subsystems is enabled by access to signals in the high-fidelity model which are otherwise unavailable during physical engine testing. The resulting linear engine model can be modularly reconfigured with different fuel subsystem and rotor subsystem models. The linear GT model is validated in closed-loop transient simulations.

Algorithms for simultaneous input and state estimation (SISE algorithms) that are optimal in the minimum-variance unbiased sense have been in development for decades. The stability of such algorithms is not guaranteed. For time invariant systems, this thesis derives necessary and sufficient stability conditions. In the square case, where the number of inputs equals the number of outputs, the exact positions of the algorithm’s poles are established. In the non-square case, the derived stability condition is formulated as a detectability condition. Those necessary and sufficient conditions are generalized to sufficient only conditions for the time varying case. Lastly, the effect of delay in the system under consideration on the SISE algorithm is explored. A general method, inspired by fixed lag smoothing, is proposed to handle cases where a general delay is present.

The EUV light source is a key enabler of modern photolithographic computer chip manufacture. In the light source, a high-power drive laser irradiates a tin fuel source to generate an EUV light-producing plasma. Regulation of the drive laser power is critical to ensure that the EUV light source generates the precise amount of light needed for the photolightographic process. The laser power can be adjusted by modulating the excitation medium, however, the amplification process is highly dynamic and exhibits transient behavior on short timescales. These fast timescale dynamics are important to understand as the EUV light source power must be tightly regulated. In this work, these dynamics are investigated towards the objective of developing a control system framework to regulate the drive laser power. An experiment to characterize the drive laser was carried out on a prototype drive laser system, and the results used to derive a model of the drive laser amplification process using system identification. A filtered output error model is developed which results in accurate simulation of the drive laser dynamic behavior. This model is then demonstrated to yield good performance for feed-forward control, using a model inversion framework. These results show that the modeling process is successful in generating a control-relevant model of the high power drive laser system.

ASML is the global leader in photolithography equipment. With advent of EUV Lithography technology, it is possible to create microchips with smaller transistors and with greater precision. As EUV Lithography technology matures, customers expect ever higher productivity from these machines. This thesis analyzes a phenomenon called Local Force, which can negatively affect the system's productivity. Additionally, this thesis proposes a method to correct for the disturbances caused by the Local Force.

A set of four experiments are proposed to characterize the nature of the Local Force. These experiments demonstrate linear relation between the amount of EUV produced and the droplet displacement and impact on the upstream droplets. Additionally the experiments identify a process window in which the droplet displacement would not affect system performance.

These findings were then used to a develop Kalman predictor and a feedforward algorithm which can compensate for the disturbances produced by the Local Force. Using data from a real machine in conjunction with a high fidelity simulation, it is shown that the algorithm can maintain the L2Dx position within the process window.

Deterministic control theory is built on the presumptive luxury of complete access to the states. This premise is false in many applications. Hence, rendering questionable, the validity of the implemented control algorithms. On the other hand, acknowledging the lack or partial access to the states is an invitation to the realms of stochastic optimal control. A field of many platonic objects \cite{penrose2006road} and folk definitions, with hopes of advancement harshly met with computational intractability.

The dissertation focuses on finding suboptimal solutions to the stochastic control problem, via utilizing the machinery developed for deterministic control. This is done through reducing the infinite dimensional information state, represented by the state filtered density, to one state value of (small) finite dimension. This reduction is guided by two arguments forming the bases of Chapters~2 and 3.

The first approach is built on statistical means, in which a point estimate, like the Maximum Likelihood Estimate, may have more claims to certainty equivalence in some applications than the typically used conditional mean. We derive a Maximum Likelihood recursive state estimator for non-linear state-space models, by combining the Expectation Maximization algorithm, and a particle filter. We prove that for nonlinear state-space systems with linear measurements and additive Gaussian noises, our formulation reduces to a gradient-free optimization in a form of a fixed-point iteration. The convergence properties of the sequences out of these iterations are inherited from the Expectation Maximization algorithm.

The second method engages directly with the control objective to achieve a state value or ``estimate'' that helps achieving this control objective. The State Selection Algorithm, which will be presented in Chapter~3, compiles the information about state statistics, dynamics, constraints, and a given controller, and returns the best state value based on optimizing a prescribed finite-horizon performance function. The set of candidate states, is provided by a particle filter. In the linear quadratic problem with polyhedral constraints, we show that the algorithm reduces to a quadratic program for the state value.