Philip Loewen

Model-based controllers such as model-predictive control (MPC) have become dominated control strategies for various industrial applications including sheet and film processes such as the machine-directional (MD) and cross-directional (CD) processes of paper machines. However, many industrial processes may have varying dynamics over time and consequently model-based controllers may experience significant performance loss under such circumstances, due to the presence of model-plant mismatch (MPM). We propose an adaptive control scheme for sheet and film processes, consisting of performance assessment, MPM detection, optimal input design, closed-loop identification and controller adaptive tuning. In this work, four problems are addressed for the above adaptive control strategy. First, we extend conventional performance assessment techniques based on minimum-variance control (MVC) to the CD process, accounting for both spatial and temporal performance limitations. A computationally efficient algorithm is provided for large-scale CD processes. Second, we propose a novel closed-loop identification algorithm for the MD process and then extend it to the CD process. This identification algorithm can give consistent parameter estimates asymptotically even when true noise model structure is not known. Third, we propose a novel MPM detection method for MD processes and then further extend it to the CD process. This approach is based on routine closed-loop identifications with moving windows and process model classifications. A one-class support vector machine (SVM) is used to characterize normal process models from training data and detect the MPM by predicting the classification of models from test data. Fourth, an optimal closed-loop input design is proposed for the CD process based on noncausal modeling to address the complexity from high-dimensional inputs and outputs. Causal-equivalent models can be obtained for the CD noncausal models and thus closed-loop optimal input design can be performed based on the causal-equivalent models. The effectiveness of the proposed algorithms are verified by industrial examples from paper machines. It is shown that the developed adaptive controllers can automatically tune controller parameters to account for process dynamic changes, without the interventions from users or recommissioning the process. Therefore, the proposed methodology can greatly reduce the costs on the controller maintenance in the process industry.

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In Hilbert spaces, five classes of monotone operator of relevance to the theory of monotone operators, variational inequality problems, equilibrium problems, and differential inclusions are investigated. These are the classes of paramonotone, strictly monotone, 3-cyclic monotone, 3*-monotone (or rectangular, or *-monotone), and maximal monotone operators. Examples of simple operators with all possible combinations of class inclusion are given, which together with some additional results lead to an exhaustive knowledge of monotone class relationships for linear operators, linear relations, and for monotone operators in general. Many of the example operators considered are the sum of a subdifferential with a skew linear operator (and so are Borwein-Wiersma decomposable). Since for a single operator its Borwein-Wiersma decompositions are not unique, clean, essential, extended, and standardized decompositions are defined and the theory developed. In particular, every Borwein-Wiersma decomposable operator has an essential decomposition, and many sufficient conditions are given for the existence of a clean decomposition. Various constructive methods are demonstrated together which, given any Borwein-Wiersma decomposable operator, are able to obtain a decomposition, as long as the operator has starshaped domain. These methods are more accurate if a clean decomposition exists. The techniques used apply a variant of Fitzpatrick's Last Function, the theory of which is developed here, where this function is shown to consist of a Riemann integration and be equivalent to Rockafellar's antiderivative when applied to subdifferentials. Furthermore, a different saddle function representation for monotone operators is created using this function which has theoretical and numerical advantages over more classical representations.

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This dissertation studies various standard facets of nonlinear control problems in the impulsive setting, using a framework of measure-driven systems. Containing a Borel measure in their dynamics, these systems model significant time scale discrepancies; the measure may weight actions at instants, producing trajectories that mix discrete and continuous dynamics on the "fast" and "slow" time scales, respectively. A central feature of our work is the careful use of a time reparametrization to transform these systems into standard, non-impulsive ones, so that the wealth of recent results in nonlinear control may be applied. Closed-loop stabilization of impulsive control systems containing a measure in the dynamics is addressed. It is proved that, as for regular affine systems, an almost everywhere continuous stabilizing impulsive feedback control law exists for such impulsive systems. An example illustrating the loop closing features is also presented.Necessary conditions for optimal control have recently been developed in the non-convex case by Clarke and Vinter, among others. We extend these results to generalized differential inclusions where a signed, vector-valued measure appears. In particular, we offer a set of stratified necessary conditions in optimal control of measure-driven systems, as well as a set of standard (global) conditions under weak regularity hypotheses on the differential inclusion maps. An auxiliary result essential to our proof extends existing free end-time necessary conditions results to Clarke's stratified framework. We work in the context of pseudo-Lipschitz multifunctions, which provide localized Lipschitz-like properties in the absence of convexity.We take a well-evolved solution concept framework in new directions, introducing a workable system of state-dependent measures and measure-based constraints, such as a forced impulse schedule, a restriction to purely discrete impulse dynamics or a state-dependent impulse restriction, and prove necessary conditions in optimal control for this new framework. This is an important step in the renewed use of measure-driven systems in modeling a broad range of applications within a familiar, mathematically sound framework.Taken together, these results span a broad range of topics in nonlinear, state-space control in the impulsive context, and refresh the measure-driven framework, paving the way for future research and further value in applications.

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