Philip Loewen

Prospective Graduate Students / Postdocs

This faculty member is currently not actively recruiting graduate students or Postdoctoral Fellows, but might consider co-supervision together with another faculty member.


Research Classification

Research Interests

Calculus of Variations
Optimal Control
Machine Learning

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Affiliations to Research Centres, Institutes & Clusters

Research Options

I am interested in and conduct interdisciplinary research.

Graduate Student Supervision

Doctoral Student Supervision (Jan 2008 - Nov 2019)
Adaptive model-predictive control and its applications in paper-making processes (2018)

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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On monotone operator classes and the Borwein-Wiersma decomposition (2013)

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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Measure-driven Impulsive Systems: Stabilization, Optimal Control and Applications (2010)

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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  • Locality preserving discriminative canonical variate analysis for fault diagnosis (2018)
    Computers & Chemical Engineering, 117, 309--319
  • Sensitivity of MIMO controller performance to model-plant mismatch, with applications to paper machine control (2014)
    Control Applications (CCA), 2014 IEEE Conference on, , 204--209
  • Iterative adaptive robust control of multivariable CD processes (2010)
    International Journal of Adaptive Control and Signal Processing, 24 (8), 657--674
  • A note on separating machine direction and cross machine data on a paper machine (2009)
    NORDIC Pulp & Paper Research Journal, 24 (3), 273--277
  • A weak maximum principle for optimal control problems with nonsmooth mixed constraints (2009)
    Set-Valued and Variational Analysis, 17 (2), 203--221
  • Iterative Feedback Tuning of Cross-directional Processes Controller (2008)
    IFAC Proceedings Volumes, 41 (2), 10945--10950
  • Online Identification and Alignment of MIMO Cross Directional Controlled Processes Using Second Order Statistics (2007)
    Control and Automation, 2007. ICCA 2007. IEEE International Conference on, , 989--994
  • epsilon-Frechet Differentiability of Lipschitz Functions and Applications (2006)
    Journal of Convex Analysis, 13 (3/4), 695
  • Identification of Symmetric Noncausal Processes: Cross-Directional Response Modelling of Paper Machines (2006)
    Decision and Control, 2006 45th IEEE Conference on, , 6744--6749
  • Subdifferential calculus in Asplund generated spaces (2006)
    Journal of mathematical analysis and applications, 322 (2), 787--795
  • On the multiplicity of Dini subgradients in separable spaces (2004)
    Nonlinear Analysis: Theory, Methods & Applications, 58 (1-2), 1--10
  • The range of the gradient of a LipschitzC 1-smooth bump in infinite dimensions (2002)
    Israel Journal of Mathematics, 132 (1), 239--251
  • A generalized variational principle (2001)
  • The range of the gradient of a continuously differentiable bump (2001)
    J. Nonlinear and Convex Analysis, 2, 1--19
  • Typical Properties of Lipschitz Functions (2000)
    Real Analysis Exchange, 26 (2), 717--726
  • Minimax linear-quadratic controller design (1999)
  • Bolza problems with general time constraints (1997)
    SIAM journal on control and optimization, 35 (6), 2050--2069
  • Multiple objective control problems via nonsmooth analysis (1996)
    IFAC Proceedings Volumes, 29 (1), 1392--1397
  • New necessary conditions for the generalized problem of Bolza (1996)
    SIAM journal on control and optimization, 34 (5), 1496--1511
  • Optimization-based teleoperation controller design (1996)
    IFAC Proceedings Volumes, 29 (1), 1844--1849
  • Epi-derivatives of integral functionals with applications (1995)
    Transactions of the American Mathematical Society, 347 (2), 443--459
  • Numerical solution of the multiple objective control system design problem for SISO systems (1995)
    American Control Conference, Proceedings of the 1995, 2, 1458--1462
  • Robust controller design for teleoperation systems (1995)
    Systems, Man and Cybernetics, 1995. Intelligent Systems for the 21st Century., IEEE International Conference on, 3, 2127--2132
  • A mean value theorem for Fréchet subgradients (1994)
    Nonlinear Analysis: Theory, Methods & Applications, 23 (11), 1365--1381
  • Generalized conjugate points for optimal control problems (1994)
    Nonlinear Analysis: Theory, Methods & Applications, 22 (6), 771--791
  • Generalized conjugate points in optimal control (1994)
    Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on, 4, 4004--4008
  • Optimal control of unbounded differential inclusions (1994)
    SIAM journal on control and optimization, 32 (2), 442--470
  • Optimal control via nonsmooth analysis (1993)
  • The adjoint arc in nonsmooth optimization (1991)
    Transactions of the American Mathematical Society, 325 (1), 39--72
  • Second-order sufficiency criteria and local convexity for equivalent problems in the calculus of variations (1990)
    Journal of mathematical analysis and applications, 146 (2), 512--522
  • An intermediate existence theory in the calculus of variations (1989)
    Annali della Scuola Normale Superiore di Pisa-Classe di Scienze, 16 (4), 487--526
  • Perturbed differential inclusion problems (1989)
    Nonsmooth Optimization and Related Topics, , 255--263
  • Variational problems with Lipschitzian minimizers (1989)
    Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 6, 185--209
  • Differential inclusions with free time (1988)
    Annales de l'Institut Henri Poincare (C) Non Linear Analysis, 5 (6), 573--593
  • Free time optimal control problems with unilateral state constraints (1988)
    Analysis and optimization of systems, , 347--360
  • The proximal subgradient formula in Banach space (1988)
    Canad. Math. Bull, 31 (3), 353--361
  • On the Lavrentiev phenomenon (1987)
    Canad. Math. Bull, 30 (1), 102--108
  • Pontryagin-type necessary conditions for differential inclusion problems (1987)
    Systems & control letters, 9 (3), 263--265
  • State constraints in optimal control: A case study in proximal normal analysis (1987)
    SIAM journal on control and optimization, 25 (6), 1440--1456
  • The proximal normal formula in Hilbert space (1987)
    Nonlinear Analysis: Theory, Methods & Applications, 11 (9), 979--995
  • The value function in optimal control: sensitivity, controllability, and time-optimality (1986)
    SIAM journal on control and optimization, 24 (2), 243--263
  • Proximal normal analysis in dynamic optimization (1985)
  • The sensitivity of optimal value functions in differential inclusion problems (1983)

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