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Daniel E Miller - One of the best experts on this subject based on the ideXlab platform.

  • classical d step ahead adaptive control revisited linear like convolution bounds and exponential stability
    Advances in Computing and Communications, 2019
    Co-Authors: Daniel E Miller, Mohamad T Shahab
    Abstract:

    11This research was supported by the Natural Sciences and Engineering Research Council of Canada.Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded Noise Gain is typically proven. In recent work it has been shown, in both the pole placement stability setting and the first-order one-step-ahead tracking setting, that if the original, ideal, Projection Algorithm is used (subject to the common assumption that the plant parameters lie in a convex, compact set and that the parameter estimates are restricted to that set) as part of the adaptive controller, then a linear-like convolution bound on the closed loop behaviour can be proven; this immediately confers exponential stability and a bounded Noise Gain, and it can be leveraged to provide tolerance to unmodelled dynamics and plant parameter variation. In this paper we extend the approach to the d- step-ahead adaptive controller setting and prove comparable properties.

  • classical d step ahead adaptive control revisited linear like convolution bounds and exponential stability extended version
    arXiv: Optimization and Control, 2019
    Co-Authors: Daniel E Miller, Mohamad T Shahab
    Abstract:

    Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded Noise Gain is typically proven. In recent work it has been shown, in both the pole placement stability setting and the first-order one-step-ahead tracking setting, that if the original, ideal, Projection Algorithm is used (subject to the common assumption that the plant parameters lie in a convex, compact set and that the parameter estimates are restricted to that set) as part of the adaptive controller, then a linear-like convolution bound on the closed loop behaviour can be proven; this immediately confers exponential stability and a bounded Noise Gain, and it can be leveraged to provide tolerance to unmodelled dynamics and plant parameter variation. In this paper we extend the approach to the d-step-ahead adaptive controller setting and prove comparable properties.

  • multi estimator based adaptive control which provides exponential stability the first order case
    Conference on Decision and Control, 2018
    Co-Authors: Mohamad T Shahab, Daniel E Miller
    Abstract:

    Classical adaptive controllers provide asymptotic stabilization; neither exponential stability nor a bounded Noise Gain is typically proven. In recent work it is shown that these desired properties can be achieved by using an estimator based on the original ideal Projection Algorithm (together with a restriction of the parameter estimates to a given compact convex set), rather than the commonly used modified classical algorithm. Here the goal is to remove the convexity requirement. To this end, we consider the first-order case with unknown plant parameters belonging to a compact uncertainty set of controllable pairs. The first step of our approach is to observe that the compact uncertainty set can be covered by a finite number of convex compact sets, each of controllable pairs. For each of the convex compact sets, we design an estimator together with the corresponding one-step-ahead controller, and apply a switching logic to choose between them. We prove that the resulting controller guarantees linear-like convolution bounds on the closed-loop behavior, which implies exponential stability and a bounded Noise Gain.

  • classical pole placement adaptive control revisited linear like convolution bounds and exponential stability
    Mathematics of Control Signals and Systems, 2018
    Co-Authors: Daniel E Miller, Mohamad T Shahab
    Abstract:

    While the original classical parameter adaptive controllers do not handle Noise or unmodelled dynamics well, redesigned versions have been proven to have some tolerance; however, exponential stabilization and a bounded Gain on the Noise are rarely proven. Here we consider a classical pole placement adaptive controller using the original projection algorithm rather than the commonly modified version; we impose the assumption that the plant parameters lie in a convex, compact set, although some progress has been made at weakening the convexity requirement. We demonstrate that the closed-loop system exhibits a very desirable property: there are linear-like convolution bounds on the closed-loop behaviour, which confers exponential stability and a bounded Noise Gain, and which can be leveraged to prove tolerance to unmodelled dynamics and plant parameter variation. We emphasize that there is no persistent excitation requirement of any sort; the improved performance arises from the vigilant nature of the parameter estimator.

  • classical discrete time adaptive control revisited exponential stabilization
    2017 IEEE Conference on Control Technology and Applications (CCTA), 2017
    Co-Authors: Daniel E Miller
    Abstract:

    Classical discrete-time adaptive controllers provide asymptotic stabilization. While the original adaptive controllers did not handle Noise or unmodelled dynamics well, redesigned versions were proven to have some tolerance; however, exponential stabilization and a bounded Gain on the Noise was rarely proven. Here we consider a classical pole placement adaptive controller using the original projection algorithm rather than the commonly modifed version; we impose the assumption that the plant parameters lie in a convex, compact set and that the parameter estimates are projected onto that set at every step. We demonstrate that the closed-loop system exhibits very desireable closed-loop behaviour: there are linear-like convolution bounds on the closed loop behaviour, which confers exponential stability and a bounded Noise Gain. We emphasize that there is no persistent excitation requirement of any sort.

Zixue Zhao - One of the best experts on this subject based on the ideXlab platform.

  • An Efficient State-Space Realization With Minimum Roundoff Noise Gain
    IEEE Transactions on Circuits and Systems I: Regular Papers, 2007
    Co-Authors: Zixue Zhao
    Abstract:

    This paper deals with efficient digital filter structures with roundoff Noise consideration. Motivated by the direct-form II transposed (DFIIt) structure in rho-operator (rhoDFIIt) an alternative structure is obtained [Li in 2005, where, instead of the first-order rho-operators in rhoDFIIt, a set of second-order polynomial operators is used. In this paper, with the rounding before multiplication implementation taken into account, the equivalent state-space realization of the proposed structure by Li is derived and its roundoff Noise performance is analyzed by deriving the roundoff Noise expressions without/with error feedback consideration. This state-space realization can be efficiently implemented and has more degrees of freedom than its counterpart rhoDFIIt, which can be utilized to minimize the roundoff Noise Gain. A genetic algorithm is proposed to efficiently solve the optimal structure problem. Extensive examples are given to illustrate the advantage of this state-space realization and support the theoretical analysis

  • on the generalized dfiit structure and its state space realization in digital filter implementation
    IEEE Transactions on Circuits and Systems I-regular Papers, 2004
    Co-Authors: Zixue Zhao
    Abstract:

    It is well known that for a digital filter of order p, the number of nontrivial parameters in the classical optimal state-space realizations is proportional to p/sup 2/, while the traditional shift operator z-based direct-form II transposed (zDFIIt) structure, though having poor numerical properties, is one of the most efficient structures, just possessing 3p+1 nontrivial parameters. In this paper, based on the concept of polynomial operators, a new structure is proposed for digital filter implementation, which is a generalization of the traditional zDFIIt and the prevailing /spl delta/DFIIt structures. This structure, denoted as /spl rho/DFIIt, possesses 3p+1 nontrivial parameters plus p parameters at choice. Expressions for evaluating the sensitivity measure and the roundoff Noise Gain are derived for the /spl rho/DFIIt structure and its equivalent state-space realization that has the same structure complexity. It is shown that the state-space realization always yields a smaller roundoff Noise Gain than the /spl rho/DFIIt structure. One of the nice properties of these two structures is that for a given digital filter, they can be optimized with the p free parameters. The optimal structure problems can be solved with exhaustive researching under practical considerations. Numerical examples are presented to illustrate the design procedure.

Ngai Wong - One of the best experts on this subject based on the ideXlab platform.

  • improved roundoff Noise performance in a direct form iir filter using a modified delta operator
    International Symposium on Circuits and Systems, 2001
    Co-Authors: Ngai Wong
    Abstract:

    Among various direct-form delta operator filters, the delta direct-form II transposed (/spl delta/DFIIt) has been shown to produce the lowest roundoff Noise in finite-word-length implementations. Recent analyses focus on the optimization of the free parameter /spl Delta/ of the delta operator, with scaling of the structure to prevent arithmetic overflow. This paper proposes a modified /spl delta/GDFIIt second-order section in which the /spl Delta/s at different branches are separately optimized to further suppress roundoff Noise Gain. Noise variance plots aGainst pole locations are presented. Closed-form expressions for the optimal filter coefficients are derived and reduction of Noise Gain is confirmed by numerical examples.

  • a generalized direct form delta operator based iir filter with minimum Noise Gain and sensitivity
    IEEE Transactions on Circuits and Systems Ii: Analog and Digital Signal Processing, 2001
    Co-Authors: Ngai Wong
    Abstract:

    This brief presents the derivation of an arbitrary order delta operator-based direct-form IIR filter with minimum roundoff Noise Gain and sensitivity. It utilizes the concept of different coupling coefficients at different branch nodes for better Noise Gain suppression. Two possible structures for realizing the inverse delta operator are considered and procedures for calculating the optimal filter coefficients are given. By means of state-space representation and matrix manipulation, it is also shown that expressions for sensitivity measures of different filter coefficients and their corresponding roundoff Noise Gain expressions are the same. This enables the simultaneous minimization of sensitivity and Noise power for the proposed generalized filter structure.

  • Roundoff Noise minimization in a modified direct-form delta operator IIR structure
    IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 2000
    Co-Authors: Ngai Wong
    Abstract:

    Among various direct-form delta operator realized filter structures, the delta transposed direct-form II (/spl delta/DFIIt) has been shown to produce the lowest roundoff Noise Gain in finite wordlength implementations. Recent analyses focus on the optimization of the free parameter /spl Delta/ of the delta operator, with scaling of the structure to prevent arithmetic overflow. This paper proposes a modified /spl delta/DFIIt second-order section in which the /spl Delta/s and filter coefficients at different branches are separately scaled to achieve improved roundoff Noise Gain minimization. Expressions for the filter coefficients are derived, and reduction of roundoff Noise Gain is verified by numerical examples.

Mohamad T Shahab - One of the best experts on this subject based on the ideXlab platform.

  • classical d step ahead adaptive control revisited linear like convolution bounds and exponential stability
    Advances in Computing and Communications, 2019
    Co-Authors: Daniel E Miller, Mohamad T Shahab
    Abstract:

    11This research was supported by the Natural Sciences and Engineering Research Council of Canada.Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded Noise Gain is typically proven. In recent work it has been shown, in both the pole placement stability setting and the first-order one-step-ahead tracking setting, that if the original, ideal, Projection Algorithm is used (subject to the common assumption that the plant parameters lie in a convex, compact set and that the parameter estimates are restricted to that set) as part of the adaptive controller, then a linear-like convolution bound on the closed loop behaviour can be proven; this immediately confers exponential stability and a bounded Noise Gain, and it can be leveraged to provide tolerance to unmodelled dynamics and plant parameter variation. In this paper we extend the approach to the d- step-ahead adaptive controller setting and prove comparable properties.

  • classical d step ahead adaptive control revisited linear like convolution bounds and exponential stability extended version
    arXiv: Optimization and Control, 2019
    Co-Authors: Daniel E Miller, Mohamad T Shahab
    Abstract:

    Classical discrete-time adaptive controllers provide asymptotic stabilization and tracking; neither exponential stabilization nor a bounded Noise Gain is typically proven. In recent work it has been shown, in both the pole placement stability setting and the first-order one-step-ahead tracking setting, that if the original, ideal, Projection Algorithm is used (subject to the common assumption that the plant parameters lie in a convex, compact set and that the parameter estimates are restricted to that set) as part of the adaptive controller, then a linear-like convolution bound on the closed loop behaviour can be proven; this immediately confers exponential stability and a bounded Noise Gain, and it can be leveraged to provide tolerance to unmodelled dynamics and plant parameter variation. In this paper we extend the approach to the d-step-ahead adaptive controller setting and prove comparable properties.

  • multi estimator based adaptive control which provides exponential stability the first order case
    Conference on Decision and Control, 2018
    Co-Authors: Mohamad T Shahab, Daniel E Miller
    Abstract:

    Classical adaptive controllers provide asymptotic stabilization; neither exponential stability nor a bounded Noise Gain is typically proven. In recent work it is shown that these desired properties can be achieved by using an estimator based on the original ideal Projection Algorithm (together with a restriction of the parameter estimates to a given compact convex set), rather than the commonly used modified classical algorithm. Here the goal is to remove the convexity requirement. To this end, we consider the first-order case with unknown plant parameters belonging to a compact uncertainty set of controllable pairs. The first step of our approach is to observe that the compact uncertainty set can be covered by a finite number of convex compact sets, each of controllable pairs. For each of the convex compact sets, we design an estimator together with the corresponding one-step-ahead controller, and apply a switching logic to choose between them. We prove that the resulting controller guarantees linear-like convolution bounds on the closed-loop behavior, which implies exponential stability and a bounded Noise Gain.

  • classical pole placement adaptive control revisited linear like convolution bounds and exponential stability
    Mathematics of Control Signals and Systems, 2018
    Co-Authors: Daniel E Miller, Mohamad T Shahab
    Abstract:

    While the original classical parameter adaptive controllers do not handle Noise or unmodelled dynamics well, redesigned versions have been proven to have some tolerance; however, exponential stabilization and a bounded Gain on the Noise are rarely proven. Here we consider a classical pole placement adaptive controller using the original projection algorithm rather than the commonly modified version; we impose the assumption that the plant parameters lie in a convex, compact set, although some progress has been made at weakening the convexity requirement. We demonstrate that the closed-loop system exhibits a very desirable property: there are linear-like convolution bounds on the closed-loop behaviour, which confers exponential stability and a bounded Noise Gain, and which can be leveraged to prove tolerance to unmodelled dynamics and plant parameter variation. We emphasize that there is no persistent excitation requirement of any sort; the improved performance arises from the vigilant nature of the parameter estimator.

Michel Gevers - One of the best experts on this subject based on the ideXlab platform.

  • roundoff Noise minimization using delta operator realizations digital filters
    IEEE Transactions on Signal Processing, 1993
    Co-Authors: Michel Gevers
    Abstract:

    The authors examine the advantages of using delta operator state space realizations rather than shift operator realizations of transfer functions in terms of minimizing roundoff Noise Gain. They give several conditions under which the optimal roundoff Noise Gain for delta operator realizations is smaller than the optimal Gain for shift operator realizations. They then illustrate that even sparse (and hence nonoptimal) delta operator realizations can have smaller roundoff Noise Gain than the optimal shift operator realizations. >

  • parametrizations in control estimation and filtering problems accuracy aspects
    1993
    Co-Authors: Michel Gevers
    Abstract:

    1 Introduction.- 1.1 Motivation and general statement of objectives.- 1.2 A historical view and some motivating examples.- 1.3 Outline of the book.- 2 Finite Word Length errors and computations.- 2.1 Introduction.- 2.2 Representations of binary numbers.- 2.3 Overflow and quantization errors.- 2.4 Arithmetic computations and roundoff errors.- 2.5 Dynamic range and scaling.- 2.6 Conclusions.- 3 Parametrizations in digital system design.- 3.1 Introduction.- 3.2 State space realization set.- 3.3 Sensitivity measure of a state space realization.- 3.4 Optimal realizations with respect to a sensitivity measure.- 3.5 Roundoff Noise Gain of state space realizations.- 3.6 Minimal roundoff Noise Gain realizations.- 3.7 Relationship between sensitivity measure and roundoff Noise Gain.- 3.8 Examples and simulations.- 3.9 Alternative approaches.- 3.10 Conclusions.- Appendix 3: Proof of Theorem 3.2.- 4 Frequency weighted optimal design.- 4.1 Introduction.- 4.2 Minimization of a frequency weighted sensitivity measure.- 4.2.1 Weighted sensitivity measure of a realization.- 4.2.2 Optimal FWL realizations.- 4.2.3 Existence and uniqueness.- 4.3 Computation of the optimal realization set.- 4.4 Numerical example.- 4.5 Conclusions.- Appendix 4.A: Proof of existence of a minimum.- Appendix 4.B: Computation of weighted Gramians.- 5 A new transfer function sensitivity measure.- 5.1 Introduction.- 5.2 Minimization of an L2 sensitivity measure.- 5.2.1 The L2 sensitivity measure of a realization.- 5.2.2 Optimal L2 sensitivity realizations.- 5.2.3 Solution of the optimal realization problem.- 5.3 Relationship between L1/L2 and L2 sensitivity measures.- 5.4 An example.- 5.5 Conclusions.- 6 Pole and zero sensitivity minimization.- 6.1 Introduction.- 6.2 A pole-zero sensitivity measure.- 6.3 The eigenvalue sensitivity problem.- 6.4 Pole sensitivity minimization and normal matrices.- 6.5 Zero sensitivity measure.- 6.6 Pole-zero sensitivity coordinate dependence.- 6.7 Optimal realizations for pole-zero sensitivity minimization.- 6.8 Numerical example.- 6.9 Conclusions.- 7 A synthetic sensitivity - roundoff design.- 7.1 Introduction.- 7.2 A synthetic FWL Noise Gain.- 7.3 Optimizing the Total Noise Gain.- 7.4 A numerical example.- 7.5 Conclusions.- Appendix 7: Existence of a constrained minimum.- 8 Sparse optimal and suboptimal realizations.- 8.1 Introduction.- 8.2 Sparse optimal realizations.- 8.2.1 Hessenberg optimal realizations.- 8.2.2 Schur optimal realizations.- 8.2.3 Sparse block-balanced realizations.- 8.3 Theoretical versus actual sensitivity measure.- 8.3.1 Pole sensitivity of Schur realizations.- 8.3.2 A numerical example.- 8.4 Sparse quasi-optimal realizations.- 8.4.1 Constrained similarity transformations.- 8.4.2 Extensions of the Bomar and Hung algorithm.- 8.5 Sparse suboptimal realizations.- 8.6 Conclusion.- 9 Parametrizations in control problems.- 9.1 Introduction.- 9.2 Implementation of a pole placement controller.- 9.2.1 The ideal pole placement controller.- 9.2.2 Finite precision aspects in a closed loop compensator: problem formulation.- 9.2.3 Sensitivity analysis and optimal structures.- 9.2.4 Roundoff Noise study and optimal realizations.- 9.2.5 Design example.- 9.3 FWL LQG controller design.- 9.3.1 The 'ideal' LQG controller.- 9.3.2 Roundoff Noise study of an LQG controller.- 9.3.3 Optimal implementations of FWL LQG controllers.- 9.3.4 Optimal FWL LQG controllers.- 9.4 Conclusions.- Appendix 9: Sensitivity functions of closed loop system.- 10 Synthetic FWL compensator design.- 10.1 Introduction.- 10.2 State space description of a compensator.- 10.3 Analysis of FWL effects of a compensator.- 10.4 Optimal FWL compensator realizations.- 10.5 A design example.- 10.6 Conclusion.- 11 Parametrizations in the Delta operator.- 11.1 Introduction and motivation.- 11.2 Delta operator parametrizations.- 11.3 Sensitivity of delta parametrizations.- 11.3.1 Sensitivity measure.- 11.3.2 Optimal realization set.- 11.3.3 Numerical example.- 11.4 Roundoff Noise analysis.- 11.4.1 Introduction.- 11.4.2 The roundoff Noise Gain of shift and delta operator realizations.- 11.4.3 Minimization of the roundoff Noise Gain.- 11.4.4 New conditions for superiority of ?-realizations.- 11.4.5 Numerical examples.- 11.5 Conclusions.- Appendix 11: Proof of Theorem 11.5.- 12 Generalized transfer function parametrizations for adaptive estimation.- 12.1 Introduction.- 12.2 Parameter estimation and the information matrix.- 12.3 Connection between parametrization and data filtering.- 12.4 Optimal and suboptimal design choices.- 12.4.1 Manipulating the information matrix with data information.- 12.4.2 A robustness property.- 12.5 ?-operator parametrizations.- 12.5.1 A transfer function in ?-operator.- 12.5.2 Computing the information matrix.- 12.5.3 Analysis of the information matrix.- 12.5.4 Comparison with ?-operator parametrizations.- 12.6 Applications in estimation and adaptive filtering.- 12.7 Conclusions.- References.