Inversion of linear and nonlinear observable systems with series-defined output trajectories

Stumper, Jean-François; Kennel, Ralph

doi:10.1109/cacsd.2010.5612841

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…It is remarked that the same parameterization (11) and ( 12) can be obtained for arbitrary non-flat outputs of a controllable and observable linear system, if the output is defined as polynomial series with undetermined coefficients [15]. Then, the outputs do not need to be redefined to flat, or controller canonical form outputs.…”

Section: Remark: Generality Of the Parameterization For Linear System...mentioning

confidence: 97%

Computationally efficient trajectory optimization for linear control systems with input and state constraints

Stumper

Kennel

2011

Proceedings of the 2011 American Control Conference

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This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory generation, and the outputs are parameterized using a polynomial basis. A method to parameterize the constraints is introduced using a result on polynomial nonpositivity. The resulting parameterized problem remains linear-quadratic and can be solved using quadratic programming. The problem can be further simplified to a linear programming problem by linearization around the unconstrained optimum. The method promises to be computationally efficient for constrained systems with a high optimization horizon. As application, a predictive torque controller for a permanent magnet synchronous motor which is based on real-time optimization is presented. I. INTRODUCTIONTrajectory optimization in real-time is an important part of many modern control systems, for instance, predictive control. The trajectory optimization problem must be solved in the sampling interval, determined by the plant dynamics. A computationally efficient solution, however, encounters two major obstacles: first, the optimization horizon has a minimum length, either to avoid suboptimality or as stability criterion, and second, the trajectory must satisfy input and state constraints to be feasible. For fast systems, many of the existing constrained predictive control schemes, which are based on numerical iterations, are not applicable.Concerning the horizon length problem, the continuous approach to predictive control is of interest [1]. Using differential flatness, the optimal control problem can be rewritten as output optimization problem. The basis function approach is applied to obtain a finite-parameter optimization problem [2] [3] [4] [5], analogeously to discrete-time optimization. A long optimization horizon is, however, obtained with comparably few optimization parameters.A remaining issue regarding computational efficiency is the inclusion of constraints. The classical method is the application of penalty functions [3]. As an alternative, a coordinate transformation was proposed to modify the constrained problem to a nonlinear unconstrained problem [6], solvable with nonlinear calculus of variations methods. The existing optimization methods with penalty functions or nonlinear coordinate transformations lead to a nonlinear or non-linear-quadratic problem, increasing the computational burden. If only feasibility is of interest, numerical procedures applying time scaling to slow down some variables can be used [1]. This paper treats the special case of the linearly constrained linear-quadratic problem. The linear structure of the system is exploited in the transformation of the problem to a finite-parameter optimization problem. The linear-quadratic structure of the problem is maintained. The unconstrained problem is solved algebraically as it is convex. A quadratic

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Section: Remark: Generality Of the Parameterization For Linear System...mentioning

confidence: 97%

Computationally efficient trajectory optimization for linear control systems with input and state constraints

Stumper

Kennel

2011

Proceedings of the 2011 American Control Conference

Self Cite

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“…Inspired by [13,23], the extraction of a previous state given the current state can be done by simultaneously solving a set of nonlinear equations, provided that the nonlinear dynamics (2) satisfy certain properties.…”

Section: Reducing Incompleteness Of Observation Sequencementioning

confidence: 99%

“…We record these bounds, as well as the observation probability value of the upper bound model to be used in the later stage (line 8-9). In the second stage, we attempt to find the smallest value for M odelC that can achieve the highest observation probability value (i.e., as the upper bound model) using a binary search scheme [4] (line [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. Let the range between the two bounds be n, then the best, worst and average time complexity of the algorithm is O(1), O(logn), and O(logn), respectively.…”

Section: Combined Criterionmentioning

confidence: 99%

HMM-based characterization of channel behavior for networked control systems

Chang

Venkatasubramanian

Enyioha

et al. 2012

Proceedings of the 1st International Conference on High Confidence Networked Systems

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We study the problem of characterizing the behavior of lossy and data corrupting communication channels in a networked control setting, where the channel's behavior exhibits temporal correlation. We propose a behavior characterization mechanism based on a hidden Markov model (HMM). The use of a HMM in this regard presents multiple challenges including dealing with incomplete observation sequences (due to data losses and corruptions) and the lack of a priori information about the model complexity (number of states in the model). We address the first challenges by using the plant state information and history of received/ applied control inputs to fill in the gaps in the observation sequences, and by enhancing the HMM learning algorithm to deal with missing observations . Further, we adopt two model quality criteria for determining behavior model complexity. The contributions of this paper include: (1) an enhanced learning algorithm for refining the HMM model parameters to handle missing observations, and (2) simultaneous use of two welldefined model quality criteria to determine the model complexity. Simulation results demonstrate over 90\% accuracy in predicting the output of a channel at a given time step, when compared to a traditional HMM based model that requires complete knowledge of the model complexity and observation sequence. ABSTRACTWe study the problem of characterizing the behavior of lossy and data corrupting communication channels in a networked control setting, where the channel's behavior exhibits temporal correlation. We propose a behavior characterization mechanism based on a hidden Markov model (HMM). The use of a HMM in this regard presents multiple challenges including dealing with incomplete observation sequences (due to data losses and corruptions) and the lack of a priori information about the model complexity (number of states in the model). We address the first challenges by using the plant state information and history of received/applied control inputs to fill in the gaps in the observation sequences, and by enhancing the HMM learning algorithm to deal with missing observations . Further, we adopt two model quality criteria for determining behavior model complexity. The contributions of this paper include: (1) an enhanced learning algorithm for refining the HMM model parameters to handle missing observations, and (2) simultaneous use of two well-defined model quality criteria to determine the model complexity. Simulation results demonstrate over 90% accuracy in predicting the output of a channel at a given time step, when compared to a traditional HMM based model that requires complete knowledge of the model complexity and observation sequence.

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Inversion of linear and nonlinear observable systems with series-defined output trajectories

Cited by 2 publications

References 14 publications

Computationally efficient trajectory optimization for linear control systems with input and state constraints

Computationally efficient trajectory optimization for linear control systems with input and state constraints

HMM-based characterization of channel behavior for networked control systems

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