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DAE Optimization

DAE Optimization. towards real-time trajectory generation for flat nonlinear control systems. Sachin Kansal, Fraser Forbes University of Alberta Martin Guay Queen’s University. Talk Outline. DAE optimization problems Current solution techniques Proposed method - Basic Idea

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DAE Optimization

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  1. DAE Optimization towards real-time trajectory generation for flat nonlinear control systems Sachin Kansal, Fraser Forbes University of Alberta Martin Guay Queen’s University

  2. Talk Outline • DAE optimization problems • Current solution techniques • Proposed method - Basic Idea • Flatness of dynamics? • Normalized NLP solution • Current and future work Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  3. DAE Optimization • General DAOP Structure • Solution Difficulties • Infinite Dimensional Problem • Integration at every iteration • Algebraic path constraints Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  4. Solution Techniques Discretization and numerical integration [Ray, 1981] CVI Polynomial u(t) & numerical integration [Hicks & Ray, 1971] CVP Discretization of control over a region, region contraction and numerical integration [Luus, 1989] IDP Polynomials for states and control & discretization of DE and constraints [Cuthrell & Biegler, 1987] CBT Polynomial structure for pseudo-outputs and subsequent discretization of path constraints [Kansal, Forbes & Guay, 2000] NNLP Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  5. NNLP - Basic Idea System flatness DE elimination from DAOP Parameterization DAOP AOP Discretization AOP NNLP Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  6. System Flatness • System flatness permits transformation of system space to a pseudo (flat)-output space • Flat output space contains all information on system dynamics! DE Equivalents in flat-output space Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  7. Parameterization A polynomial structure with unknown coefficients is chosen for the flat output which defines: Hence defining: Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  8. Normalized AOP DAOP AOP Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  9. Discretization • Time is discretized • Continuous-time inequality constraints are enforced at the grid points • Affects only path inequality constraints Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  10. NNLP Solution NNLP Solved with standard NLP solvers, e.g., SQP methods Optimal Input Trajectory t0 tf Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  11. Results • Method tested on a number of benchmark DAOP problems • Consistent or Better Results • Significant Improvement in Computation Time/Load • Particularly suitable for RTO Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  12. Current Work • Solution Issues • Discretization of continuous algebraic constraints • Initial conditions and bounds for decision variables • Real-Time Implementation • Problems that can be handled • Major implementation and solution issues • Extension to approximately flat systems Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

  13. Questions? Sachin Kansal, Fraser Forbes - U of A Martin Guay - Queen’s U.

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