Exchanged Supervisory Control .


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Outline. Supervisory control overviewEstimator-based direct supervisory controlEstimator-based nonlinear supervisory controlExamples. Supervisory control. chief. process. . . s. controller 1. controller n. . . . . . . y. u. w. . . s. Inspiration: in the control of complex and exceedingly indeterminate frameworks, customary systems taking into account a solitary controller don't give acceptable performanc
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Instructional exercise on Logic-based Control Switched Supervisory Control Jo ã o P. Hespanha University of California at Santa Barbara

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Summary Supervisory control outline Estimator-based straight supervisory control Estimator-based nonlinear supervisory control Examples

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Supervisory control Motivation: in the control of complex and exceptionally unverifiable frameworks, conventional procedures in light of a solitary controller don\'t give palatable execution. manager exogenous unsettling influence/commotion s exchanging signal measured yield w controller 1 s y bank of hopeful controllers handle u controller n control flag Key thoughts: Build a bank of option controllers Switch among them online in light of estimations For straightforwardness we expect an adjustment issue, generally controllers ought to have a reference input r

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Supervisory control Motivation: in the control of complex and profoundly indeterminate frameworks, conventional strategies in view of a solitary controller don\'t give palatable execution. administrator exogenous unsettling influence/commotion s exchanging signal measured yield w controller 1 s y bank of applicant controllers handle u controller n control flag Supervisor: puts in the input circle the controller that appears to be additionally encouraging in light of the accessible estimations ordinarily rationale based/cross breed framework

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Multi-controller s exchanging signal controller 1 s bank of hopeful controllers y u measured yield control flag controller n Conceptual graph : not proficient for some controllers & unrealistic for precarious controllers

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Multi-controller s exchanging signal controller 1 s bank of competitor controllers y u measured yield control flag controller n Given a group of ( n - dimensional) competitor controllers s exchanging signal y u measured yield control flag

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Multi-controller exchanging times s( t ) exchanging signal s = 1 s = 1 s = 3 s = 2 t Given a group of ( n - dimensional) competitor controllers s exchanging signal y u measured yield control flag

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Supervisor y measured yield boss u control flag s exchanging signal y u Typically a mixture system:  " constant state d " discrete state ceaseless vector field discrete move work yield work

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Types of supervision Pre-steered supervision Performance-based supervision (coordinate) s = 2 keep controller while watched execution is satisfactory when execution of current controller gets to be distinctly unsuitable, change to controller that prompts to best expected execution in view of accessible information s = 1 s = 3 attempt one controllers after another in a pre-characterized succession stop when the execution appears to be worthy Estimator-based supervision (circuitous) gauge prepare demonstrate from watched information select controller in view of current gauge – Certainty Equivalence not powerful when the quantity of controllers is substantial

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Summary Supervisory control review Estimator-based direct supervisory control Estimator-based nonlinear supervisory control Examples

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Estimator-based supervision\'s setup: Example #1 handle control flag u y measured yield Process is thought to be obscure parameters p * =( a * , b * ) 2 P › [–1,1] £ {–1,1} we consider three hopeful controllers : controller C 1 : u = 0 to be utilized when a * · –.1 controller C 2 : u = 1.1 y to be utilized when a * > –.1 & b * = –1 controller C 3 : u = – 1.1 y to be utilized when a * > –.1 & b * = +1 handle parameter p * is equivalent to p › ( a,b ) 2 P utilize controller C q with controller choice capacity

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Estimator-based supervision\'s setup w exogenous aggravation/clamor control flag prepare u y measured yield unmodeled elements Process is thought to be in a family M p " small group of frameworks around an "ostensible" process display N p parametric vulnerability for every procedure in a family M p , no less than one applicant controller C q , q 2 Q gives sufficient execution. controller choice capacity controller C q with q = c ( p ) gives satisfactory execution prepare in M p, p 2 P

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Estimator-based chief: Example #1 y measured yield – y multi-estimator + – u control flag + Process is thought to be obscure parameters p * =( a * , b * ) 2 P › [–1,1] £ {–1,1} Multi-estimator 8 p =( a , b ) 2 P › [–1,1] £ {–1,1} y p " gauge of the yield y that would be right if the parameter was p= ( a,b ) e p " yield estimation blunder that would be little if the parameter was p= ( a,b ) consider the y p comparing to p = p * Since P has endlessly numerous components, this multi-estimator would need to be limitless dimensional !? (not a decent multi-estimator)

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Estimator-based boss: Example #1 y measured yield – y exchanging signal choice rationale multi-estimator + s – u control flag + Process is thought to be obscure parameters p * =( a * , b * ) 2 P › [–1,1] £ {–1,1} Multi-estimator 8 p =( a , b ) 2 P › [–1,1] £ {–1,1} y p " gauge of the yield y that would be right if the parameter was p= ( a,b ) e p " yield estimation mistake that would be little if the parameter was p= ( a,b ) Decision rationale : handle likely in M p ought to utilize C q , q = c ( p ) e p little set s = c ( p ) Certainty identicalness propelled

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Estimator-based director y measured yield – y exchanging signal choice rationale multi-estimator + s – u control flag + Process is thought to be in family prepare in M p , p 2 P controller C q , q = c ( p ) gives sufficient execution Multi-estimator y p " gauge of the procedure yield y that would be right if the procedure was N p e p " yield estimation mistake that would be little if the procedure was N p Decision rationale : prepare likely in M p ought to utilize C q , q = c ( p ) e p little set s = c ( p ) Certainty proportionality roused

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Estimator-based manager y measured yield – y exchanging signal choice rationale multi-estimator + s – u control flag + A soundness contention can\'t be founded on this on the grounds that ordinarily procedure in M p ) e p little yet not the opposite Process is thought to be in family prepare in M p, p 2 P controller C q , q = c ( p ) gives satisfactory execution Multi-estimator y p " gauge of the procedure yield y that would be right if the procedure was N p e p " yield estimation blunder that would be little if the procedure was N p Decision rationale : handle likely in M p ought to utilize C q , q = c ( p ) e p little set s = c ( p ) Certainty comparability enlivened

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Estimator-based boss y measured yield – y exchanging signal choice rationale multi-estimator + s – u control flag + Process is thought to be in family handle in M p, p 2 P controller C q , q = c ( p ) gives sufficient execution Multi-estimator y p " gauge of the procedure yield y that would be right if the procedure was N p e p " yield estimation blunder that would be little if the procedure was N p perceptible signifies "little e p ) little state" Decision rationale : general framework is distinguishable through e p set s = c ( p ) general state is little e p little Certainty equality motivated, however formally advocated by perceptibility

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Performance-based supervision measured yield y exchanging signal choice rationale execution screen s u control flag Candidate controllers: Performance screen: p q " measure of the normal execution of controller C q gathered from past information Decision rationale : p s is worthy keep current controller p s is unsatisfactory change to controller C q relating to best p q

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Abstract supervision Estimator and execution based structures have a similar basic engineering multi-est. on the other hand perf. screen choice rationale exchanging signal w s multi-controller u handle y measured yield control motion In this discussion we will concentrate generally on an estimator-based manager…

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Abstract supervision Estimator and execution based structures have a similar basic engineering multi-estimator choice rationale exchanging signal w s multi-controller u prepare y measured yield control flag exchanged framework

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The four fundamental properties (1-2) : Example #1 Multi-estimator is Process is Matching property: At slightest one of the e p is "little" Why? choice rationale e p* is "little" basically a necessity on the multi-estimator exchanging signal perceivable signifies "little e p ) little state" s Detectability property: For every p 2 P , the exchanged framework is recognizable through e p when s = c ( p ) file of controller that settles forms in M p

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Detectability a framework is discernible if for each combine eigenvalue/eigenvector ( l i , v i ) of A < [ l i ] ¸ 0 ) C v i ¹ 0 for short: match ( A , C ) is perceptible From answer for direct ODEs… ¹ 0 (expecting A diagonalizable, generally terms in t k e l i t show up) y ( t ) limited ) an i C v i = 0 (for < [ l i ] ¸ 0 ) an i = 0 (for < [ l i ] ¸ 0 ) y ( t ) limited Lemma: For any noticeable system: y ( t ) bounded ) x ( t ) limited & y ( t ) ! 0 ) x ( t ) ! 0

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Detectability framework is recognizable if for each combine eigenvalue/eigenvector ( l i , v i ) of A < [ l i ] ¸ 0 ) C v i ¹ 0 Lemma: For any perceptible system: y ( t ) bounded ) x ( t ) limited & y ( t ) ! 0 ) x ( t ) ! 0 Lemma: For any discernible framework, there exists a network K to such an extent that is asymptotically steady (all eigenvalues of A – KC with negative genuine part) Can re-compose framework as (yield infusion) asympt. stable affirms that: y is limited/! 0 ) x is limited/! 0

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The four essential properties (1-2) : Example #1 noticeable signifies "little e p ) little sta

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