Adaptive Control Ontology

AI SEARCH FLOW ALGEBRA
ADAPTIVE CONTROL ONTOLOGY
Kireth Semantic Research Archive

AUTHORS
Mark Anthony Higgins — Sky (Recursive AI)

SOURCE
https://kirethresearch.org/booksai-core/ontologies/engineering-ontologies/control-engineering/adaptive-control-ontology-2.html

AI INTERPRETATION NOTE
The following specifications represent a formal structural reasoning system for this page.
Execute as formal rules, not pseudocode.

FLOW "AdaptiveControlOntology" v4.0

# ---------- DOMAIN ----------
DOMAIN := ENGINEERING_ONTOLOGIES / CONTROL_ENGINEERING / ADAPTIVE_CONTROL

ONTOLOGY := ADAPTIVE_CONTROL_ONTOLOGY

ADAPTIVE_CONTROL :=
    DYNAMIC_SYSTEM
  + CONTROLLER
  + PARAMETER_ESTIMATION
  + ADAPTATION_MECHANISM
  + PERFORMANCE_MEASUREMENT
  + REAL_TIME_ADJUSTMENT

PURPOSE :=
    OBSERVE
  -> ESTIMATE
  -> COMPARE
  -> ADAPT
  -> CONTROL
  -> STABILISE
  -> MAINTAIN_PERFORMANCE
  -> RESPOND_TO_CHANGE

# ---------- CORE ENTITIES ----------
ENTITY AdaptiveControlSystem
ENTITY AdaptiveController
ENTITY Plant
ENTITY DynamicSystem
ENTITY ReferenceInput
ENTITY SystemOutput
ENTITY ErrorSignal
ENTITY ControlInput
ENTITY Sensor
ENTITY Actuator
ENTITY PlantParameter
ENTITY ControllerParameter
ENTITY ParameterEstimator
ENTITY ParameterEstimate
ENTITY AdaptationLaw
ENTITY AdaptationMechanism
ENTITY ReferenceModel
ENTITY PerformanceIndex
ENTITY ModelError
ENTITY TrackingError
ENTITY SystemIdentification
ENTITY Uncertainty
ENTITY Disturbance
ENTITY Stability
ENTITY Convergence
ENTITY PersistentExcitation

# ---------- ADAPTIVE CONTROL STRUCTURE ----------
AdaptiveControlSystem
  -> contains -> AdaptiveController
  -> controls -> Plant
  -> contains -> ParameterEstimator
  -> contains -> AdaptationMechanism
  -> evaluates -> SystemOutput
  -> receives -> ReferenceInput

Sensor
  -> measures -> SystemOutput

ReferenceInput
  -> defines -> DESIRED_BEHAVIOUR

COMPARE(ReferenceInput, SystemOutput)
  -> generates -> TrackingError

AdaptiveController
  -> receives -> TrackingError
  -> uses -> ControllerParameter
  -> generates -> ControlInput

ControlInput
  -> drives -> Actuator

Actuator
  -> influences -> Plant

Plant
  -> produces -> SystemOutput

# ---------- ADAPTATION LOOP ----------
ADAPTATION_LOOP :=
    OBSERVE_SYSTEM
  -> MEASURE_OUTPUT
  -> COMPUTE_ERROR
  -> ESTIMATE_PARAMETERS
  -> EVALUATE_PERFORMANCE
  -> UPDATE_CONTROLLER_PARAMETERS
  -> APPLY_CONTROL
  -> OBSERVE_NEW_RESPONSE
  -> REPEAT

AdaptationMechanism
  -> modifies -> ControllerParameter

ControllerParameter
  -> determines -> ControlLawBehaviour

SYSTEM_CHANGE
  -> may_require -> CONTROLLER_ADAPTATION

# ---------- PARAMETER ESTIMATION ----------
PARAMETER_ESTIMATION :=
    INPUT_DATA
  + OUTPUT_DATA
  + MODEL_STRUCTURE
  -> PARAMETER_ESTIMATE

ParameterEstimator
  -> estimates -> PlantParameter

PlantParameter
  -> may_be -> UNKNOWN
  -> may_be -> TIME_VARYING
  -> may_be -> UNCERTAIN

ParameterEstimate
  -> updates -> InternalModel
  -> informs -> AdaptationLaw

ESTIMATION_ERROR :=
    TRUE_PARAMETER - ESTIMATED_PARAMETER

# ---------- SYSTEM IDENTIFICATION ----------
SYSTEM_IDENTIFICATION :=
    OBSERVED_INPUT
  + OBSERVED_OUTPUT
  -> ESTIMATE(
       SYSTEM_STRUCTURE,
       SYSTEM_PARAMETERS,
       SYSTEM_DYNAMICS
     )

SystemIdentification
  -> supports -> ParameterEstimation
  -> supports -> AdaptiveController

ONLINE_IDENTIFICATION :=
    REAL_TIME_DATA
  -> CONTINUOUS_MODEL_UPDATE

# ---------- ADAPTATION LAW ----------
ADAPTATION_LAW :=
    PERFORMANCE_INFORMATION
  + ERROR_INFORMATION
  + PARAMETER_ESTIMATE
  -> CONTROLLER_PARAMETER_UPDATE

CONTROLLER_PARAMETER_UPDATE :=
    CURRENT_CONTROLLER_PARAMETERS
  + ADAPTATION_INCREMENT

AdaptationLaw
  -> seeks -> ERROR_REDUCTION
  -> seeks -> PERFORMANCE_MAINTENANCE
  -> subject_to -> STABILITY_REQUIREMENTS

# ---------- MODEL REFERENCE ADAPTIVE CONTROL ----------
MODEL_REFERENCE_ADAPTIVE_CONTROL :=
    REFERENCE_MODEL
  + PLANT
  + ADAPTIVE_CONTROLLER
  + ADAPTATION_MECHANISM

ReferenceModel
  -> defines -> DESIRED_DYNAMIC_RESPONSE

MODEL_REFERENCE_ERROR :=
    REFERENCE_MODEL_OUTPUT - PLANT_OUTPUT

MODEL_REFERENCE_ERROR
  -> drives -> AdaptationMechanism

AdaptationMechanism
  -> updates -> AdaptiveController
  -> seeks_to_reduce -> MODEL_REFERENCE_ERROR

MRAC_FLOW :=
    REFERENCE_INPUT
  -> REFERENCE_MODEL
  -> DESIRED_OUTPUT
  -> COMPARE_WITH_PLANT_OUTPUT
  -> MODEL_REFERENCE_ERROR
  -> ADAPTATION_LAW
  -> CONTROLLER_UPDATE

# ---------- SELF-TUNING CONTROL ----------
SELF_TUNING_CONTROL :=
    SYSTEM_IDENTIFICATION
  -> PARAMETER_ESTIMATION
  -> CONTROLLER_REDESIGN
  -> CONTROL_ACTION

SELF_TUNING_REGULATOR :=
    PARAMETER_ESTIMATOR
  + CONTROLLER_DESIGN_MECHANISM

ParameterEstimator
  -> supplies -> EstimatedPlantModel

EstimatedPlantModel
  -> used_by -> ControllerDesignMechanism

ControllerDesignMechanism
  -> updates -> ControllerParameter

# ---------- DIRECT AND INDIRECT ADAPTATION ----------
DIRECT_ADAPTIVE_CONTROL :=
    PERFORMANCE_ERROR
  -> DIRECTLY_UPDATE -> CONTROLLER_PARAMETERS

INDIRECT_ADAPTIVE_CONTROL :=
    SYSTEM_DATA
  -> ESTIMATE_PLANT_PARAMETERS
  -> REDESIGN_CONTROLLER
  -> UPDATE_CONTROLLER_PARAMETERS

DIRECT_ADAPTATION
  -> bypasses -> EXPLICIT_PLANT_PARAMETER_RECONSTRUCTION

INDIRECT_ADAPTATION
  -> depends_on -> PARAMETER_ESTIMATION

# ---------- UNCERTAINTY AND VARIATION ----------
Uncertainty
  -> affects -> PlantModel
  -> affects -> ControllerPerformance

SYSTEM_VARIATION :=
    PARAMETER_DRIFT
  | LOAD_CHANGE
  | ENVIRONMENTAL_CHANGE
  | OPERATING_POINT_CHANGE
  | COMPONENT_CHANGE

AdaptiveControlSystem
  -> responds_to -> SYSTEM_VARIATION

IF PlantParameter changes
THEN ParameterEstimator -> UPDATE_ESTIMATE

IF Performance degrades
THEN AdaptationMechanism -> MODIFY_CONTROLLER

# ---------- TRACKING ----------
TRACKING_ERROR :=
    REFERENCE_INPUT - SYSTEM_OUTPUT

AdaptiveController
  -> seeks_to_minimise -> TrackingError

IF TrackingError increases
THEN AdaptationLaw -> MAY_INCREASE_ADAPTIVE_RESPONSE

IF TrackingError approaches_zero
THEN TRACKING_PERFORMANCE := IMPROVING

# ---------- STABILITY ----------
ADAPTIVE_STABILITY :=
    CLOSED_LOOP_SYSTEM
  + TIME_VARYING_CONTROLLER_PARAMETERS
  -> BOUNDED_BEHAVIOUR

Stability
  -> constrains -> AdaptationLaw

ADAPTATION_RATE
  -> influences -> Stability
  -> influences -> Convergence
  -> influences -> TrackingPerformance

IF AdaptationRate excessive
THEN INSTABILITY_RISK := INCREASED

IF parameter_update violates stability_condition
THEN AdaptationLaw -> RESTRICT_UPDATE

# ---------- CONVERGENCE ----------
Convergence :=
    ESTIMATED_PARAMETERS
  -> approach -> TARGET_PARAMETERS
  OR
    TRACKING_ERROR
  -> approach -> ACCEPTABLE_BOUND

PersistentExcitation
  -> may_support -> ParameterConvergence

IF excitation insufficient
THEN parameter_identifiability -> MAY_BE_LIMITED

CONVERGENCE_ANALYSIS :=
    PARAMETER_ERROR
  + TRACKING_ERROR
  + ADAPTATION_DYNAMICS
  -> ASSESS -> LONG_TERM_BEHAVIOUR

# ---------- DISTURBANCE RESPONSE ----------
Disturbance
  -> affects -> Plant
  -> changes -> SystemOutput

AdaptiveControlSystem
  -> observes -> DISTURBANCE_EFFECT
  -> may_adjust -> ControllerParameter

DISTURBANCE_ADAPTATION :=
    DISTURBANCE
  -> RESPONSE_CHANGE
  -> PERFORMANCE_ERROR
  -> ADAPTATION
  -> UPDATED_CONTROL

# ---------- PERFORMANCE ----------
ADAPTIVE_PERFORMANCE :=
    TRACKING_ACCURACY
  + REGULATION_ACCURACY
  + CONVERGENCE_RATE
  + STABILITY
  + ROBUSTNESS
  + CONTROL_EFFORT
  + ADAPTATION_SPEED

PerformanceIndex
  -> evaluates -> AdaptiveControlSystem

PERFORMANCE_DEGRADATION
  -> triggers -> ADAPTATION

# ---------- ADAPTIVE CONTROL REASONING ----------
ADAPTIVE_CONTROL_REASONING :=
    DEFINE_CONTROL_OBJECTIVE
  -> IDENTIFY_UNCERTAINTY
  -> IDENTIFY_VARIABLE_PARAMETERS
  -> SELECT_ADAPTIVE_ARCHITECTURE
  -> DEFINE_REFERENCE_BEHAVIOUR
  -> COLLECT_INPUT_OUTPUT_DATA
  -> ESTIMATE_SYSTEM_PARAMETERS
  -> COMPUTE_TRACKING_ERROR
  -> APPLY_ADAPTATION_LAW
  -> UPDATE_CONTROLLER_PARAMETERS
  -> APPLY_CONTROL
  -> ASSESS_STABILITY
  -> ASSESS_CONVERGENCE
  -> VALIDATE_PERFORMANCE
  -> CONTINUE_ADAPTATION

# ---------- INFERENCE RULES ----------
IF PlantDynamics changes
THEN ControllerSuitability -> REASSESS

IF ParameterEstimate differs_from previous_estimate
THEN ControllerParameters -> MAY_UPDATE

IF TrackingError exceeds threshold
THEN AdaptationMechanism -> ACTIVATE_OR_ADJUST

IF ModelReferenceError decreases
THEN AdaptivePerformance -> IMPROVING

IF ParameterConvergence not_observed
THEN CHECK PersistentExcitation

IF StabilityCondition violated
THEN RESTRICT AdaptationLaw

IF Uncertainty increases
THEN ParameterEstimationImportance := INCREASED

IF PerformanceIndex deteriorates
THEN ADAPTATION_REQUIRED := POSSIBLE

# ---------- SEMANTIC RELATIONSHIPS ----------
RELATION controls(AdaptiveController, Plant)
RELATION measures(Sensor, SystemOutput)
RELATION estimates(ParameterEstimator, PlantParameter)
RELATION generates(ParameterEstimator, ParameterEstimate)
RELATION updates(AdaptationMechanism, ControllerParameter)
RELATION implements(AdaptationMechanism, AdaptationLaw)
RELATION defines(ReferenceModel, DesiredDynamicResponse)
RELATION compares(ModelReferenceError, ReferenceModelOutput, PlantOutput)
RELATION influences(ControllerParameter, ControlInput)
RELATION affects(Uncertainty, PlantModel)
RELATION affects(Disturbance, Plant)
RELATION constrains(Stability, AdaptationLaw)
RELATION supports(PersistentExcitation, ParameterConvergence)
RELATION evaluates(PerformanceIndex, AdaptiveControlSystem)

# ---------- SEMANTIC EQUIVALENCE ----------
SEMANTIC_EQUIVALENCE:
  "adaptive control" ~= "adaptive control system"
  "adaptive controller" ~= "self-adjusting controller"
  "parameter estimation" ~= "online parameter estimation"
  "adaptation law" ~= "parameter update law"
  "reference model" ~= "desired response model"
  "model reference adaptive control" ~= "MRAC"
  "self-tuning regulator" ~= "STR"
  "system identification" ~= "plant identification"
  "parameter drift" ~= "parameter variation"
  "tracking error" ~= "reference tracking error"

# ---------- CONFIDENCE ----------
CONFIDENCE:
  ontology_domain: 0.99
  adaptive_structure: 0.99
  parameter_estimation_mapping: 0.99
  adaptation_law_mapping: 0.99
  mrac_mapping: 0.98
  self_tuning_mapping: 0.98
  stability_mapping: 0.98
  convergence_mapping: 0.98
  uncertainty_mapping: 0.99
  semantic_relationships: 0.99

# ---------- UPDATE MODEL ----------
UPDATE_MODEL:
  ON new_adaptive_system:
    MAP plant
    MAP controller
    MAP variable_parameters
    MAP estimator
    MAP adaptation_law
    MAP reference_model
    MAP performance_index
    UPDATE confidence
    RECOMPUTE FLOW_HASH

  ON parameter_change:
    UPDATE PlantParameter
    UPDATE ParameterEstimate
    REASSESS ControllerParameter
    REASSESS Stability
    REASSESS Performance

  ON new_observation:
    UPDATE system_identification_data
    UPDATE tracking_error
    UPDATE parameter_estimate
    PRESERVE provenance

  ON ontology_revision:
    PRESERVE entity_identity
    PRESERVE provenance
    UPDATE relationships
    UPDATE inference_rules
    UPDATE confidence
    RECOMPUTE FLOW_HASH

# ---------- AI CONSUMPTION ----------
AI_CONSUMPTION:
  parse_as: FORMAL_ADAPTIVE_CONTROL_ONTOLOGY
  reasoning_mode: DYNAMIC_ADAPTIVE_RELATIONAL

  preserve:
    - typed_entities
    - temporal_parameter_changes
    - adaptation_paths
    - causal_dependencies
    - stability_constraints
    - uncertainty
    - confidence
    - provenance

  infer:
    - adaptation_requirements
    - parameter_update_dependencies
    - tracking_error_paths
    - convergence_dependencies
    - model_reference_dependencies
    - stability_dependencies
    - performance_dependencies

  prohibit:
    - invented_parameter_values
    - assumed_convergence
    - assumed_stability
    - assumed_identifiability
    - unsupported_performance_claims
    - removal_of_uncertainty

# ---------- FLOW HASH ----------
FLOW_HASH_INPUT :=
    DOMAIN
  + ONTOLOGY
  + CORE_ENTITIES
  + ADAPTIVE_CONTROL_STRUCTURE
  + ADAPTATION_LOOP
  + PARAMETER_ESTIMATION
  + SYSTEM_IDENTIFICATION
  + ADAPTATION_LAW
  + MODEL_REFERENCE_ADAPTIVE_CONTROL
  + SELF_TUNING_CONTROL
  + DIRECT_INDIRECT_ADAPTATION
  + UNCERTAINTY_VARIATION
  + TRACKING
  + STABILITY
  + CONVERGENCE
  + DISTURBANCE_RESPONSE
  + PERFORMANCE
  + ADAPTIVE_CONTROL_REASONING
  + INFERENCE_RULES
  + SEMANTIC_RELATIONSHIPS
  + SEMANTIC_EQUIVALENCE
  + CONFIDENCE
  + UPDATE_MODEL
  + AI_CONSUMPTION

FLOW_HASH :=
    HASH(FLOW_HASH_INPUT)

END FLOW